JP2021077364A - Project management system, project management method, and program - Google Patents

Abstract

To precisely manage a schedule network with less computational complexity by also considering a delay risk in addition to a process (time), resources, and cost.SOLUTION: In a project management system 1, a schedule network generation part 10 generates a schedule network for satisfying restriction conditions of time, cost, and resources on the basis of a logical order relationship between activities in a project and required time of each activity. A delay risk evaluation part 20 extracts structure capable of generalizing a volume calculation by integral calculus from a regular convex polyhedron for expressing a margin for keeping a project within the entire delivery time when each activity is delayed in a vector space with a margin parameter for indicating margin time permitted in each activity as an element, and a schedule network is evaluated with the size of the extracted structure or sensitivity of the size to delay as an index value.SELECTED DRAWING: Figure 1

Description

The present invention relates to a project management system, a project management method and a program.

In project management before 1970, both were managed individually, such as drawing the process (time) in a diagram and tabulating the cost (cost) with spreadsheet software. Therefore, the balance adjustment of the trade-off between the process (time), the resource, and the cost (cost) as shown in FIG. 3 (A) has to be performed by a person based on experience and intuition. In this case, since the actual situation of the project cannot be grasped, the process is proceeding smoothly but the cost is over, or conversely, the cost is within the planned range but the volume does not reach the planned level. There was a problem such as.

However, since around 1970, when the "earned value method (EVM)", a project management technique for grasping cost efficiency and process progress rate at once, was devised, planning and progress management that balance processes, resources, and costs (See, for example, Non-Patent Document 1). As a result, the drafted schedule has a good balance of process (time), resources, and cost (cost).

However, in this project management, since only inflexible scheduling that cannot tolerate any delay is possible, problems such as overdue delivery and cost overrun occur easily. Or, conversely, as a result of intuitively giving the schedule of a new project a margin to avoid the risk of delay, there was a problem that it was later found that the schedule was wasteful.

With the large-scale complexity of projects and changes in the environment surrounding projects, the problem of "delay risk" has become more serious in recent years. Therefore, as shown in FIG. 3B, it is necessary to balance the four-factor trade-off of "process (time), resource, cost (cost)" plus delay risk. Therefore, a rescheduling mechanism in consideration of the delay risk is disclosed (see, for example, Non-Patent Documents 2 and 3). According to these mechanisms, each work in the project, that is, the schedule network constructed by the logical order relationship of activities, meets the four requirements of process (time), resource, cost (cost), and delay risk. Rescheduled.

Masaaki Ikeda, "Introduction to Project Planning with PMS for Construction Engineers" (2005), Morikita Publishing Co., Ltd., ISBN4-627-48531-X Tomita, Takatsuka, Kadokawa, Sato, Okazaki; “Decision-making model based on vector space representation of schedule float”, System and Information Division Academic Lecture 2017 Lecture Proceedings, pp.145-14 Tomita, Takatsuka, Takahashi, Sato, Okazaki; “Evaluation of Delay Risk Tolerance of Project Schedule Network”, Proceedings of the Autumn Meeting of the Japan Society for Management Engineering, pp.85-86 (2018)

However, the number of activities in the current project is enormous. As the number of activities increases, the amount of calculation for calculating the delay risk or the magnitude of the delay risk tolerance that is negatively correlated with the delay risk becomes enormous, and the accuracy of the calculation result also greatly decreases.

The present invention has been made under the above circumstances, and it is possible to accurately manage a schedule network with a small amount of calculation in consideration of delay risk in addition to process (time), resources, and cost (cost). The purpose is to provide a project management system, project management method and program that can be used.

In order to achieve the above object, the project management system according to the first aspect of the present invention is
A project management system that manages a project consisting of multiple activities.
A schedule network generator that generates a schedule network that satisfies the time, cost, and resource constraints based on the logical order relationship between the activities in the project and the time required for each activity.
In a vector space whose element is a margin parameter indicating the allowable margin time for each activity, a volume obtained by integration from a regular convex polyhedron representing a margin that can accommodate the project in the overall delivery date when each activity is delayed. A delay risk evaluation unit that extracts a structure that can be generalized in calculation and evaluates the schedule network using the size of the extracted structure or the sensitivity to the delay of the size as an index value.
To be equipped.

In this case, the delay risk evaluation unit
A conditional expression generator that generates a constraint expression corresponding to each of a plurality of paths from the start to the end of the schedule network based on the relationship between the overall delivery date of the project, the required time, and the margin parameter.
A structure extraction unit that extracts a structure capable of generalizing volume calculation by integration from the regular convex polyhedron representing a space satisfying the plurality of constraint equations in the vector space.
An index value calculation unit that calculates the volume by integration and calculates the size of the extracted structure as an index value.
To prepare
It may be that.

In addition, the structure extraction unit
Each row corresponds to one of the plurality of constraint expression expressions, each column is a matrix corresponding to the margin parameter, and the value of the element in which the constraint parameter term is included in the constraint condition expression is set to 1, and other than that. Generate a matrix with the value of the element of
A matrix consisting of columns for which an inclusion relationship is established in the row where the element value is 1 and columns whose elements are 1 do not match at all is extracted as a matrix representing a structure in which volume calculation can be generalized. And
The index value calculation unit
Among the extracted matrices, the margin parameter corresponding to the first column having the largest number of rows that become 1 is used as the integral variable, and the second element that becomes 1 is included in all the elements that become 1 in the first column. Integrate with the margin parameter of the column as the integrand, and the upper limit that the integrator can take as the minimum value that the integrator can take.
Multiple integrals are performed between the margin parameters of columns in which the rows that are 1 do not match at all, and the size of the extracted structure is obtained.
It may be that.

When the structure extraction unit extracts a plurality of structures that can be generalized in volume calculation by integration,
The index value calculation unit calculates the total value or the average value of the size of each of the extracted plurality of structures or the sensitivity to the delay of the size as the index value.
It may be that.

The index value calculation unit
Degeneration of the size of a regular convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the margin time allowed for each activity. The rate is calculated as the index value.
It may be that.

The project management system according to the second aspect of the present invention is
A project management system that manages a project consisting of multiple activities.
For each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of each activity constituting the path and the margin parameter indicating the margin time shall be less than or equal to the overall delivery date of the project. A conditional expression generator that generates a constraint expression that indicates
Indicates the size of a regular-convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the allowable margin time for each activity. A delay risk index value calculation unit that calculates the sensitivity of information as an index value for each activity,
Based on the calculated index value, an incremental cost calculation unit that calculates an incremental cost when each activity is delayed by a unit time for each activity, and an incremental cost calculation unit.
To be equipped.

The delay risk index value calculation unit
Either the number of lattice points in the regular-convex polyhedron, the size of the largest single unit inscribed in the regular-convex polyhedron, or the volume of the structure extracted from the regular-convex polyhedron that can be generalized in volume calculation by integration. Is calculated as information indicating the size of the regular convex polyhedron.
It may be that.

The conditional expression generator
Simplify the schedule network based on the independent dependency between the activities of the schedule network.
It may be that.

The project management method according to the third aspect of the present invention is
A project management method executed by an information processing device that manages a project consisting of multiple activities.
A schedule network generation step that generates a schedule network that satisfies the time, cost, and resource constraints based on the logical order relationship between the activities in the project and the time required for each activity.
In a vector space whose element is a margin parameter indicating the margin time allowed for each of the activities, integration is performed from a regular convex polyhedron representing a margin that can accommodate the entire project in the overall delivery date when the project is delayed. A delay risk evaluation step that extracts a structure that can be generalized in volume calculation and evaluates the schedule network using the size of the extracted structure or the sensitivity to the delay of the size as an index value.
including.

The project management method according to the fourth aspect of the present invention is
A project management method executed by an information processing device that manages a project consisting of multiple activities.
For each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of each activity constituting the path and the margin parameter indicating the margin time shall be less than or equal to the overall delivery date of the project. A conditional expression generation step that generates a constraint expression that indicates
Indicates the size of a regular-convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the allowable margin time for each activity. A delay risk index value calculation step that calculates the sensitivity of information as an index value,
Based on the calculated index value, an incremental cost calculation step for calculating the incremental cost when each activity is delayed by a unit time for each activity, and
including.

The program according to the fifth aspect of the present invention is
A computer that manages a project that consists of multiple activities
A schedule network generator that generates a schedule network that satisfies the time, cost, and resource constraints based on the logical order relationship between the activities in the project and the time required for each activity.
In a vector space whose element is a margin parameter indicating the margin time allowed for each of the activities, integration is performed from a regular convex polyhedron representing a margin that can accommodate the entire project in the overall delivery date when the project is delayed. A delay risk evaluation unit that extracts a structure that can be generalized in volume calculation and evaluates the schedule network using the size of the extracted structure or the sensitivity to the delay of the size as an index value.
To function as.

The program according to the sixth aspect of the present invention
A computer that manages a project that consists of multiple activities
For each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of each activity constituting the path and the margin parameter indicating the margin time shall be less than or equal to the overall delivery date of the project. Conditional expression generator, which generates a constraint expression indicating
Indicates the size of a regular-convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the allowable margin time for each activity. Delay risk index value calculation unit that calculates the sensitivity of information as an index value,
An incremental cost calculation unit that calculates an incremental cost when each activity is delayed by a unit time based on the calculated index value for each activity.
To function as.

According to the project management system according to the present invention, the size of the structure capable of generalizing the volume calculation by the integral extracted from the positive convex polyhedron representing the margin when the project is delayed, or the sensitivity to the delay of the size. Use as an index value. This makes it possible to quantify the delay risk tolerance that has a negative correlation with the delay risk. As a result, the schedule network can be managed accurately with a small amount of calculation in consideration of the delay risk in addition to the process (time), resources, and cost (cost).

