JP5458350B2 - Task graph analysis device and task graph analysis program - Google Patents

Description

  The present invention relates to a task graph analysis device and a task graph analysis program, and more particularly to a technique for analyzing a task graph composed of a plurality of tasks constituting a schedule using a critical path.

  Conventionally, task graphs (also called PERT diagrams, arrow diagrams, clinical paths, care maps, etc.) are used as means for analyzing a critical path composed of a plurality of tasks. In this task graph, the longest sequence of tasks that have no time margin is called a critical path, and the task of scheduling is to focus on the tasks on the critical path. Evaluation for each task on the critical path is performed for the required processing time of each task (see, for example, Patent Documents 1 to 4), and is performed for probabilistic statistical calculation of tasks appearing on the critical path (for example, (See Non-Patent Document 1).

Japanese Patent Laid-Open No. 6-19998 Japanese Examined Patent Publication No. 6-42253 JP 2008-171153 A JP 2008-287509 A

Information Processing Society of Japan, "Fake path elimination method in statistical static delay analysis" 20010111; 2001 (2): 81-8

  By the way, in large-scale task systems, it is generally said that tasks on the critical path are within 20% of all tasks. For this reason, at least about 20% of the tasks that are considered important must be carefully focused. Also, when it is desired to shorten the schedule time, it is necessary to pay attention to the task on the critical path and reduce the time of the task.

  On the other hand, there are many parallel paths for tasks not included in the critical path that occupy 80% of the large-scale task system. Further, the interference due to the probability variation of these parallel paths or the net increase due to the passage of time or the like generates quasi-critical paths such as the second critical path and the third critical path. For this reason, appropriate handling of tasks not included in the critical path is becoming more important in scheduling.

  However, in the above conventional technique, since evaluation is performed only for the most critical task, there is a problem in that it is impossible to immediately grasp how many other critical tasks exist. In addition, when calculating an evaluation value of a task using probabilistic statistics, it is necessary to execute the entire task system many times, and there is a problem that it takes a lot of time for the calculation.

  That is, in the method of evaluating a task based only on the critical path, information on the entire system is lost, and therefore, the semi-critical path cannot be correctly evaluated. In order to prevent this, the entire task system needs to be executed many times. For this reason, for example, when the total number of tasks is very large in a large-scale project, the total number survey is impossible due to the remaining capacity, or the number of times information is acquired in a mission critical system is limited in the first place. When there is a restriction regarding task information acquisition, sufficient evaluation cannot be performed.

  The present invention has been made to solve such problems, and each task can be evaluated not only for the critical path but also for the semi-critical path without executing the entire task system many times. The purpose is to do so.

In order to solve the above-described problem, in the present invention, n tasks {v ₁ , v ₂ ,..., V _n } to be scheduled and a start temporarily set at the beginning and end of the n tasks. Task v _i (i = 0, 1,..., N, n + 1) to task v _j (j = 0, 1,..., N, n + 1) belonging to the task system including task v ₀ and end task v _{n + 1} Each of the critical paths up to and including task v _i (i = 0, 1,..., N, n + 1) is calculated as the total number of tasks included in each critical path starting from task v _{i. It} is calculated as an evaluation value of _i .

According to the present invention configured as described above, not only the critical path of the entire system from the start task v ₀ to the end task v _{n + 1} but also the partial critical path from the task v _i to the task v _j is calculated. so that the evaluation value of the task v _i by the number of tasks included on all of the critical path that starts the task v _i is counted is calculated. For this reason, unlike the conventional technology that only evaluates the tasks included in the path for only the critical path of the entire system, in addition to the tasks on the critical path of the entire system, it is not on the critical path of the entire system. Evaluation values can also be obtained for tasks. Moreover, since the evaluation value is calculated simply by counting the number of tasks as described above rather than by a complicated calculation such as probabilistic statistics, the evaluation value can be obtained without executing the entire task system many times. Can do. Thus, according to the present invention, each task can be evaluated not only for the critical path but also for the semi-critical path without executing the entire task system many times.