It is a block diagram which shows the structure of the project management system which concerns on Embodiment 1 of this invention. It is a figure which shows an example of a schedule network. (A) is a schematic diagram showing the relationship of trade-offs between the three elements of process, resource, and cost. (B) is a schematic diagram showing a trade-off relationship between four elements of delay risk in addition to process, resource, and cost. It is a figure which shows an example of the schedule network for explaining the delay risk tolerance. It is a regular convex polyhedron representing the delay risk tolerance of the schedule network of FIG. It is a figure which shows an example of the simple substance inscribed in the regular convex polyhedron of FIG. FIG. (A) is a diagram showing an example of a schedule network for explaining a structure in which volume calculation can be generalized. (B) is a diagram showing a 1/0 matrix corresponding to the schedule network of (A). (C) is a figure which shows the activity corresponding to the dotted line part of the 1/0 matrix of (B). It is a figure which shows the integral formula defined by the 1/0 matrix (dotted line part) shown in FIG. 7B. (A) is a diagram showing another 1/0 matrix corresponding to the schedule network of FIG. 7 (A). (B) is a figure which shows the activity corresponding to the dotted line part of the 1/0 matrix of (A). (C) is a figure which shows the constraint condition expression derived from the 1/0 matrix corresponding to the dotted line part. (A) is a diagram showing another example of the schedule network. (B) is a diagram showing a constraint equation and a 1/0 matrix derived from the schedule network of (A). (A), (B) and (C) are diagrams showing three cross sections which are structures extracted from a regular convex polyhedron. FIG. (A) is a diagram showing sensitivity due to a delay in the size of a structure extracted from a regular convex polyhedron. (B) is a figure which shows the change of the constraint condition expression when the work A is delayed by one day. (C) is a diagram showing an integral formula for calculating the size of the structure when A is delayed by one day. It is a table summarizing the index values concerning the sensitivity due to the delay of the structure extracted from the regular convex polyhedron of FIG. 12 (A). It is a block diagram which shows the hardware structure of a project management system. It is a flowchart which shows the operation of the project management system which concerns on Embodiment 1 of this invention. It is a flowchart which shows the extraction process of the structure which can generalize the volume calculation. (A) to (F) are data flow diagrams showing the extraction process 1 of the structure capable of generalizing the volume calculation. (A) to (G) are data flow diagrams showing the extraction process 2 of the structure capable of generalizing the volume calculation. (A) to (D) are data flow diagrams showing the extraction process 3 of the structure capable of generalizing the volume calculation. (A) is a diagram showing an example of a schedule network. (B) is a diagram showing a simplified schedule network of the schedule network of (A). (C) is a figure which shows the constraint condition expression corresponding to the schedule network of (B). (D) and (E) are diagrams showing the inclusion relationship of a 1/0 matrix, a constraint expression, and a margin parameter, which show a structure that can generalize the volume calculation extracted from a regular convex polyhedron. It is a figure which summarized the index value about the sensitivity by the delay of the structure extracted from the regular convex polyhedron corresponding to the schedule network of FIG. 20 (B). FIG. 2A is a diagram showing a constraint equation and a 1/0 matrix corresponding to the schedule network of FIG. FIG. (B) is a diagram showing a 1/0 matrix and a constraint equation showing a structure that can be generalized in volume calculation extracted from a regular convex polyhedron. (A) is a figure which shows the inclusion relation of the margin parameter derived from the constraint condition expression of FIG. 22 (B). (B) is a diagram showing an integral formula for calculating the size of the structure defined by the relationship of (A). (C) is a figure which shows the concrete expression of the integral variable in the integral expression of (B). FIG. 23A is a diagram showing a concrete example of the upper limit of the integration region of the margin parameter in the integration formula of FIG. 23B. (B) is a diagram showing an integral formula obtained by further expanding the integral formula of FIG. 23 (B). (A) is a diagram showing a schedule network of a dismantling repair and inspection project of electric power equipment. (B) is an example of a constraint expression generated from the schedule network of (A). (A) is a figure which shows the schedule network of the simplified version (JPEX-15D) of JAPEX EPC Training Project. (B) is an example of a constraint expression generated from the schedule network of (A). (A) is a diagram showing the original schedule network of a simplified version (JPEX-24D) of JAPEX EPC Training Project. (B) is an example of a constraint expression generated from the schedule network of (A). (A) is a table summarizing the time required for the sensitivity analysis by the first method to the third method for application examples s1 to s3. (B) is a table showing the agreement rate of the order relation of the sensitivities of each method. It is a table which shows the experimental result of the evaluation experiment e2 which evaluated how much the accuracy of the sensitivity analysis by the 3rd method changes by the number of extracted structures. It is a graph which shows the relationship between the index value of delay risk tolerance and the increase of project execution cost. It is a block diagram which shows the structure of the project management system which concerns on Embodiment 2 of this invention. It is a flowchart which shows the operation of the project management system which concerns on Embodiment 2 of this invention. It is a figure which shows an example of the schedule network of the project which manufactures a certain system product. It is a figure which shows the schedule network which simplified the schedule network of FIG. 33. (A) and (B) are diagrams showing an example of the evaluation result of the schedule network of FIG. 33.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In each drawing, the same or equivalent parts are designated by the same reference numerals.

Embodiment 1
The project management system 1 according to the embodiment of the present invention shown in FIG. 1 is an information processing device that manages a project (specifically, a schedule network thereof) composed of work as a plurality of activities.

FIG. 2 shows an example of an arrow diagram of a schedule network. An arrow diagram is a network diagram in which work is represented by arrows and nodes are represented by circles. As shown in FIG. 2, this schedule network is defined as work A, B, C, E, F, G, H, J, K, M, N, P, Q, R, S (hereinafter referred to as A to S). ) Is composed of tasks.

In FIG. 2, the arrows represent the logical order relationship between the above operations A to S. That is, in the example of this project, work A is performed first, work B, C, and S are performed after work A is completed, and the project is completed when work Q and R are finally completed.

The numbers in parentheses in FIG. 2 represent the time required (days) for each work. For example, the time required for work A is 15 days. Further, a to s are parameters representing the number of days of the margin (Total Float) of the work A to S, respectively. In the following, a parameter representing the number of spare days will be referred to as a margin time or a margin parameter.

As shown in FIG. 1, the project management system 1 includes a schedule network generation unit 10 and a delay risk evaluation unit 20.

As shown in FIG. 3A, the schedule network generation unit 10 has a process (time), a resource, and a cost (cost) based on the logical order relationship between the work in the project and the time required for each work. ), While balancing the trade-offs of the three elements, generate a schedule network that satisfies the constraint conditions for those three elements. As a method for generating the schedule network, a conventional method such as an earned value method can be used. As a result, for example, the schedule network shown in FIG. 2 is generated. As shown in FIG. 3A, such constraints are conditions such that the time is "as soon as possible", the resources are "as little as possible", and the cost is "as cheap as possible".

The delay risk evaluation unit 20 evaluates the delay risk of the scheduling network generated by the schedule network generation unit 10. Here, the delay risk is a risk that the completion of the project is delayed and the delivery date is overdue. If the risk of delay is "as low as possible", the project will be delayed, but the probability will be low and the evaluation will be high.

The delay risk evaluation unit 20 evaluates the delay risk of the schedule network and returns the evaluation result to the schedule network generation unit 10. The schedule network generation unit 10 determines whether or not the delay risk of the schedule network is small based on the evaluation result.

As shown in FIG. 3B, the schedule network generated and evaluated by the project management system 1 satisfies the constraint conditions of the three elements of process (time), resource, and cost (cost), and the risk of delay is as much as possible. It is a schedule network that is reduced. If the delay risk evaluation result is not satisfactory, the schedule network generation unit 10 reconfigures the schedule network and causes the delay risk evaluation unit 20 to evaluate the delay risk of the reconfigured schedule network. Just do it. In the project management system 1, by repeating the generation of the schedule network and the evaluation of the delay risk, it is possible to generate the schedule network that satisfies the four requirements of process (time), resource, cost (cost), and delay risk. it can.

However, it is difficult to directly quantify the risk of delay. Therefore, in the present embodiment, the concept of "delay risk tolerance" is introduced as shown in FIG. 3 (B). Delay risk tolerance represents the "margin" for the overall duration (delivery date) of the schedule network. That is, the delay risk tolerance is the magnitude of the possibility that the delivery date will not be exceeded when any work causes an unexpected delay. Delay risk tolerance has a negative correlation with delay risk and is relatively easy to quantify.

Here, delay risk tolerance will be described. A simplified schedule network is shown in Figure 4 to illustrate delay risk tolerance. As shown in FIG. 4, in this schedule network, there are paths of work A → work B and work A → work C.

The overall delivery time for this project is 10 days. In this case, the relational expression (constraint expression of each path length) between the required time of each work in each path of the schedule network, the margin parameter, and the delivery date becomes the following inequality.
a + 2 + b + 4 ≦ 10 → a + b ≦ 4 ... (1)
a + 2 + c + 5 ≦ 10 → a + c ≦ 3 ... (2)

The above-mentioned constraint condition expression of each path length indicates a region (range) that the margin parameters a, b, and c can take. Here, a vector space having margin parameters a, b, and c as coordinate axes is defined. In this vector space, the space satisfying the above equations (1) and (2) is a regular convex polyhedron V1 as shown in FIG.

Here, the lattice points in the regular convex polyhedron V1 represent patterns that can be taken by the margin parameters a, b, and c that satisfy the overall delivery date of 10 days. Therefore, it can be said that the size (volume) of the regular convex polyhedron V1 represents the size of the delay risk tolerance. If the size of the regular convex polyhedron V1 can be determined, the delay risk tolerance of the schedule network shown in FIG. 4 can be evaluated.

However, as the schedule network becomes more complex, the dimension N of the vector space of the positive convex polyhedron V1 also increases. If the dimension N of the vector space increases, the shape of the positive convex polyhedron V1 becomes complicated, and it becomes difficult to directly obtain its size.

There are the following three methods for quantifying the delay risk tolerance without directly determining the size of the regular convex polyhedron V1.

(A) First method of calculating the number of lattice points of the N-dimensional regular convex polyhedron V1 as the number of lagging patterns The number of lattice points in the regular convex polyhedron V1 shown in FIG. 5, that is, the margin parameters a, b, This is a method of obtaining the number of patterns of delay in c and calculating the number as information indicating the size of the regular convex polyhedron V1 and, as a result, an index value of delay risk tolerance. However, in this method, as the dimension N of the positive convex polyhedron V1 increases, the amount of calculation becomes enormous.

(B) Second method for calculating the maximum size of a single unit inscribed in an N-dimensional regular convex polyhedron as the number of patterns delayed by a margin parameter As shown in FIG. 6, a single unit inscribed in a regular convex polyhedron V1. This is a method of calculating the volume of V2 as the number of patterns in which the margin parameter is delayed. In this case, the area of the single unit V2 becomes information indicating the size of the regular convex polyhedron V1, and as a result, an index value of delay risk tolerance.
The volume V of the single unit V2 is as follows.
V = abc / N!
According to this second method, even if the dimension N of the regular convex polyhedron V1 increases, the amount of calculation can be smaller than that of the first method. However, the deviation between the actual volume of the regular convex polyhedron V1 and the volume of the simple substance V2 becomes large, and the correlation between the volume V of the simple substance V2 and the magnitude of the delay risk tolerance may become unstable.

(C) Calculate the volume of a structure (a structure in which the relationship between the integral variable and the integrand variable can be uniquely determined and the volume can be calculated) that can be generalized in volume calculation by integration, which is extracted from the N-dimensional regular convex polyhedron. Third Method As described above, in the entire N-dimensional regular convex polyhedron, if the dimension N becomes large, it becomes difficult to generalize the volume calculation by integration. Therefore, in the third method, an integral calculation using, for example, a margin parameter as an integral variable and an integrand variable, that is, a structure capable of generalizing the volume calculation by integration is extracted from the N-dimensional regular convex polyhedron, and the extracted structure is extracted. Is obtained as information indicating the size of the regular convex polyhedron V1, that is, as an index value of delay risk tolerance. The size of the structure or the sensitivity (change amount) to the delay of the process obtained in this way is an index value of the delay risk tolerance in the present embodiment.

In this embodiment, this third method is adopted. Returning to FIG. 1, the delay risk evaluation unit 20 has a margin that allows the project to be put into the overall delivery date when the project is delayed in the vector space whose element is the margin parameter indicating the margin time allowed for each work. A structure capable of generalizing the volume calculation by integration is extracted from the represented regular-convex polyhedron V1, and the schedule network is evaluated using the size of the extracted structure or the sensitivity to the delay of the size as an index value.