It is a block diagram which shows the function structural example of the task graph analyzer by this embodiment. It is a figure which shows an example of the task information by this embodiment. It is a figure which shows the preceding / following relationship of each task in case of n = 1. It is a figure which shows the example of the task graph displayed when n = 1. It is a figure which shows the preceding / following relationship of each task in the case of n = 2. It is a figure which shows the example of the task graph displayed when n = 2. It is a figure which shows the example of the task graph displayed when n = 3. It is a figure which shows the example of the task graph displayed when n = 4. It is a figure which shows the example of the task graph of the type | system | group which has many tasks. It is a figure which shows the example of the task graph displayed when n = 2 and a some critical path exists. It is a figure which shows an example regarding task arrangement | positioning.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram illustrating a functional configuration example of a task graph analysis apparatus according to the present embodiment. As shown in FIG. 1, the task graph analysis apparatus 10 of this embodiment analyzes a schedule composed of n tasks (n is an integer of 1 or more), and includes a task information input unit as its functional configuration. 1, a temporary task setting unit 2, a critical path calculation unit 3, an evaluation value calculation unit 4, and a map display unit 5. In the following is assumed for the sake of convenience that represents the n-number of tasks _{v 1,} v 2, · ·, in _{v n.}

  The function configurations 1 to 5 included in the task graph analysis apparatus 10 can be realized by any of a hardware configuration, a DSP, an MPU, and software. For example, when implemented by software, the task graph analysis apparatus 10 of the present embodiment is actually configured with a computer CPU or MPU, RAM, ROM, and the like, and a program stored in the RAM or ROM operates. realizable.

  Therefore, it can be realized by recording a program that causes the computer to perform the above-described functions on a recording medium such as a CD-ROM, and causing the computer to read the program. As a recording medium for recording the program, a flexible disk, a hard disk, a magnetic tape, an optical disk, a magneto-optical disk, a DVD, a nonvolatile memory card, a semiconductor memory, and the like can be used in addition to the CD-ROM. It can also be realized by downloading the program to a computer via a network such as the Internet.

  The task graph analyzer 10 is connected to an input device 20 such as a keyboard and a mouse, and a display device 30 such as a liquid crystal display. The task information input unit 1 of the task graph analysis device 10 inputs task information regarding n tasks from the input device 20. The task information input here includes task identification information for identifying n tasks, order information indicating the processing order on the schedule of n tasks, and time information indicating the required processing time of n tasks ( Corresponding to the load information of the present invention).

FIG. 2 is a diagram illustrating an example of task information according to the present embodiment. The task identification information may be a unique ID for each task or a task name. In addition, other information may be used as long as each task can be uniquely identified. FIG. 2 shows an example of using task name _{v 1,} v 2, · ·, a _{v n} as a task identification information.

The order information is information representing the preceding / following relationship of tasks. For example, for each task, a set of task identification information of a task that is processed one before and the task identification information of a task that is processed one after is used as order information. In the example of FIG. 2, there is no previous task preceding task v ₁ (that is, task v ₁ is processed first), and the succeeding other task is task v ₂ . It shows that there is. Further, it is indicated that the immediately preceding other task preceding task v ₂ is task v ₁ and the succeeding immediately following other task is task v ₃ .

  Note that when there are two or more tasks to be processed one preceding in advance, the task identification information of the two or more tasks is stored in the item of the preceding task. Similarly, when there are two or more tasks to be processed one after, the task identification information of the two or more tasks is stored in the item of the subsequent task. Here, an example in which a set of a preceding task and a succeeding task is used as the order information has been described.

The time information is information representing the time required to process each task. In the example of FIG. 2, the required processing time of task v ₁ is t ₁ and the required processing time of task v ₂ is t ₂ . Here, the time information is the required processing time of the task, but a set of processing start time and end time may be the time information. Moreover, although time information is used here, it is not limited to this. Information other than time can be used as long as the information indicates the task load. For example, as information other than time, information such as the cost required for processing the task, the physical distance of the information transmission path within the task, the influence level of the environment affected by the task, indirect observation values and index values related to the task, etc. It may be used.

  More specifically, in scheduling based on task graphs for various fields as described below, attributes as shown in parentheses can be used as task load information. Project management (time, cost), processor development (time, wiring distance), computer system (time, cost), medical care (time, cost, impact on the human body, indirect observations such as weight and dosage), education (Education effect index such as deviation value), administration (time, cost, disaster recovery priority), chemistry (time, cost), communication (time, equipment load index), logistics (time, cost, luggage weight), manufacturing (time) , Cost, number of parts used, number of parts in stock).