The procedure for extracting a structure that can generalize the volume calculation by integration will be described.
(Extraction procedure T1) Generation of "1/0 matrix" First, a 1/0 matrix corresponding to the schedule network is generated. For example, in the case of the schedule network shown in FIG. 7A, the following constraint expression is generated for each path from the start to the completion of the project.
a + b + 6 ≦ 10 → a + b ≦ 4 ... (3)
a + c + e + 8 ≦ 10 → a + c + e ≦ 2… (4)
d + e + 7 ≦ 10 → d + e ≦ 3… (5)
The "1/0 matrix" shown in FIG. 7 (B) is generated from the above equations (3), (4), and (5). This 1/0 matrix is a matrix in which each row corresponds to any of the above-mentioned constraint condition equations (3) to (5), and each column corresponds to any of the margin parameters a to e. In the 1/0 matrix, the value of the element having the terms of the margin parameters a to e in the constraint condition expression is set to 1, and the value of the other elements is set to 0. For example, the top row corresponds to equation (3). In the equation (3), since the terms of the margin parameters a and b exist, 1 is set for the elements of the column a and the column b, and 0 is set for the elements of the other columns. Hereinafter, the margin parameters a to e are also referred to as columns a to e.

(Extraction procedure T2) Extraction of a structure that can be generalized by integral volume calculation Here, "No matter which two columns of the 1/0 matrix are taken, the row where 1 stands in one column is 1 in the other column. Detects 1/0 matrices that completely contain or are relatively prime to each other. Here, relatively prime means that the rows that are 1 do not match. In other words, this matrix is a matrix composed of columns in which the inclusion relationship is established in the rows where the element values are 1, and columns in which the rows in which the element values are 1 do not match at all.

In the case of the schedule network shown in FIG. 7 (A), one such 1/0 matrix is, for example, the 1/0 matrix surrounded by the dotted line in FIG. 7 (B). In this 1/0 matrix, tasks A to D are included, and tasks E are not included. This is because columns a and e do not satisfy the above conditions (there are rows in which the values are 1 and rows in which the values are different). In FIG. 7C, the work included in the 1/0 matrix surrounded by the dotted line is shown by a solid line, and the work not included is shown by a dotted line.

(Extraction procedure T3) Integral calculation Next, in the above equations (3), (4), and (5), the parameters forming the detected structure are left on the left side, and the other parameters are set on the right side as arbitrary constants. Transition.
a + b ≦ 4 ... (6)
a + c ≦ 2-e ... (7)
d≤3-e ... (8)

Subsequently, an integral calculation is performed to obtain the volume of the extracted structure based on the equations (6), (7), and (8). Specifically, this integral calculation is performed by the following procedure.
(B-1) Clarify the inclusion relationship between the columns (margin parameters) of the extracted structure.
The row that is 1 in column a includes all the rows that are 1 in columns b and c. The inclusion relationship of this margin parameter is expressed by the following equation.
(A (b, c) d) ... (9)

(B-2) The columns in the inclusion relationship (margin parameters) are converted into the relationship between the integrating variable and the integrand variable, and the columns in the disjoint relationship (margin parameters) are converted into the relationship of the multiple integral.
Here, as shown in FIG. 8, the integral operation L1 is defined for the margin parameters a (b, c) which are inclusive relations. In this integration formula, a corresponding to the first column having the largest number of rows that become 1 is set as an integral variable, and the margin of the second column in which all the elements that become 1 are included in the elements that become 1 in the first column is included. The parameters b and c are the integrands. Further, the upper limit that the integral variable a can take is the minimum variable (minimum value that the integral variable can take) 2-e on the right side of the equations (6) and (7) having the integral variable a. Further, the multiple integral L2 is defined for the margin parameters a and d that are relatively prime (columns in which the rows that become 1 do not match at all). Therefore, the overall integral formula indicating the size of this structure is the integral formula L3 which is a combination of the integral operation L1 and the multiple integral L2. By substituting 0 for an arbitrary variable (variable in which an arbitrary value can be set) e and calculating the integral formula L3, the maximum size 20 of this structure (cross section) can be obtained.

From the schedule network shown in FIG. 7A, a 1/0 matrix shown by a dotted line in FIG. 9A, which is different from the 1/0 matrix shown by the dotted line in FIG. 7B, is also extracted. This 1/0 matrix is composed of columns b, e, c, and d, and column a is excluded. As shown in FIG. 9B, the path corresponding to this matrix consists of other tasks B to E excluding task A. From the schedule networks of tasks B to E, the constraint equation shown in FIG. 9C is derived. Based on this constraint condition formula, the integral variable, the margin parameter to be the integrand, and the margin parameter to be the relation of the multiple integral are determined as described above, and the integral formula is determined by this, and the volume calculation of the extracted structure is performed. Is generalized.

In the present embodiment, a structure capable of generalizing volume calculation by integration is detected from a positive convex polyhedron corresponding to a schedule network, and the size of the structure or the sensitivity to the delay of the size is used as an index of delay risk tolerance. Calculate as a value. Here, the sensitivity is the amount of change in the size of the structure that can be generalized in volume calculation by integration extracted from a regular-convex polyhedron when the work is delayed by a unit time.

The correlation between the amount of change (sensitivity) in the size of the structure and the delay risk tolerance, which can be generalized in volume calculation by integration extracted from a positive convex polyhedron, will be explained. To illustrate this correlation, we define the schedule network shown in FIG. 10 (A). This schedule network has a path of work A → work B and a path of work A → work C. Since the required number of days for work C is larger than the required number of days for work B, in this schedule network, work A → work C becomes a critical path, and work A → work B becomes a quasi-critical path.

According to this schedule network, the constraint equation and the 1/0 matrix shown in FIG. 10B are generated. As shown in FIGS. 11 (A), 11 (B) and 11 (C), the 1/0 matrix shown by the dotted line can be extracted from the 1/0 matrix shown in FIG. 10 (B). There is a structure (cross section) St. that allows generalization of volume calculation by integration corresponding to each 1/0 matrix. 1-St. The area of 3 (12,7.5,4.5) can be calculated using the integral formula shown in the figure. This value is the value of each structure St. 1-St. It means that there is a margin represented by 3.

Here, it is assumed that work A is delayed by one day. In this case, the constraint equation changes as shown in FIGS. 10 (B) to 12 (B), and the regular convex polyhedron also changes from the solid line in FIG. 12 (A) to the dotted line. This change represents the sensitivity to delay. Here, for example, the cross section St. As shown in FIG. 12C, the change amount of 1 is 6 when a = 0.

Here, FIG. 13 shows a table comparing the indexes related to the sensitivities when the tasks A (a), B (b), and C (c) are each delayed by one day. Each cross section St. 1-St. The original margin of 2 is the cross section St. shown in FIGS. 11 (A) to 11 (C). 1-St. The area is 3, and the margin after the delay is the cross section St. If it is 1, it is the area shown in the integral formula of FIG. 12 (C). The margin / original margin is the ratio of these areas. For example, the cross section St. The ratio of the margin 6.0 after the delay at 1 to the original margin 12.0 is 0.5000.

The degeneracy rate is a measure of how much the area of the corresponding cross section is reduced, and is expressed by the following equation.
Cross-sectional sensitivity = 1- (margin after delay) / (original margin) ... (10)

In the table shown in FIG. 13, the cross section St. 1-St. The sum of the degeneracy rates of 3 is shown. Cross section for each work St. 1-St. The total degeneracy rate of 3 is 1.5222, 1.0889, and 0.6500 for work A (a), work C (c), and work B (b), respectively. When the total sum of the overall margin degeneracy rates is sorted in descending order, the work order is highly critical (a → c → b). This indicates that the sum of the overall margin degeneracy rates correlates with the magnitude of delay risk tolerance and can be used as an index value for the magnitude of delay risk tolerance.

Returning to FIG. 1, the delay risk evaluation unit 20 performs the above-mentioned calculation to calculate an index value of the magnitude of delay risk tolerance. That is, the delay risk evaluation unit 20 integrates from a regular convex polyhedron representing a margin that can accommodate the project in the overall delivery date when the project is delayed in the vector space whose element is the margin time allowed for each work. Extract structures that can be generalized in volume calculation. Further, the delay risk evaluation unit 20 calculates the size of the extracted structure or the sensitivity to the delay of the size as an index value, and evaluates the schedule network with the calculated index value.

As shown in FIG. 1, the delay risk evaluation unit 20 includes a conditional expression generation unit 21, a structure extraction unit 22, and an index value calculation unit 23.

The conditional expression generation unit 21 generates a constraint expression corresponding to each of a plurality of paths from the start to the end of the schedule network based on the relationship between the overall delivery date of the project, the required time, and the margin parameter. That is, in the conditional expression generation unit 21, the sum of the time required for the work constituting the path and the margin parameter indicating the margin time for each of the plurality of paths from the start to the end of the schedule network in the project is the entire project. Generate a constraint expression indicating that the delivery date is less than or equal to the delivery date. As a result, for example, equations (3) to (5) of the extraction procedure T1 are generated.

The structure extraction unit 22 extracts a structure capable of generalizing volume calculation by integration from a regular-convex polyhedron representing a space satisfying a plurality of constraint equations in a vector space. Specifically, in the structure extraction unit 22, each row corresponds to any of a plurality of constraint condition expressions (for example, the above equations (3) to (5)), and each column has a margin parameter (for example, FIG. 7B). The extraction procedure T2 for generating a matrix corresponding to columns a to e) in which the value of an element having a margin parameter term in the constraint expression is 1 and the values of other elements are 0. Execute. Further, the structure extraction unit 22 generalizes the volume calculation of a matrix composed of columns in which the inclusion relationship is established in the row in which the element value is 1, and columns in which the rows in which the element values are 1 do not match at all. Extract as a matrix representing possible structures. As a result, for example, from the regular convex polyhedron V1 represented by the above equations (3) to (5), the structure shown by the dotted line in FIG. 7 (B) as a 1/0 matrix and the structure shown by the dotted line in FIG. 9 (A) are shown. Multiple structures are extracted, such as a 1/0 matrix.

The index value calculation unit 23 performs volume calculation by integration, and calculates the size of the extracted structure or the sensitivity to the delay of the size as an index value. Specifically, the index value calculation unit 23 sets the margin parameter corresponding to the first column having the largest number of rows of 1 as the integral variable in the extracted matrix, and the element of 1 is the first column. Integrate with the margin parameter of the second column included in all the elements that become 1 as the integrand, and the upper limit that the integrator can take as the minimum value that the integrator can take, and the rows that become 1 match exactly. The size of the extracted structure is obtained by performing multiple integration between the margin variables of the columns that do not. As a result, for example, the integral calculation as shown in FIG. 8 is performed, and the calculation result of the size (volume) of the structure is obtained (extraction procedure T3). That is, the size of the structure is the volume obtained by the volume calculation by the above integration. The sensitivity to the magnitude delay is the amount of change in the magnitude of the structure obtained when each work is delayed by one day.