The temporary task setting unit 2 temporarily sets the 0th task information as the start task v _{0 at} the head of the _n tasks v _{1 to} v n to which the task information is input by the task information input unit 1, and n The (n + 1) th task information is provisionally set as the end task v _{n + 1} at the end of the task. The contents of the task information temporarily set here are the same as the task information as shown in FIG. 2 input by the task information input unit 1. The start task _{v 0} and ending tasks _{v n + 1} of the required processing time _{t 0, t n + 1} is respectively a predetermined value.

Critical path calculating section 3, the n input by the task information input unit 1 and the task information of the task v ₁ to v _n, the task provisional setting unit 2 temporarily set started task v ₀ and ending tasks v _{n + 1} Based on the task information, the critical paths from the task v _i (i = 0, 1,..., N, n + 1) to the task v _j (j = 0, 1,..., N, n + 1) are respectively calculated. For each critical path, a set of tasks included on the path is obtained.

A known technique can be applied to the critical path calculation method itself. In the present embodiment, it is assumed that the critical path calculation unit 3 calculates a critical path according to the following procedure. First, the earliest start time and earliest end time of the start task v ₀ are calculated based on the time information included in the task information. Next, the earliest start time and earliest end time of the subsequent task following the start task v ₀ are calculated in order according to the preceding / following relationship between the tasks indicated by the order information. Then, when it reaches the end tasks v _{n + 1,} we calculate the latest end time and latest start time in reverse order toward the preceding task from its termination task v _{n + 1.} Here, the difference between the earliest start time and the latest start time is defined as slack, and the critical path is obtained by tracing back the path without slack, that is, the path without margin time, from task v _i or task v _j. .

Here, the calculation contents of the critical path calculation unit 3 for obtaining the critical path will be described in detail. First, the entire system including the task input by the task information input unit 1 and the start task v ₀ and the end task v _{n + 1} temporarily set by the task temporary setting unit 2 is represented as L _all = {v ₀ , v ₁ , v ₂ ,. , V _n , v _{n + 1} }. L _all is a set representing tasks of the entire system, v _i (i = 0, 1,..., N, n + 1) is an individual task, and n is the total number of tasks. At this time, there is only one critical path of the entire system from the start task v ₀ to the end task v _{n + 1} . Separately from this, when an arbitrary i is selected and the task v _i is assumed to be an end task, there is only one critical path from the start task v ₀ to the arbitrary task v _i . Hereinafter, the critical path of the entire system from the start task v ₀ to the arbitrary task v _i is referred to as “total critical path”, and the other partial critical paths are referred to as “partial critical paths”. In addition, when the term “critical path” is simply used, it includes both the entire critical path and the partial critical path.

Here, L _cp ⁱ = {v ₀ ,..., V _i } ⊂L _all can be taken as a set of tasks included on the partial critical path from the start task v ₀ to the arbitrary task v _i . Set L _cp ⁱ can also be extended with respect to when i = 0 and i = n + 1, ^{_{respectively, L cp 0 = {v 0}} } ⊂L all, L cp n + 1 = {v 0, ··, v i, · •, v _{n + 1} } ⊂L _all .

Furthermore, a set L _cp ^j is selected such that task v _i is included on a partial critical path where arbitrary j (j = 0, 1,..., N, n + 1) is selected and task v _j is assumed to be an end task. Then, a set L _p ^{i, j} of tasks included on the partial critical path is defined as follows.
^{_{L cp i ⊆L cp j ⇒ L}} p i, j = (L cp i xorL cp j) ∪ {v i}
^{_{L cp i ¬⊆L cp j ⇒ L}} p i, j = φ ( empty set)
Note that here, the logical operator “¬” representing the meaning of “negation” is used as a set for the symbol “を” representing the set, but in this specification, for convenience, “¬” is not used as the logical operator. It is used as a symbol that negates the meaning of the set symbol. For example, in the case of "L _cp ⁱ ¬⊆L _cp ^j", it is intended to mean that the "subset of L _cp ^j is not an L _cp ^i".

That is, the set L _p ^{i, j} is in the preceding relationship of the previous task from the start task v ₀ to the arbitrary task v _i among the tasks included in the partial critical path from the start task v ₀ to the arbitrary task v _j. This is a set of tasks in which each task included in the partial critical path to a certain task is removed. In other words, the set L _p ^{i, j} represents a set of tasks included on the partial critical path from the arbitrary task v _i to the arbitrary task v _j .