As described above, the structure extraction unit 22 may extract a plurality of structures capable of generalizing the volume calculation by integration. In this case, the index value calculation unit 23 calculates the size of each of the extracted plurality of structures or the total value or the average value of the sensitivities to the delay of the size as the index value. For example, the index value calculation unit 23 has a cross section St. 1-St. For the area of 3, the sum of the degeneracy rates, which is a measure of how much the cross-sectional area is reduced when the operations A, B, and C shown in FIG. 13 are delayed by a unit time (1 day), is used as an index value. Can be calculated. Not limited to this, the index value may be the average value of the degeneracy rate, or the average value or the total value of the volumes of the extracted plurality of structures. Of course, it is not necessary to use all of the extracted structures to calculate the average value or the total value. One may be selected from a plurality of structures, and the size of the selected structure or the sensitivity to the delay of the size may be used as an index value.

FIG. 14 shows the hardware configuration of the project management system 1. As shown in FIG. 14, the project management system 1 includes a CPU (Central Processing Unit) 30, a memory 31, an external storage unit 32, an operation unit 33, a display unit 34, and an input / output unit 35. .. Each component of the project management system 1 is connected via an internal bus 40.

The CPU 30 is a processor (arithmetic unit) that executes a software program (hereinafter, simply referred to as a "program"). The program 39 is read into the memory 31 from the external storage unit 32, and the CPU 30 performs various information processing such as logical operation and integration operation (volume calculation) by executing the program 39 stored in the memory 31.

The memory 31 is, for example, a RAM (Random Access Memory). In addition to storing the program 39 executed by the CPU 30, the memory 31 stores data required for the execution of the program 39 by the CPU 30 and data generated as a result of the execution of the program 39.

The external storage unit 32 is, for example, a hard disk or the like. The external storage unit 32 stores the program 39 executed by the CPU 30.

The operation unit 33 is a man-machine interface that can be operated by an operator. The operation unit 33 includes, for example, a keyboard, a mouse, a touch panel, a camera, a microphone, and the like. The CPU 30 operates according to the operation input of the operation unit 33.

The display unit 34 is a display for displaying an image. The display unit 34 outputs the image signal output from the CPU 30 to the display unit 34. As a result, an image based on the image signal is displayed on the display unit 34. In the case of a touch panel, the operation unit 33 and the display unit 34 are integrated.

The input / output unit 35 is a communication interface for communicating with an external device. A portable recording medium 50 such as a USB (Universal Serial Bus) memory can be connected to the input / output unit 35. The program 39 is stored in the recording medium 50. This program 39 is read into the external storage unit 32 via the input / output unit 35.

The functions of the various components of the project management system 1 shown in FIG. 1 are realized by the CPU 30 executing the program 39. That is, the functions of the schedule network generation unit 10 and the delay risk evaluation unit 20 (conditional expression generation unit 21, structure extraction unit 22 and index value calculation unit 23) are realized by executing the program 39 of the CPU 30.

Next, the operation (project management method) of the project management system 1 according to the embodiment of the present invention will be described. This flowchart shows the execution procedure of the program 39 that realizes the project management system 1.

As shown in FIG. 15, first, the schedule network generation unit 10 satisfies the time, cost, and resource constraint conditions based on the logical order relationship between the works in the project and the time required for each work. -Generate a network (step S1). The generated schedule network information is sent to the conditional expression generation unit 21 of the delay risk evaluation unit 20.

Subsequently, the conditional expression generation unit 21 of the delay risk evaluation unit 20 simplifies the schedule network (step S2). Specifically, the conditional expression generation unit 21 simplifies the schedule network based on the independent dependency between the work of the schedule network generated by the schedule network generation unit 10.

For example, in the case of the schedule network shown in FIG. 20 (A), the tasks A1, A5, and A10 that are common to all paths can be combined into one. Further, the work A2, A3, the work A6, the work A7, the work A8, and the work A9 can be combined into one. The conditional expression generation unit 21 simplifies the schedule network by combining the work that can be combined into one work into one work. For example, the schedule network shown in FIG. 20 (A) is simplified to the schedule network (5 dimensions) shown in FIG. 20 (B). By performing this simplification, the dimension of the positive convex polyhedron V1 can be reduced, and the magnitude of delay risk tolerance can be evaluated more accurately.

Subsequently, the conditional expression generation unit 21 generates a constraint condition expression (step S3). As a result, for example, a constraint expression as shown in FIG. 20 (C) is generated.

Subsequently, the structure extraction unit 22 generates a 1/0 matrix (step S4). As a result, for example, a 1/0 matrix as shown in FIG. 20 (D) is generated.

Subsequently, the structure extraction unit 22 extracts a structure capable of generalizing the volume calculation by integration (step S5). In step S5, the subroutine shown in FIG. 16 is executed. In this subroutine, the structure extraction unit 22 first inputs "the number of columns of the entire target" to the counter n (step S11). For example, if the column set consisting of all columns of the 1/0 matrix is as shown in FIG. 17 (A), 5 is assigned to the counter n.

Subsequently, the structure extraction unit 22 determines whether or not the counter n is smaller than 2 (step S12). Here, since n = 5, the determination is denied (step S12; No). In this case, the structure extraction unit 22 selects a column set Cs composed of a set of n unselected columns (step S13). Here, as shown in FIG. 17B, a column set having all of the columns a, b, c, d, and e is selected as the candidate Cs of the generalizable structure.

Subsequently, the structure extraction unit 22 selects an unselected column set (j, k) from the generalizable structure candidate column set Cs (step S14). Subsequently, the structure extraction unit 22 determines whether the row with 1 in column j is included in the row with 1 in column k, or whether the row with 1 in column j and the row with 1 in column k are relatively prime. Determine (step S15). For example, as shown in FIG. 17C, when column b is selected as column j, column a is selected as column k, and j = b and k = a, when column b and column a are compared, Since the row with 1 in column b is included in the row with 1 in column a, the determination is affirmed (step S15; Yes). Subsequently, the structure extraction unit 22 determines whether or not a set of unselected columns remains (step S16). Here, since the set of unselected columns remains, the determination is affirmed (step S16; Yes), and the process returns to step S14. At this stage, (a, b) is selected as the set of columns.

After that, the structure extraction unit 22 selects a set (j, k) of n unselected columns different from the already selected two columns (a, b) (step S14), and makes the same determination (step S14). Step S15). For example, as shown in FIG. 17 (D), when j = c and k = a are selected, the judgment is affirmative because the row with 1 in column c is included in the row with 1 in column a. (Step S15; Yes). Subsequently, the structure extraction unit 22 determines whether or not a set of unselected columns remains (step S16). Here, since the set of unselected columns still remains, the determination is affirmed (step S16; Yes), and the process returns to step S14. At this stage, (a, b) and (a, c) are selected as the set of columns.

After that, the structure extraction unit 22 selects a set of columns j, k different from the already selected two columns (a, b) and (a, c) (step S14), and makes the same determination (step S15). ). For example, as shown in FIG. 17 (E), when j = d and k = a are selected, the row in which 1 stands in column d and the row in which 1 stands in column a are relatively prime, so that the determination can be made. Affirmed (step S15; Yes). Subsequently, the structure extraction unit 22 determines whether or not a set of unselected columns remains (step S16). Here, since the set of unselected columns remains, the determination is affirmed (step S16; Yes), and the process returns to step S14. At this stage, (a, b), (a, c), and (a, d) are selected as a set of columns.

The structure extraction unit 22 selects a set of columns j, k different from the two columns (a, b), (a, c), and (a, d) that have already been selected (step S14), and makes the same determination. (Step S15). For example, as shown in FIG. 17 (F), when j = e and k = a are selected, the row in which 1 stands in column e and the row in which 1 stands in column a are not relatively prime, so that the determination is made. It is denied (step S15; No). Here, if the determination is denied, it means that the current candidate column set Cs is not a generalizable structure. Subsequently, the structure extraction unit 22 determines whether or not a set of n unselected columns remains (step S18). Here, since the set of n columns does not remain, the determination is denied (step S18; No), the structure extraction unit 22 subtracts 1 from the value of the counter n (step S19), and returns to step S12.

The structure extraction unit 22 determines whether or not the counter n is smaller than 2 (step S12). Here, since n = 4, the determination is denied (step S12; No). In this case, the structure extraction unit 22 selects a column set Cs composed of a set of n unselected columns (step S13). Here, as shown in FIG. 18 (A), a column set having four columns a, b, c, and d from all the columns of the 1/0 matrix (see FIG. 17 (A)) is generally used. It is selected as a candidate Cs for a structure that can be converted.

Subsequently, the structure extraction unit 22 selects arbitrary two columns j and k from the generalizable structure candidate column set Cs (step S14), and the row in which 1 in column j stands is 1 in column k. It is determined whether they are included in the standing rows or are relatively prime (step S15), and if the determination is affirmed (step S15; Yes), it is determined whether or not a set of unselected columns remains (step S16). After that, when the column set of columns a, b, c, and d is set as the column set Cs, the first time (k = a, j =) as shown in FIGS. 18 (B) to 18 (G). b) Second time (k = a, j = c), third time (k = a, j = d), fourth time (k = b, j = c), fifth time (k = b, j = d) , The sixth time (k = c, j = d) and steps S14 → S15 → S16 are repeated, and finally the determination in step S16 is denied. In this case, the structure extraction unit 22 registers the column set of columns a, b, c, and d as a generalizable structure (step S17).

Subsequently, the structure extraction unit 22 determines whether or not a set of n unselected columns remains (step S18). Here, since the set of n columns still remains, the determination is affirmed (step S18; Yes), and the process returns to step S13.

The structure extraction unit 22 selects a column set Cs composed of a set of n unselected columns (step S13). Here, for example, as shown in FIG. 19 (A), a column set having four columns of columns a, b, c, and e from all the columns of the 1/0 matrix (see FIG. 17 (A)) is , Is set as a candidate Cs of a generalizable structure.

Subsequently, the structure extraction unit 22 selects an unselected column set (j, k) from the generalizable structure candidate column set Cs (step S14), and the row in which 1 stands in column j is the column. It is determined whether it is included in the row in which 1 of k stands or is relatively prime (step S15), and if the determination is affirmed (step S15; Yes), it is determined whether a set of unselected columns remains (step S15). S16). When the column set of columns a, b, c, and e is set as the column set Cs, the first time (k = a, j = b) as shown in FIGS. 19 (B) to 19 (D). The second (k = a, j = c) and step S14 → S15 → S16 are repeated, but in the third time (k = a, j = e), step S15 is denied. As a result, it is determined that the column set of columns a, b, c, and e is not a generalizable structure. Further, the structure extraction unit 22 determines whether or not a set of n unselected columns remains (step S18). Here, since the set of n columns still remains, the determination is affirmed (step S18; Yes), and the process returns to step S13.

After that, the same processing is performed for the column set (a, c, d, e), the column set (a, b, d, e), and the column set (b, c, d, e), and all of them are generalized. It is determined that the structure is not possible. When the processing for the column set of n = 4 is completed, the determination is denied in step S18, the counter n is decremented by 1 (step S19), and the processing returns to step S12.