For example, when n = 1, the set of tasks of the entire system is L _all = {v ₀ , v ₁ , v ₂ }, the start task is v ₀ , and the end task is v ₂ . At this time, the preceding / following relationship of these three tasks is v ₀ → v ₁ → v ₂ as shown in FIG. 3 (when n = 1, there can be no other connection relationship). The critical path calculation unit 3 adds a partial criticality from an arbitrary task v _i to an arbitrary task v _j in addition to the set L _p ^0,2 of each task included in the entire critical path from the start task v ₀ to the end task v _2. A set of tasks L _p ^0,0 , L _p ^0,1 , L _p ^1,0 , L _p ^1,1 , L _p ^1,2 , L _p ^2,0 , L _p ^2,1 included in the path , L _p ^2,2 is obtained.

Here, the respective sets L _p ^{i, j} (i = 0, 1, 2, j = 0, 1, 2) obtained by the critical path calculation unit 3 are as follows.
L _p ^0,0 = (L _cp ⁰ xorL _cp ⁰ ) ∪ {v ₀ } = {v ₀ }
L _p ^0,1 = (L _cp ⁰ xorL _cp ¹ ) ∪ {v ₀ } = {v ₀ , v ₁ }
L _p ^0,2 = (L _cp ⁰ xorL _cp ² ) ∪ {v ₀ } = {v ₀ , v ₁ , v ₂ }
L _p ^1,0 = φ
L _p ^1,1 = (L _cp ¹ xorL _cp ¹ ) ∪ {v ₁ } = {v ₁ }
L _p ^1,2 = (L _cp ¹ xorL _cp ² ) ∪ {v ₁ } = {v ₁ , v ₂ }
L _p ^2,0 = φ
L _p ^2,1 = φ
L _p ^2,2 = (L _cp ² xorL _cp ² ) ∪ {v ₂ } = {v ₂ }

For each task v _i (i = 0, 1,..., N, n + 1), the evaluation value calculation unit 4 calculates the total number of tasks included in each critical path starting from the task v _i (the same task is one count) is calculated as the evaluation value of the task v _i. In this embodiment, the evaluation value of each task corresponding to the task set L _all of the entire system is called a superimposed path score S, and the superimposed path score S is defined as in the following (Equation 1). Here, s _i is a superimposed path score in the set L _all for an arbitrary task v _i .

For example, when n = 1, the evaluation value calculation unit 4 calculates the superimposed path score S = {s ₀ , s ₁ , s ₂ } as follows.
s ₀ = | L _p ^0,0 ∪L _p ^0,1 ∪L _p ^0,2 |
= | {V ₀ } ∪ {v ₀ , v ₁ } ∪ {v ₀ , v ₁ , v ₂ } |
= | {V ₀ , v ₁ , v ₂ } | = 3
s ₁ = | L _p ^1,0 ∪L _p ^1,1 ∪L _p ^1,2 |
= | Φ∪ {v ₁ } ∪ {v ₁ , v ₂ } |
= | {V ₁ , v ₂ } | = 2
s ₂ = | L _p ^2,0 ∪L _p ^2,1 ∪L _p ^2,2 |
= | Φ∪φ∪ {v ₂ } |
= | {V ₂ } | = 1

Here, superimposed path scores s _i to the task v _i, if there is shortened or extended any changes, such as processing time for the task v _i, corresponding to the number of corresponding superimposed path scores s _i task Means being affected. For this reason, the superimposed path score s _i calculated by the evaluation value calculation unit 4 of the present embodiment can be positioned as an index representing the importance of the task v _i in each critical path.

Map display unit 5 includes n tasks v ₁ to v _n of the task information inputted by the task information input unit 1, the task temporary setting unit 2 of the temporarily set start task v ₀ and ending tasks v _{n + 1} tasks Based on the task identification information and the order information included in the information, the preceding and succeeding relationship of each of the tasks v _{0 to} v _{n + 1} is displayed on the display device 30 as a task graph (in this embodiment, this is referred to as “superimposed path score map”). To do. The time map display unit 5 in accordance with the magnitude of the calculated superimposed path scores S (superimposed path scores s _i of each task v _i) by the evaluation value calculation unit 4, prior Follows outputted from the task v _i The display mode (for example, thickness, hue, density) of the line representing the difference is made different.