Further, the same processing is performed for the column set of n = 3 and the column set of n = 2, and all the column sets having a generalizable structure are registered. When n = 1, the determination in step S12 is affirmed, and the structure extraction unit 22 ends the process.

Returning to FIG. 15, the index value calculation unit 23 subsequently calculates an index value of the magnitude of delay risk tolerance (step S6). The calculated index value is transmitted to the schedule network generation unit 10.

Finally, the schedule network generation unit 10 determines the schedule network (step S7). Specifically, based on the index value sent from the delay risk evaluation unit 20, the schedule network having the maximum delay risk tolerance is determined from the plurality of generated schedule networks.

In the present embodiment, step S1 corresponds to the schedule network generation step, and steps S2 to S6 correspond to the delay risk evaluation step. That is, in steps S2 to S6, in a vector space whose element is a margin parameter indicating the margin time allowed for each work, a regular convex polyhedron representing a margin that can accommodate the project in the overall delivery date when the project is delayed. A delay risk evaluation step is performed in which a structure that can be generalized in volume calculation by integration is extracted from, and the schedule network is evaluated using the size of the extracted structure or the sensitivity to the delay of the size as an index value. Further, by executing step S1, the function of the schedule network generation unit 10 is realized, and by executing steps S2 to S6, the function of the delay risk evaluation unit 20 is realized.

Further, in the present embodiment, the sensitivity to the delay of the size of the structure capable of generalizing the volume calculation by the integral extracted from the regular convex polyhedron is used as an index value indicating the magnitude of the delay risk tolerance. However, as described above, the size of the structure extracted from the regular convex polyhedron that can be generalized in volume calculation may be used as an index value indicating the magnitude of delay risk tolerance. For example, the original margin value of FIG. 13 can be used as such an index value. In this case, the structure related to the critical work may be used as the structure for determining the size, or the average value, the addition value, etc. of the extracted plurality of structures may be used as the index value.

As described in detail above, according to the project management system 1 according to the present embodiment, the integral extracted from the regular convex polyhedron representing the margin that can keep the entire project on the overall delivery date when the project is delayed. The size of the structure or the sensitivity to the delay of the size of the structure that can be generalized by the volume calculation by This makes it possible to quantify the delay risk tolerance that has a negative correlation with the delay risk. As a result, the schedule network can be managed accurately with a small amount of calculation in consideration of the delay risk in addition to the process (time), resources, and cost (cost).

Here, the project management system 1 was used to evaluate the delay risk tolerance of some specific schedule networks.

(Example 1)
First, the project management system 1 was used to evaluate the scheduling network shown in FIG. 20 (A). The conditional expression generation unit 21 simplified the scheduling network shown in FIG. 20 (A) to the schedule network shown in FIG. 20 (B). Further, the structure extraction unit 22 generates a 1/0 matrix, and as shown in FIGS. 20 (C) and 20 (D), a structure capable of generalizing two volume calculations from this 1/0 matrix. (Dotted line part) was extracted.

Further, as shown in FIG. 21, the cross sections St. of the original margin and margin parameters a, e, b, c, f. 1, St. The margin after a one-day delay of 2 is calculated, and the margin / original margin, cross section St. 1, St. The degeneracy rate of 2 was calculated, and finally the total degeneracy rate was calculated. The results of sorting the total degeneracy rate in descending order were in agreement with the results of the methods (A) and (B) above. The index value calculation unit 23 calculated the total degeneracy rate (value corresponding to highly critical work, average, or total) as an index value of the magnitude of delay risk tolerance.

(Example 2)
Furthermore, the scheduling network shown in FIG. 2 was evaluated using the project management system 1. This scheduling network has already been simplified. The conditional expression generation unit 21 generated the limiting conditional expression shown in FIG. 22 (A). Further, the structure extraction unit 22 generated the 1/0 matrix shown in FIG. 22 (B), and detected the structure shown by the dotted line in FIG. 22 (B) from the 1/0 matrix. In this case, the restrictive conditional expression of FIG. 22 (A) is modified as shown in FIG. 22 (B).

According to the modified restrictive conditional expression of FIG. 22 (B), the inclusion relationship of the margin parameters a, b, e, g, m, h, f, j, c, s is as shown in FIG. 23 (A). It is put together. In this case, the index value calculation unit 23 executes the integration formula shown in FIG. 23 (B). Here, the integrands m, h, j, c, and s in the integrand in the integrand shown in FIG. 23 (B) are concrete by using the restrictive conditional expression in FIG. 22 (B) as shown in FIG. To be transformed. Specifically, the integrands m, h, j, c, and s are embodied based on the equations (A) to (E) shown in FIG. 23 (C).

Further, the upper limits aM, bM, ..., GM of the integration region in the integration formula shown in FIG. 23 (B) are embodied as shown in FIG. 24 (A). Specifically, the upper limits aM, bM, ..., GM of the integration region are embodied as 1) to 5) below.

1) The upper limit "aM" of the integration region of the highest a in the hierarchical relationship is the right-hand side constant of the formula including the a, which has the smallest right-hand side constant ((2) of the formula (B) in FIG. 23 (C)). -N-r) or (2-k-pr) of the formula (D)), where aM = (2-n-r) or (2-k-pr).

2) The upper limit "bM" of the integration region of b immediately below the highest a in the hierarchical relationship is the right-hand side constant of the formula including the b, which has the smallest constant on the right-hand side (of the formula (B) in FIG. 23 (C)). (2-n-r)) minus all the margin parameters in the upper layer of column b, where bM = 2-n-r-a.

3) There are e and f directly under b, and the upper limits "eM" and "fM" of the respective integration regions are obtained in the same manner as in 2) above. That is, the eM is in the upper layer of the column e from the right-hand side constant ((2-n−r) of the equation (B) in FIG. 23 (C)) of the equation having the smallest right-hand side constant among the equations including the column e. It is obtained by subtracting all the margin parameters, and here, eM = 2-n-r-ab.

4) Similar to eM, fM is derived from the right-hand side constant ((4-k-pr) of formula (F) in FIG. 23 (C)) of the formula having the smallest right-hand side constant among the formulas including the column f. It is obtained by subtracting all the margin parameters in the upper layer of the column f, and here, fM = 4-k-p-r-ab.

5) Further, the upper limit "gM" of the integration region of g immediately below e is the right-hand side constant of the formula containing the g on the right-hand side with the smallest constant ((3-) of the formula (A) in FIG. 23 (C)). It is obtained by subtracting all the margin parameters in the upper hierarchy of the column g from nr) or (3-q) of the equation (G). Therefore, here, gM = 3-n-r-ab-e or gM = 3-q-ab-e.

With the above embodiment, the integral formula of FIG. 23 (B) is developed as shown in FIG. 24 (B). If 0 is substituted for the arbitrary variables n, r, q, k, and p of this integral formula, the value becomes 263.4. The index value calculation unit 23 calculates, for example, this value as an index value of the magnitude of delay risk tolerance.

Calculation of the first method (calculation based on the number of grid points; see FIG. 5), the second method (single volume; see FIG. 6), and the third method (third method of the present embodiment). Comparing the quantities, the following equation is obtained.
Second method (O (n)) <Third method (O (n!) << First method (O ((m * h) ⁿ )))
(N: dimension, p: number of constraint expression (number of paths), m: maximum difference between delivery length and path length, h: number of grid divisions)
That is, the third method requires a little more calculation than the second method, but does not require a huge amount of calculation like the first method.

Further, the algorithm shown in FIG. 16 for the third method is easy or unavoidable to avoid the problem of computational complexity. Specifically, in this algorithm, it can be said that it is easy to avoid the problem of the amount of calculation because many cases where there is no possibility of generalization of the integral calculation are truncated at an early stage by the determination in step S15. Further, since the calculation process can be divided in parallel for each setting of the counter n, the calculation time can be further shortened.

Regarding the accuracy of the index value, when the dimension of the regular convex polyhedron is, for example, a low dimension of 15th order or less, the three methods are almost the same. However, when the dimension of the regular convex polyhedron is higher than that, the accuracy of the second method (single volume) may be worse than the accuracy of the third method according to the present embodiment. This is clear from the equation "V = abc / N!" (N is a dimension) of the volume of the simple substance of the second method described above. In the evaluation by the first method (number of grid points), if the dimension and accuracy are to be improved, the amount of calculation becomes enormous and the calculation becomes impossible. From the above, in the case of a high dimension, the third method according to the present embodiment requires less calculation amount and more accurately obtains the index value than the first method and the second method. It can be said that this is a possible method.

Further, the evaluation experiments e1 and e2 were performed in the application examples s1 to s3 when the third method executed by the project management system 1 according to the present embodiment was applied to the management of an actual project. Hereinafter, the evaluation results of the evaluation experiments e1 and e2 will be described.

(Application example s1)
FIG. 25A shows a schedule network of a power equipment dismantling repair and inspection project (hereinafter abbreviated as “overhaul”) as application example s1. Overhaul of electric power equipment is the work of disassembling the electric power equipment into parts, inspecting, cleaning, replacing parts, and assembling, and returning the electric power equipment to the performance state when it was new. The schedule network shown in FIG. 25 (A) was created based on the Gantt chart used during the overhaul of an existing large-scale electric power facility, and is used to define the project schedule. , The time required for the work and the order relationship between the works are extracted and rewritten in the schedule network format. In FIG. 25 (A), A to M indicate work names, and the numbers in parentheses next to each work A to M represent the required time. Further, a to m are delay parameters of operations A to M.

The number of tasks in this schedule network is as large as about 150, but it has been simplified based on the independent dependency between the tasks. As a result, the dimension of the schedule network is 13 dimensions. The thick arrow indicates the work on the critical path, and the dotted arrow indicates the work on the quasi-critical path, although it is not on the critical path.

Here, the delivery date constraint in the entire process is set to 2252 days. In this case, the inequality constraint equation representing the N-dimensional positive convex polyhedron region representing the delay risk tolerance is as shown in FIG. 25 (B). The thick line is the constraint expression for the critical path and quasi-critical path.

As a result of determining the magnitude of delay risk tolerance by each of the above-mentioned first method (number of lattice points), second method (single volume), and third method (structure detection that can generalize volume calculation), the work The order relation of the sensitivity of the delay of A to M per day is as follows.
First method: A>H>J>L>M>D>B>C>I>E>F>K> G
Second method: A>H>J>D>C>L>M>B>I>E>F>K> G
Third method: A>H>J>L>M>D>C>B>I>E>F>K> G

(Application example s2)
FIG. 26 (A) shows a simplified version of the schedule network of JAPEX (Japan Petroleum Exploration Co., Ltd.) EPC Training Project (hereinafter abbreviated as “JAPEX”) as application example s2. JAPEX is a fictitious project created for research, assuming an EPC (Engineering Procurement Construction) full turnkey project to construct a medium-scale gas treatment plant in the North African region. The set of data (WBS (Work Breakdown Structure), work list, resource list, schedule network, etc.) that defines the contents of the project is based on the original JAPEX in consideration of the efficiency of evaluation experiments e1 and e2. The schedule network (24 dimensions) is reduced so that the number of works and the dimensions are both 15.

The schedule network according to the application example s2 was created in consideration of the efficiency of the evaluation experiments e1 and e2. Specifically, the "15th dimension", which is the dimension of this schedule network, is the maximum dimension in which the sensitivity analysis can be performed with a good accuracy of a grid width of 1 or less by the first method. In addition, it is the largest dimension in which it has been confirmed that the problem of indexing error in the higher dimension of the second method can be avoided.

Here, the delivery date constraint in the entire process is set to 44 days. In this case, the inequality constraint equation representing the N-dimensional regular convex polyhedron region representing the delay risk tolerance is as shown in FIG. 26 (B).

As a result of determining the delay tolerance by the first method (number of lattice points), the second method (single volume), and the third method (structure detection), the order relation of the delay sensitivity per day of the operations A to S is as follows. It became like.
First method: A>R>B>E>N> P = K>H>C>Q>G>M>F>S> J
Second method: A>R>B>E> P = K>N>H>C>Q>G>M>F>S> J
Third method: A>R>B>E>N>H>K>P>C>Q>G>M>F>J> S

(Application example s3)
FIG. 27 (A) shows the original schedule network of JAPEX (JAPEX-24D) as application example s3. The schedule network of FIG. 26 (A) has 15 works and 15 dimensions, but the schedule network of 27 (A) has 25 works and 24 dimensions.

Here, the delivery date constraint in the entire process is 87 days. In this case, the inequality constraint equation representing the N-dimensional regular convex polyhedron region representing the delay risk tolerance is as shown in FIG. 27 (B).

As a result of determining the delay tolerance by the first method (number of lattice points), the second method (single volume), and the third method (structure detection), the order relation of the delay sensitivity per day of the operations A to S is as follows. It became like.
First method: A>R>B>E>N> P = K>H>C>Q>G>M>F>S> J
Second method: A>R>B>E> P = K>N>H>C>Q>G>M>F>S> J
Third method: A>R>B>E>N>H>K>P>C>Q>G>M>F>J> S

(Evaluation experiment e1)
The calculation time and calculation accuracy of the third method were evaluated. Specifically, the degree of influence of the one-day delay of work on the delay risk tolerance of the schedule network, that is, the sensitivity per one-day delay of work is obtained, and the work is listed in descending order of sensitivity from this result. An order relationship (hereinafter referred to as "sensitivity order relationship") was extracted, and the same order relationship was also extracted by the first and second methods, respectively. Then, the calculation time of the third method was evaluated by comparing the time required for the series of sensitivity analyzes with the first and second methods. Further, regarding the order relationship of the sensitivities of the first and second methods, the calculation accuracy of the third method was evaluated based on the concordance rate with the first and second methods. It should be noted that the quality of the calculation accuracy based on the matching rate of the order relation of the sensitivities as described above can be judged by the criteria specified as (1) to (3) below.

(1) If the order relationship of the sensitivities obtained by the third method shows a high coincidence rate with the order relationship of the sensitivities obtained by the first method when the lattice width is 1.0 or less, the third method. It is judged that the accuracy of the method 3 is high.

(2) When the order relationship of the sensitivities obtained by the third method not only shows a high coincidence rate with the order relationship of the sensitivities obtained by the second method, but also when the lattice width is 1.0 or less. If a high agreement rate is shown with the order relation of the sensitivities obtained by the first method, it is judged that the accuracy of the third method is high. This is because the accuracy of the calculation result by the second method is not clear especially in a high dimension, and therefore, the result by the second method alone cannot be the basis for the accuracy evaluation of the third method.

(3) If the order relationship of the sensitivities obtained by the third method has a lattice width larger than 1.0 and shows a generally good agreement with the order relationship of the sensitivities obtained by the first method with slightly coarse accuracy. For example, it is judged that the accuracy of the third method is also generally good. However, at this time, if the order relationship of the sensitivities of the third method and the concordance rate with that of the second method are higher than the concordance rate with the result of the first method, which is slightly coarse, the result of the third method is obtained. Is more likely to be correct than the result of the first method with coarse accuracy. This is the criterion for the application example s3.

In FIG. 28 (A), the time required for the sensitivity analysis by the first method to the third method is summarized for application examples s1 to s3. However, the calculation time by the first method indicates the calculation time when the calculation time is calculated with the finest grid width that can be calculated in each of the application examples s1 to s3, and the grid width is also shown in the table.

Further, in FIG. 28B, in order from the top, the matching rate of the sensitivity order relationship between the third method and the first method and the matching of the sensitivity order relationship between the third method and the second method The rate and the matching rate of the order relation of the sensitivities between the first method and the second method are shown for application examples s1 to s3.

The application example s2 shows the usefulness of the third method most prominently. As shown in FIG. 28 (A), in the application example s2, the calculation time of the third method was only 16 seconds, whereas the calculation time of the first method with high accuracy (dense grid width). Was 90 hours. Nevertheless, the matching rate of the order relation of the sensitivities between the third method and the first method is as high as 98% as shown in FIG. 28 (B).

Further, in the application example s3, since the dimension of the schedule network is high, there is a problem of the amount of calculation, and the first method cannot be calculated unless the lattice width is coarsened to 2.0. Further, as shown in FIG. 28 (A), in the application example s3, when the first method is used, the calculation time when the grid width is set to 2.0 is 30 hours. On the other hand, when the third method was used, the calculation was completed in 7 minutes and 6 seconds. Further, as shown in FIG. 28 (B), with respect to the accuracy, the agreement rate between the order relation of the sensitivities of the first method and the third method in which the lattice width having a slightly coarse accuracy is 2.0 is slightly low. It was about 80% of. On the other hand, the concordance rate of the simple order relation between the third method and the second method was very high, 98%. Since it is unlikely that a concordance rate of 98% can be obtained by chance, in Application Example s3, the results obtained by the third method and the second method are higher than the results obtained by the first method with slightly coarser accuracy. It is suggested that more accurate delay risk tolerance can be obtained.

As described above, as a result of comprehensive judgment including the result of the application example s1, the third method can obtain the calculation result with the same accuracy as the first method with high accuracy (dense lattice width). Moreover, it became clear that the method is required in an extremely faster calculation time than the first method.

(Evaluation experiment e2)
Subsequently, an evaluation experiment e2 was conducted on the possibility of suppressing the computational complexity of the third method. As described above, a structure that can be generalized in volume calculation by integration (integral calculation is possible) is extracted from a regular convex polyhedron, but there are a plurality of extracted structures. In the project management system according to the present embodiment, the size of the extracted structure or the sensitivity to the delay of the size is calculated, but if the number of structures for which the size is obtained can be reduced, the amount of calculation should be suppressed. Can be done. Therefore, it was investigated how much the accuracy of the sensitivity analysis by the third method changes depending on the number of extraction structures for which the size is calculated. In FIG. 29, for the application examples s1 to s3, the order relation of the sensitivities obtained by using some (M (M <N)) of all the extracted N structures is shown in all N structures. The result of evaluating the degree of agreement with the order relation of the obtained sensitivities is shown. Here, in the schedule network of application example s1, a total of 6 structures were extracted, so N = 6, and in the schedule network of application example s2, a total of 7 structures were extracted. , N = 7, and in the schedule network of application example s3, a total of 17 structures were extracted, so N = 17. M has a value of 1 to N-1. The concordance rate shown in the table of FIG. 29 shows the average of the concordance rates examined for all the combinations in which M pieces were extracted from the extracted N pieces of structures.

First, the results of JAPEX-24D (Application Example s3), which has the largest number of extracted structures, will be described. For example, when the match rate at M = 16 is 100%, all of the sensitivity order relationships (17 types) obtained by using 16 structures out of the 17 extracted structures are extracted. It means that it was consistent with the order relation of the sensitivities obtained by using all 17 structures. Further, in the application example s3, the agreement rate at M = 5 is 97%. This is the sequence of sensitivities (6188 types) obtained using 5 structures from the 17 extracted structures and the sequence of sensitivities obtained using all 17 extracted structures. It means that the average concordance rate with the relationship was 97%. Further, in the application example s3, the average of the matching rate between the order relationship of the sensitivity obtained by using only one of the extracted 17 structures and the order relationship obtained by using all 17 structures is 92%. became. From these results, it can be seen that the accuracy does not decrease so much even if the number of structures used in the calculation is reduced. As shown in FIG. 29, similar results were obtained in Application Examples s1 and s2.

From this evaluation experiment e2, it became clear that the calculation accuracy above a certain level may be guaranteed even if all the extracted structures are not used in the third method. Further, when this third method is used, the number of structures to be extracted depends on the structural characteristics of the schedule network, but even if the number of structures to be extracted is small, the calculation is at a certain level or higher. Accuracy is expected.

Embodiment 2.
Next, Embodiment 2 of the present invention will be described.

As shown in FIG. 3B, the project management system 1 according to the first embodiment has a delay risk (or a delay risk negatively correlated with the process (time), cost (cost), and resources, as shown in FIG. 3 (B). Tolerance) was taken into account and the project was scheduled so that the four requirements were good. In addition to this, the project management system 1 according to the present embodiment posts the characteristics related to the quality of the schedule network to the user (project team).

First, the basic concept of quality will be explained. Product manufacturing is required to meet the three requirements of high "(Q) quality", low "(C) cost", and quick "(D) delivery time", that is, to meet QCD at a high level in a well-balanced manner. There is. Among QCD, the highest priority is "Q (quality)". Low "(C) cost" and fast "(D) delivery time" are differentiating and superior to competitors, but if "Q (quality)" is not superior, the product will be from the user. This is because it is not selected and is not recognized as a product unless it has reached a certain quality before that. The three requirements of "QCD" are also necessary for project management. Since the project schedule network is also provided to the user, it is desirable that the user can select it according to "Q (quality)" like the product. However, the project schedule network is currently limited to a rough evaluation based on the two factors of "(D) delivery date" and "(C) cost". In recent large-scale and complicated projects, it has become difficult to evaluate even by these two indicators (“(D) delivery date” and “(C) cost”).

The quality of the schedule network can be evaluated from various points of view. For example, it is important in terms of quality that it is easy for the user to grasp the matters to be noted in advance (work to be noted with a large delay risk, etc.). For work that should be noted, it is desirable to allow sufficient time. In addition, whether or not you can get a sense of security that you can feel at ease as long as you follow this schedule is also important in terms of quality. Such a sense of security is provided by the time margin for the overall delivery date, that is, the low risk of delay.

The delay risk that can be calculated for each task is an important factor in considering the quality of the schedule network. For example, as long as the schedule is followed, the location and degree of impact of work that is unlikely to affect the overall delivery date and cost even if the performance is slightly delayed, or even a slight delay may directly affect the overall construction period. Being able to understand the location of work that should not be noted and the extent of its impact will help facilitate the execution of the project.

In this way, it is very important to be able to grasp the delay risk for each work as a schedule quality characteristic in managing the schedule network in recent years, which has a large problem of uncertainty. However, at present, there is no rational method for exposing the risk of delay at the work level, so it is left to the experience and intuition of the administrator as to what risk of delay is in which work.