FIG. 4 is a diagram illustrating an example of the superimposed path score map displayed by the map display unit 5 when n = 1. When n = 1, the preceding / following relationship of the three tasks v ₀ , v ₁ , v ₂ is v ₀ → v ₁ → v ₂ as shown in FIG. The map display unit 5 draws each task v ₀ , v ₁ , v ₂ with a circle, displays the task name v ₀ , v ₁ , v ₂ in each circle, and displays the superimposed path score s ₀ , s _1. , S ₂ are indicated by numbers. Further, the map display unit 5 displays the line thickness of the preceding / following relationship connecting the tasks by changing the thickness depending on the superimposed path scores s ₁ and s ₂ of the task having the following relationship. Yes. Specifically, the larger the superimposed path scores s ₁ and s ₂ are, the thicker the line is displayed.

Next, the case where n = 2 will be described. When n = 2, as shown in FIG. 5, two arrangement methods are conceivable as the preceding / following relationship of tasks. In the pattern 1 shown in FIG. 5A, the tasks v ₀ , v ₁ , v ₂ , v ₃ are connected linearly as in the case of n = 1. On the other hand, in the pattern 2 shown in FIG. 5 (b), it takes two paths branching from the start task v _0, respectively connected to the task v ₁ and task v _2. In FIG. 5, tasks surrounded by a frame indicate tasks that constitute the entire critical path. A broken-line arrow indicates a state in which there is a slack and there is a slack and a partial critical path is searched from the subsequent task, but not included in the route, although there is a preceding / following relationship between tasks connected by the broken line.

In the case of pattern 1 with n = 2, the superimposed path score S = {s ₀ , s ₁ , s ₂ , s ₃ } can be calculated in the same manner as in the case of n = 1. On the other hand, n = 2 If the pattern 2, starting superimposed path scores tasks _{v 0} Task _v 1 branching from, _v superimposed path scores _s 1 corresponding to _{2, s 2,} also started task _{v 0} associated with these s ₀ to appear distinctive appearance. The calculation process of the superimposed path scores s ₀ , s ₁ , s ₂ , and s ₃ corresponding to the tasks v ₀ , v ₁ , v ₂ , and v ₃ in the pattern 2 is shown below.

In the case of pattern 2 where n = 2, the critical path calculation unit 3 performs the entire critical path from the start task v ₀ to the end task v ₃ and the arbitrary task v _i to the arbitrary task v _j (i = 0, 1, 2, 3, j = 0, 1, 2, 3) a set of tasks L _p ^0,0 , L _p ^0,1 , L _p ^0,2 , L _p ^0,3 , L _p ^1,0 , L _p ^1,1 , L _p ^1,2 , L _p ^1,3 , L _p ^2,0 , L _p ^2,1 , L _p ^2,2 , L _p ^2,3 , L _p ^{3 , 0} , L _p ^3,1 , L _p ^3,2 , L _p ^3,3 are obtained as follows.

L _p ^0,0 = (L _cp ⁰ xorL _cp ⁰ ) ∪ {v ₀ } = {v ₀ }
L _p ^0,1 = (L _cp ⁰ xorL _cp ¹ ) ∪ {v ₀ } = {v ₀ , v ₁ }
L _p ^0,2 = (L _cp ⁰ xorL _cp ² ) ∪ {v ₀ } = {v ₀ , v ₂ }
L _p ^0,3 = (L _cp ⁰ xorL _cp ³ ) ∪ {v ₀ } = {v ₀ , v ₁ , v ₃ }
L _p ^1,0 = φ
L _p ^1,1 = (L _cp ¹ xorL _cp ¹ ) ∪ {v ₁ } = {v ₁ }
L _p ^1,2 = φ
L _p ^1,3 = (L _cp ¹ xorL _cp ³ ) ∪ {v ₁ } = {v ₁ , v ₃ }
L _p ^2,0 = φ
L _p ^2,1 = φ
L _p ^2,2 = (L _cp ² xorL _cp ² ) ∪ {v ₂ } = {v ₂ }
L _p ^2,3 = φ
L _p ^3,0 = φ
L _p ^3,1 = φ
L _p ^3,2 = φ
L _p ^3,3 = (L _cp ³ xorL _cp ³ ) ∪ {v ₃ } = {v ₃ }