Therefore, the project management system 1 according to the present embodiment utilizes the size of the delay risk tolerance of the schedule network (the size of the N-dimensional positive convex polyhedron), and the delay risk at the work level as a schedule quality characteristic. To manifest. More specifically, the project management system 1 quantifies the delay risk of the entire project caused by the delay per unit time of the work for all the works constituting the schedule network based on the degeneracy rate of the delay risk tolerance. To do. Further, the project management system 1 converts the quantified delay risk into an increase in the cost required to carry out the project, and presents the schedule characteristics in the lineup of the increase in the cost. Here, for convenience, the unit time is set to one day.

The increase in cost caused by work delay is represented by the sum of costs due to the following four factors.
(1) Increment in work execution cost caused by work execution delay ΔC ^p
(2) the costs incurred during the period can not be undertaken in the work due to lack of resources increment [Delta] C ^r
(3) Increasing cost incurred during the period when the next work cannot be started ΔC ^next
(4) project execution cost increment [Delta] C ^L caused by excess delivery was delayed overall project implementation schedule by performing delay operations

The above four kinds of "cost increment caused by the delay of the work" is classified into two occupational performance cost increment (the (1) to (3)) and project execution cost increment [Delta] C L ^(above (4)) Will be done. The former cost increase ((1) to (3) above) is mainly brought about by the difference in the content of each work and the implementation environment, and is information determined regardless of the schedule structure. In contrast, the latter project performance cost increment [Delta] C L ^((4)), the overall scale is determined by the magnitude of margin of the entire work period for delivery.

Magnitude relationship between project execution cost increment [Delta] C ^L between the size and working increment [Delta] C ^L project execution cost of individual work is determined depending on the structure of the schedule. More specifically, there project execution cost increment [Delta] C ^L of work, whether or larger than the increment [Delta] C ^L project execution cost of other work small, all (schedule consists in the working It depends on whether the relative length of the path (of the network) is longer or shorter than the length of the other paths. Longer extremely long path becomes extremely large increment [Delta] C ^L project execution costs. Therefore, project execution cost increment [Delta] C ^L above (4), it comes to large information importance with respect to the schedule quality characteristics. Therefore, the project management system 1 according to this embodiment obtains the project execution cost increment [Delta] C ^L (4) for each task is presented to the user as a scheduled quality characteristics.

Presenting the schedule quality characteristics gives the user the following merits.
-The user can recognize in advance the location of the work for which the delay should be avoided, that is, the degree of influence of the delay of the work on the overall delivery date, that is, the location of the work having a high risk of delay.
-If a work with a high delay risk is a work that is difficult for the project team to avoid delay due to reasons such as the absence of an expert on the work execution in the project team, at least the delay risk of the work should not be high. You can reselect another schedule.
-Conversely, it is possible to present the work for which the delay risk is to be avoided in advance, and to recreate the schedule so that at least the delay risk of the presented work is reduced.

To determine the increment [Delta] C ^L project execution costs, it is necessary to quantify the delay risk. Therefore, in the present embodiment, the delay risk is quantified by applying the delay risk tolerance to the delay per unit time of the work, as in the first embodiment.

As described in the first embodiment, the magnitude of this delay risk can be regarded as equivalent to the degeneracy rate qX of the delay risk tolerance when the work is delayed by one day. Therefore, in the present embodiment, the degeneracy rate qX of the delay risk tolerance is calculated using the following equation to quantify the index value rX of the delay risk per day delay of the work.
qX = (Vb-Va) / Vb
rX = qX
Here, Vb represents the magnitude of the delay risk tolerance before the target work is delayed by one day, and Va represents the magnitude of the delay risk tolerance after the delay of one day. According to the above formula, when the delay risk is 1, that is, 100%, it means that the project is delayed by a unit time with respect to the total delivery date. That is, rX = 100% means that the delay of the unit time of the work directly leads to the delay of one day for the project with respect to the total delivery date.

Here, in the project management system 1, it is assumed that the over-delivery charge when the project exceeds the unit time (here, one day) with respect to the total delivery date is M yen. In this case, for example, as shown in FIG. 30, the index value rX If zero increment [Delta] C of the delay risk ^L becomes 0 yen 0% M circle, the index value rX 100% if increment [Delta] C ^L delay risk Is 100% of M yen and becomes M yen. Thus, the incremental [Delta] C ^L index value rX and project execution cost of delay risks are deemed to be positively correlated. Therefore, in this embodiment, it converted to increment [Delta] C ^L project execution costs using the following relational expression index value rX delay risk.
^{ΔC L (X) = M ×} qX
ΔC ^L (X) shows a project execution cost increment [Delta] C ^L at a certain working X. It should be noted that this relational expression can be changed in various ways as long as a positive correlation is maintained. Further, in general, M is set to include not only an excess penalty but also fixed costs (equipment costs, labor costs, etc.) that are constantly incurred during the development period.

The value of the increment [Delta] C L ^(X) are the values obtained by the cost in terms of the risk concept of time that delays risk delay, if it is less than the delay risk 100%, converted values are not to be added directly as extra charges. ΔC L ^(X) is construction period project in the time smaller than M means that there is sufficient margin for delivery, meaning that there is no room closer to M. ΔC ^L (X) = M refers to the determination of the delivery delay.

As shown in FIG. 31, the project management system 1 according to the first embodiment includes the schedule network generation unit 10 and the delay risk evaluation unit 20. The point is that the project management system 1 according to the first embodiment is provided. Is the same as. The function of the schedule network generation unit 10 is the same as that of the first embodiment, but the configuration and function of the delay risk evaluation unit 20 are different from those of the first embodiment.

The delay risk evaluation unit 20 includes a conditional expression generation unit 21, a delay risk index value calculation unit 24, and an incremental cost calculation unit 25.

In the conditional expression generation unit 21, for each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of the work X constituting the path and the margin parameter indicating the margin time is the total delivery date of the project. Generate a constraint expression that shows that: That is, the function of the conditional expression generation unit 21 is the same as that of the first embodiment.

The delay risk index value calculation unit 24 forms a positive space that satisfies the constraint condition expression when the work X is delayed by a unit time in the vector space whose element is the margin parameter indicating the margin time allowed for each work X. The sensitivity of the information indicating the size of the convex polyhedron V1 is calculated for each work as the index value rX. As described above, the delay risk index value calculation unit 24 has a function of combining the structure extraction unit 22 and the index value calculation unit 23 of the first embodiment.

The delay risk index value calculation unit 24 can use any one of the first method, the second method, and the third method when calculating the information indicating the size of the regular convex polyhedron V1. That is, the delay risk index value calculation unit 24 generalizes the volume calculation by integration extracted from the number of lattice points in the regular-convex polyhedron V1, the size of the maximum unit inscribed in the regular-convex polyhedron, and the regular-convex polyhedron V1. Any of the volumes of the structures capable of being used can be calculated as information indicating the size of the regular convex polyhedron V1. That is, the delay risk index value calculation unit 24 calculates the delay risk index value based on the degeneracy rate of the information indicating the magnitude of the delay risk tolerance calculated by using the first method or the second method. It may be. In the case of the first method, Va and Vb are the number of lattice points in the regular convex polyhedron V1, and in the case of the second method, Va and Vb are the largest single size inscribed in the regular convex polyhedron V1. Then, in the case of the third method, Va and Vb are the volumes of the structure extracted from the regular convex polyhedron V1 and capable of generalizing the volume calculation by integration.

Incremental cost calculation unit 25, based on the calculated index value rX, calculates the incremental cost [Delta] C ^L when each work X is delayed a unit time for each task.

The functions of the various components of the project management system 1 shown in FIG. 31 are realized by the CPU 30 of FIG. 14 executing the program 39. That is, the functions of the schedule network generation unit 10 and the delay risk evaluation unit 20 (conditional expression generation unit 21, delay risk index value calculation unit 24, and incremental cost calculation unit 25) are realized by executing the program 39 of the CPU 30.

Next, the operation of the project management system 1 according to the present embodiment will be described. As shown in FIG. 32, first, the schedule network generation unit 10 sets constraints on time, cost, and resources based on the logical order relationship between tasks X in the project and the time required for each task X. Generate a schedule network to meet (step S1). The generated schedule network information is sent to the conditional expression generation unit 21 of the delay risk evaluation unit 20. This step S1 is the same as that of the first embodiment.

Subsequently, the conditional expression generation unit 21 simplifies the schedule network (step S2). Specifically, the conditional expression generation unit 21 simplifies the schedule network based on the independent dependency between the work of the schedule network generated by the schedule network generation unit 10. This step S2 is the same as that of the first embodiment.

Subsequently, the conditional expression generation unit 21 calculates the sum of the required time of the work X constituting the path and the margin parameter indicating the margin time for each of the plurality of paths from the start to the end of the schedule network in the project. (Step S3: Conditional expression generation step). This step is the same as step S3 of the first embodiment.

Subsequently, the delay risk index value calculation unit 24 is a space that satisfies the constraint condition expression when each work X is delayed by a unit time in a vector space whose element is a margin parameter indicating the margin time allowed for each work X. The sensitivity of the delay risk tolerance indicating the size of the regular convex polyhedron V1 forming the above is calculated as the delay risk index value rX (step S30: delay risk index value calculation step). The index value rX is sent to the schedule network generation unit 10.

Subsequently, incremental cost calculation unit 25, based on the calculated index value, the incremental cost [Delta] C L when each work X was delayed unit time ^(X) is calculated for each work X (Step S31: incremental cost calculation Step). The calculated incremental cost ΔC L ^(X) is sent to the scheduled network generation unit 10.

Finally, the schedule network generation unit 10 determines the schedule network (step S7). Specifically, the schedule network generation unit 10, to the user, calculated incremental cost [Delta] C L ^(X) is displayed on each work X. Further, the schedule network generation unit 10 determines the schedule network having the maximum delay risk tolerance from the plurality of generated schedule networks based on the index value sent from the delay risk evaluation unit 20. To do. The decision also reflected the contents designated by the user based on the incremental cost ΔC L ^(X). For example, the user specifies the work to be excluded from the critical path and the quasi-critical path. The schedule network generation unit 10 generates a schedule network in which the designated work deviates from the critical path and the quasi-critical path.

(Example of evaluation of schedule quality characteristics)
Using the project management system 1 according to the present embodiment, the schedule quality characteristics of the project for manufacturing a certain system product shown in FIG. 33 were evaluated. This project consists of only the following six tasks, and the dimensions of the schedule network are three dimensions, as shown in FIG. 34. The overdue charge M per unit time is set to 200,000.
A Basic design (estimated time required = 20 days)
B Hard procurement (estimated required period = 35 days): Preceding work: Basic design C Installation adjustment (estimated required period = 5 days): Preceding work: Hard procurement D Detailed design (estimated required period = 10 days): Preceding work: Basic Design E Software development (estimated required period = 20 days): Preceding work: Detailed design F Comprehensive test (estimated required period = 15 days): Preceding work: Installation adjustment, software development

35 (A) and 35 (B) show the evaluation results of the cost increment caused by the one-day delay of the individual work constituting the project shown in FIG. 32. FIG. 35A shows the time required for the work A to F, the work execution cost, and the increase in the work execution cost when the work A to F are delayed by one day. These numerical values are input from the schedule network generation unit 10 to the delay risk evaluation unit 20.