Further, the evaluation value calculation unit 4 calculates the superimposed path score S = {s ₀ , s ₁ , s ₂ , s ₃ } as follows.
s ₀ = | L _p ^0,0 ∪L _p ^0,1 ∪L _p ^0,2 ∪L _p ^0,3 |
= | {V ₀ } ∪ {v ₀ , v ₁ } ∪ {v ₀ , v ₂ } ∪ {v ₀ , v ₁ , v ₃ } |
= | {V ₀ , v ₁ , v ₂ , v ₃ } | = 4
s ₁ = | L _p ^1,0 ∪L _p ^1,1 ∪L _p ^1,2 ∪L _p ^1,3 |
= | Φ∪ {v ₁ } ∪φ∪ {v ₁ , v ₃ } |
= | {V ₁ , v ₃ } | = 2
s ₂ = | L _p ^2,0 ∪L _p ^2,1 ∪L _p ^2,2 ∪L _p ^2,3 |
= | Φ∪φ∪ {v ₂ } ∪φ |
= | {V ₂ } | = 1
s ₂ = | L _p ^3,0 ∪L _p ^3,1 ∪L _p ^3,2 ∪L _p ^3,3 |
= | Φ∪φ∪φ∪ {v ₃ } |
= | {V ₃ } | = 1

The map display unit 5 displays the preceding / following relationship of the tasks v _{0 to} v _{3 on} the display device 30 as a superimposed path score map. FIG. 6 is a diagram illustrating an example of a superimposed path score map displayed by the map display unit 5 in the case of pattern 2 where n = 2. In this case, the preceding / following relationship of the four tasks v ₀ , v ₁ , v ₂ , v ₃ is the same as that in FIG. The map display unit 5 draws each task v ₀ , v ₁ , v ₂ , v ₃ with a circle, displays the task name v ₀ , v ₁ , v ₂ , v ₃ in each circle, and also displays a superimposed path The scores s ₀ , s ₁ , s ₂ , and s ₃ are displayed as numbers. In addition, the map display unit 5 displays the thickness of the line of the preceding / following relationship between tasks depending on the superimposed path scores s ₁ , s ₂ , s ₃ of the tasks in the following relationship.

In the case of n ≧ 3, the superimposed path score S can be calculated in the same manner and the superimposed path score map can be displayed. FIG. 7 is a diagram illustrating an example of a superimposed path score map of various patterns obtained when n = 3. Although the pattern 1 shown in FIG. 7 (a) is similar to the case n = 1, the the pattern 2-4 shown in FIG. 7 (b) ~ (d) , which branch tasks _{v 3} is the overall critical path It can be seen that the surrounding environment changes depending on whether it is connected to the task, and this appears in the superimposed path score S.

In the pattern 5 shown in FIG. 7 (e), as a characteristic of the superimposed path score S, the same regardless of whether the _two tasks v ₁ and v ₂ branched from the start task v ₀ are located on the entire critical path. Evaluation values are taken (s ₁ = 2 and s ₂ = 2). In the pattern 6 of FIG. 7F, the tasks v ₂ and v ₃ other than the entire critical path have the same evaluation value (s ₂ = 1, s ₃ = 1). From these, superimposed path scores s _i of a task v _i is important index that depends on the number of tasks on the subsequent partial critical path expresses the surrounding environment while influenced the overall critical path I understand that.

FIG. 8 is a diagram illustrating an example of a superimposed path score map of various patterns obtained when n = 4. Pattern 1 in FIG. 8A shows a state in which a plurality of tasks v ₃ and v ₄ are arranged in a nested manner. Pattern 2 in FIG. 8B shows a state in which a plurality of tasks v ₃ and v ₄ are arranged in series after branching. In patterns 3 and 4 in FIGS. 8C and 8D, a task v ₄ has a preceding relationship of a plurality of tasks v ₁ and v ₃ and a partial critical path is in the preceding relationship. _{1, v} by either related to either ₃ shows how the task _v 1, _v superimposed path scores _s 1 _{3, s 3} is changed. Furthermore, pattern 5 in FIG. 8E shows an example in which the task arrangement becomes more complicated.

As can be seen from FIG. 8, when the entire schedule system composed of a plurality of tasks is expressed, there is diversity in the arrangement of each task. Therefore, as the number of tasks included in the system increases, presentation of only the value of the superimposed path score s _i may cause confusion in understanding the system. Therefore, the map display unit 5 as in the present embodiment is provided, it is preferable to display the visually superimposed path score map form in accordance with the nature of the superposed path scores s _i.