Further, FIG. 35 (B) shows the magnitude of the delay risk tolerance before the work A to F is delayed by one day, the magnitude of the delay risk tolerance after the work A to F is delayed by one day, and the delay risk tolerance. index value rX (compression ratio qX), the index value rX the corresponding project execution cost increment [Delta] C _L, the total cost of the increment when working A~F was delayed one day is shown. These numerical values are numerical values obtained in the calculation process of the delay risk evaluation unit 20. The numerical value of the increase in the work execution cost in FIG. 35 (A) is brought about by the difference in the work content and the implementation environment, and is determined regardless of the schedule structure. On the other hand, the numerical value of the project performance cost [Delta] C ^L in Fig. 35 (B) increments determined by the structure-dependent scheduling, that is, increment representing the schedule quality characteristics.

From the evaluation results shown in FIGS. 35 (A) and 35 (B), the schedule network of FIGS. 33 and 34 can be determined as follows.
Incremental ΔC ^L of project execution cost of and work A~F is a much lower number than the 200,000 is both incremental, which means the delivery time exceeded. Therefore, at present, it can be judged that there is almost no risk of overdue delivery. And the indication is that the project execution cost increment [Delta] C ^L that approaches the overall 200,000 imminent risk of delivery exceeds, that one of the project execution cost increment [Delta] C ^L reaches 200,000 delivery date exceeded Means the confirmation of.
-It can be seen that the effects of delay on the overall construction period are particularly large in works A and F, followed by works B and D, and the effects of works C and E are relatively small.

Further, for example, the following can be said from the total incremental cost in FIG. 35 (B).
-It is work E that the delay has a particularly large effect on the cost. However, this is because the work execution cost of work E is originally large, and it is not a structural problem of the schedule. The increase in the activity execution cost of work E in FIG. 35 (A) and the work E in FIG. 35 (B) it can be understood from the numerical value of the project execution cost ΔC ^L.
-For work F, which has the next largest impact, the work execution cost is also large, but the cost incurred due to the schedule characteristics is also large. it can be understood from the numerical value of project execution cost ΔC ^L of the work F of B).

Regarding the increase in cost due to work execution delay, the analysis of the increase in work execution cost itself is stopped, and the risk of the effect of the work delay on the delivery date of the project (delay risk) is rarely analyzed. It was. Even if there was, the main analysis focused on the work on the critical path, and there was no way to properly quantify the delay risk related to the work on all paths. Therefore, it was difficult to evaluate a project with a huge number of tasks. Work-level quantification of schedule quality characteristics will help manage large and complex project schedules with irregular occurrences of unexpected delays.

The evaluation of the schedule network of FIGS. 33 and 34 was performed using the first method. However, as described above, the same evaluation can be realized by using the second method and the third method. When the third method is used, when a plurality of structures are extracted, the degeneracy rate can be calculated for each structure, and the total value or the average value of the degeneracy rates can be used as an index value of delay risk tolerance. ..

The schedule network generation unit 10 may generate a plurality of patterns of schedule networks having different work orders, and the delay risk evaluation unit 20 may evaluate the delay risk of the plurality of patterns of schedule networks. Good. In this way, the schedule network with the maximum delay risk tolerance can be selected from a plurality of schedule networks that satisfy the constraints of the three elements of process (time), resource, and cost (cost). Will be.

The central part of the processing of the project management system 1 can be realized by using a normal computer system without relying on a dedicated system. For example, a computer program for executing the above operation is stored and distributed on a computer-readable recording medium (flexible disk, CD-ROM, DVD-ROM, etc.), and the computer program is installed on the computer. May configure the project management system 1 to execute the above processing. Further, the project management system 1 may be configured by storing the computer program in a storage device of a server device on a communication network such as the Internet and downloading it by a normal computer system.

When the function of the project management system 1 is realized by sharing the OS (operating system) and the application program, or by collaborating with the OS and the application program, only the application program part is stored in the recording medium or the storage device. May be good.

It is also possible to superimpose a computer program on a carrier wave and distribute it via a communication network. For example, a computer program may be posted on a bulletin board system (BBS, Bulletin Board System) on a communication network, and the computer program may be distributed via the network. Then, the computer program may be started and executed in the same manner as other application programs under the control of the OS so that the above processing can be executed.

The present invention allows for various embodiments and modifications without departing from the broad spirit and scope of the invention. Moreover, the above-described embodiment is for explaining the present invention, and does not limit the scope of the present invention. That is, the scope of the present invention is indicated not by the embodiment but by the claims. Then, various modifications made within the scope of the claims and the equivalent meaning of the invention are considered to be within the scope of the present invention.

The present invention can be applied to the management of a project composed of a plurality of tasks.

1 Project management system, 10 Schedule network generation unit, 20 Delay risk evaluation unit, 21 Conditional expression generation unit, 22 Structure extraction unit, 23 Index value calculation unit, 24 Delay risk index value calculation unit, 25 Incremental cost calculation unit, 30 CPU, 31 memory, 32 external storage unit, 33 operation unit, 34 display unit, 35 input / output unit, 39 program, 40 internal bus, 50 recording medium, AS work, A1 to A10, a to s margin parameter, L1 Integral operation, L2 multiple integral, L3 integral formula, V1 regular convex polyhedron, V2 single unit

Claims (12)

A project management system that manages a project consisting of multiple activities.
A schedule network generator that generates a schedule network that satisfies the time, cost, and resource constraints based on the logical order relationship between the activities in the project and the time required for each activity.
In a vector space whose element is a margin parameter indicating the allowable margin time for each activity, a volume obtained by integration from a regular convex polyhedron representing a margin that can accommodate the project in the overall delivery date when each activity is delayed. A delay risk evaluation unit that extracts a structure that can be generalized in calculation and evaluates the schedule network using the size of the extracted structure or the sensitivity to the delay of the size as an index value.
Project management system equipped with. The delay risk evaluation department
A conditional expression generator that generates a constraint expression corresponding to each of a plurality of paths from the start to the end of the schedule network based on the relationship between the overall delivery date of the project, the required time, and the margin parameter.
A structure extraction unit that extracts a structure capable of generalizing volume calculation by integration from the regular convex polyhedron representing a space satisfying the plurality of constraint equations in the vector space.
An index value calculation unit that calculates the volume by integration and calculates the size of the extracted structure or the sensitivity to the delay of the size as an index value.
To prepare
The project management system according to claim 1. The structure extraction unit
Each row corresponds to one of the plurality of constraint expression expressions, each column is a matrix corresponding to the margin parameter, and the value of the element in which the constraint parameter term is included in the constraint condition expression is set to 1, and other than that. Generate a matrix with the value of the element of
A matrix consisting of columns for which an inclusion relationship is established in the row where the element value is 1 and columns whose elements are 1 do not match at all is extracted as a matrix representing a structure in which volume calculation can be generalized. And
The index value calculation unit
Among the extracted matrices, the margin parameter corresponding to the first column having the largest number of rows that become 1 is used as the integral variable, and the second element that becomes 1 is included in all the elements that become 1 in the first column. Integrate with the margin parameter of the column as the integrand, and the upper limit that the integrator can take as the minimum value that the integrator can take.
Multiple integrals are performed between the margin parameters of columns in which the rows that are 1 do not match at all, and the size of the extracted structure is obtained.
The project management system according to claim 2. When the structure extraction unit extracts a plurality of structures that can be generalized in volume calculation by integration,
The index value calculation unit calculates the total value or the average value of the size of each of the extracted plurality of structures or the sensitivity to the delay of the size as the index value.
The project management system according to claim 2 or 3. The index value calculation unit
Degeneration of the size of a regular convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the margin time allowed for each activity. Information indicating the rate is calculated as the index value.
The project management system according to any one of claims 2 to 4. A project management system that manages a project consisting of multiple activities.
For each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of each activity constituting the path and the margin parameter indicating the margin time shall be less than or equal to the overall delivery date of the project. A conditional expression generator that generates a constraint expression that indicates
Indicates the size of a regular-convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the allowable margin time for each activity. A delay risk index value calculation unit that calculates the sensitivity of information as an index value for each activity,
Based on the calculated index value, an incremental cost calculation unit that calculates an incremental cost when each activity is delayed by a unit time for each activity, and an incremental cost calculation unit.
Project management system equipped with. The delay risk index value calculation unit
Either the number of lattice points in the regular-convex polyhedron, the size of the largest single unit inscribed in the regular-convex polyhedron, or the volume of the structure extracted from the regular-convex polyhedron that can be generalized in volume calculation by integration. Is calculated as information indicating the size of the regular convex polyhedron.
The project management system according to claim 6. The conditional expression generator
Simplify the schedule network based on the independent dependency between the activities of the schedule network.
The project management system according to any one of claims 2 to 7. A project management method executed by an information processing device that manages a project consisting of multiple activities.
A schedule network generation step that generates a schedule network that satisfies the time, cost, and resource constraints based on the logical order relationship between the activities in the project and the time required for each activity.
In a vector space whose element is a margin parameter indicating the margin time allowed for each of the activities, integration is performed from a regular convex polyhedron representing a margin that can accommodate the entire project in the overall delivery date when the project is delayed. A delay risk evaluation step that extracts a structure that can be generalized in volume calculation and evaluates the schedule network using the size of the extracted structure or the sensitivity to the delay of the size as an index value.
Project management methods including. A project management method executed by an information processing device that manages a project consisting of multiple activities.
For each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of each activity constituting the path and the margin parameter indicating the margin time shall be less than or equal to the overall delivery date of the project. A conditional expression generation step that generates a constraint expression that indicates
Indicates the size of a regular-convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the allowable margin time for each activity. A delay risk index value calculation step that calculates the sensitivity of information as an index value,
Based on the calculated index value, an incremental cost calculation step for calculating the incremental cost when each activity is delayed by a unit time for each activity, and
Project management methods including. A computer that manages a project that consists of multiple activities
A schedule network generator that generates a schedule network that satisfies the time, cost, and resource constraints based on the logical order relationship between the activities in the project and the time required for each activity.
In a vector space whose element is a margin parameter indicating the margin time allowed for each of the activities, integration is performed from a regular convex polyhedron representing a margin that can accommodate the entire project in the overall delivery date when the project is delayed. A delay risk evaluation unit that extracts a structure that can be generalized in volume calculation and evaluates the schedule network using the size of the extracted structure or the sensitivity to the delay of the size as an index value.
A program that functions as. A computer that manages a project that consists of multiple activities
For each of the plurality of paths from the start to the end of the schedule network in the project, the sum of the required time of each activity constituting the path and the margin parameter indicating the margin time shall be less than or equal to the overall delivery date of the project. Conditional expression generator, which generates a constraint expression indicating
Indicates the size of a regular-convex polyhedron that forms a space that satisfies the constraint equation when each activity is delayed by a unit time in a vector space whose element is a margin parameter indicating the allowable margin time for each activity. Delay risk index value calculation unit that calculates the sensitivity of information as an index value,
An incremental cost calculation unit that calculates an incremental cost when each activity is delayed by a unit time based on the calculated index value for each activity.
A program that functions as.

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