In general, individual tasks belonging to one system are often arranged based on a branch. FIG. 9 is a diagram illustrating an example of a superimposed path score map of a system having a large number of tasks. In the system shown in FIG. 9, the seven tasks v _{0 to} v ₆ have a preceding / following relationship in which two branches are taken. The superimposed path scores s _{0 to} s ₁₅ in such a task arrangement configuration are as shown in FIG. 9, and the superimposed path score s _i tends to increase in series from the end task v ₁₅ to the start task v _0. I understand that there is.

Therefore, by utilizing the property that all the superimposed path scores s _i are values of 1 or more, logarithmic values (= logs _i ) of the respective superimposed path scores s _i are taken, and the logarithmic values thereof are superimposed path scores in the system. By dividing by the logarithmic value of the maximum value of s _i , a superimposed path score s _i ′ in which the value increases linearly from the end task v ₁₅ toward the start task v ₀ can be set. The superimposed path score s _i ′ is a value such that 0 ≦ s _i ′ ≦ 1. By reflecting this in the thickness, hue, and density of the line indicating the preceding / following relationship in the superimposed path score map, the line thickness, hue, and density are visually substantially uniform according to the size of the superimposed path score s _i ′. Can appear to change.
s _i '= logs _i / log {max (S)}

Taking the thickness of the line as an example, for a task v _i having a subsequent relationship, the subsequent task is, for example, v _j . In this case, prior subsequent relationships thickness of the line showing the b _i, if the step of adjusting the thickness b _i of the line and k + 1 stage, can be defined the following equation.
b _i = 1 + k · s _i ′
Here, due to the definition of the superimposed path score S, a relationship of s _i > s _j is established for the tasks v _i and v _j on the partial critical path. Therefore, one when the s _i> s _j to the thickness of the line showing the previous trailing relationship with b _i, to mean that it is not followed as the critical path when the s _i ≦ s _j, 1 No. thin thickness This is expressed in a superimposed path score map with a broken line.

This superimposed path score map can be used not only when expressing the entire system but also when expressing a part of the system. When expressing a part of the system, it is convenient to calculate the superimposed path score S ″ corresponding to the task to be displayed as follows.
s _i ″ = logs _i / log {max (S ′)}

It is assumed that there is only one partial critical path from the start task v ₀ to an arbitrary task v _i as an assumption of the description so far, but it is also superimposed when there are a plurality of partial critical paths with the same condition. It is clear that the pass score S can be calculated. As an example, verification is performed using the superimposed path scores s ₀ and s ₂ in the pattern 2 with n = 2 shown in FIG.

Assume that not only the task v ₁ but also the task v ₂ is searched as a partial critical path when the partial critical path is traced from the task v ₃ in the set L _all of the tasks in the entire system when n = 2. That is, as shown in FIG. 10, the connection line indicating the preceding / following relationship between the task v ₂ and the task v ₃ was not a broken line but a solid line (there was no slack between the task v ₂ and the task v ₃ ). And

In this case, although there is no change in the calculated environment as compared with the case of FIG. 5 (b) for superimposing path scores s ₁ and superimposed path scores s ₃ tasks v ₃ tasks v _1, superimposed path scores s task v ₀ Regarding the superimposed path score s ₂ of ₀ and task v ₂ , a change occurs in the calculation environment, and the superimposed path scores s ₀ and s ₂ are calculated as follows.
s ₀ = | L _p ^0,0 ∪L _p ^0,1 ∪L _p ^0,2 ∪L _p ^0,3 |
= | {V ₀ } ∪ {v ₀ , v ₁ } ∪ {v ₀ , v ₂ } ∪ {v ₀ , v ₁ , v ₂ , v ₃ } |
= | {V ₀ , v ₁ , v ₂ , v ₃ } | = 4
s ₂ = | L _p ^2,0 ∪L _p ^2,1 ∪L _p ^2,2 ∪L _p ^2,3 |
= | Φ∪φ∪ {v ₂ } ∪ {v ₂ , v ₃ } |
= | {V ₂ , v ₃ } | = 2

As can be seen from the results of calculation as described above, even when a plurality of partial critical path exists, subsequent tasks v _1, v ₂ for the tasks v ₀ is diagram that is connected from the same task as shown in FIG. 10 Since it is not different from the case of 6, the superimposition pass score s ₀ has no change in the net value. On the other hand, as for task v ₂ , compared with FIG. 6, in the case of FIG. 10, one task v ₃ is added as a subsequent task on the partial critical path, so that the value of the superimposed path score s ₂ increases by one. Yes. Thus, even when there are a plurality of partial critical paths from the subsequent task, the superimposed path score S can be calculated without contradiction.

As described above in detail, the task graph analysis apparatus 10 according to the present embodiment includes n tasks v _{1 to} v _n and a start task v ₀ and an end task v _{n + 1} provisionally set at the beginning and end thereof. the critical path from task v _i belonging to task system to the task v _j is calculated, to calculate the total number of tasks included on each critical path that starts from the task v _i as a superposition path scores S tasks v _i ing.

  According to the task graph analysis apparatus 10 of the present embodiment configured as described above, in addition to tasks existing on the entire critical path of the entire system, superimposing paths are also applied to tasks on partial critical paths that are not on the entire critical path. A score S can be obtained. Moreover, since the superimposed path score S is calculated not simply by a complicated calculation such as probabilistic statistics but simply by counting the number of tasks, the superimposed path score S can be obtained without executing the entire task system many times. Can do. Thus, each task can be evaluated not only for the entire critical path but also for the semi-critical path without executing the entire task system many times.

  Further, in the present embodiment, by representing the calculated superimposed path score S in a task graph processed into a superimposed path score map, the range and degree of task influence can be easily recognized visually.

In the above embodiment, in order to calculate the superimposed path score S over the entire set L _all , it is necessary to obtain all tasks that can be taken as the set L _p ^{i, j} , and the critical path calculation unit 3 is all The partial critical path corresponding to i (i = 0, 1,..., N + 1) must be elucidated. On the other hand, the calculation of the superimposed path score S may be algorithmized as follows.

First, consider the tasks v ₀ , v _i , v _x , v _y , v _z , and v _{n + 1,} and assume that the following relations hold in the partial critical paths of these tasks.
L _cp ⁱ ⊂L _cp ^x , L _cp ⁱ ⊂L _cp ^{y
_{L cp z ¬⊂L cp i, L}} cp z ¬⊂L cp x, L cp z ¬⊂L cp y
^{_{L cp i ¬⊂L cp z, L}} cp x ¬⊂L cp z, L cp y ¬⊂L cp z
An example of task placement at this time is shown in FIG.

When the above relationship holds, a set of tasks L _p ^{i, 0} , L _p ^{i, i} , L _p ^{i, x} , L _p ^{i, y} , L _p ^{i, z} , on the partial critical path starting from task v _i L _p ^{i, n + 1} can be described as follows.
L _p ^{i, 0} = φ
^{_{L p i, i = (L}} cp i xorL cp i) ∪ {v i} = {v i}
^{_{L p i, x = (L}} cp i xorL cp x) ∪ {v i} = {v i, ··, v x}
^{_{L p i, y = (L}} cp i xorL cp y) ∪ {v i} = {v i, ··, v y}
L _p ^{i, z} = φ
^{_{L p i, n + 1 =}} (L cp i xorL cp n + 1) ∪ {v i} = {v i, ··, v x, ··, v n + 1}

Further, when considering the set sum of these sets L _p ^{i, 0} , L _p ^{i, i} , L _p ^{i, x} , L _p ^{i, y} , L _p ^{i, z} , L _p ^{i, n + 1} , Can be calculated.
^{_{L p i, 0 ∪L p i}} , i ∪L p i, x ∪L p i, y ∪L p i, z ∪L p i, n + 1
= Φ∪ {v _i } ∪ {v _i ,..., V _x } ∪ {v _i ,..., V _y } ∪φ∪ {v _i , ..., v _x , ..., v _{n + 1} }
_{= {V i, ··, v} x, ··, v y, ··, v n + 1}
In other words, the formula for calculating the superposed path scores s _i task v _i can be modified as follows: (Equation 2).

Furthermore, assuming that there moiety one critical path is only from the task v _i, for any 0 ≦ j ≦ n + 1, and all x such that 0 ≦ x ≦ n + 1,0 ≦ y ≦ n + 1, x ≠ y When y is considered, (Formula 2) can be modified in consideration of the condition of {v _x | v _x εL _cp ^x } ∩ {v _y | v _y εL _cp ^y } = φ. Since this condition means that finite additivity holds, (Equation 2) can be transformed into the following (Equation 3).

Is used to thus obtained (Equation _{3) {v j | v j} ∈L cp j, L cp j ⊃L cp i} is that the task _{v j} exists originally set L _p ^i, in ^j It is obtained. That there are tasks v _j in the set L _p ^{i, j} is a set L _p ^i, it means that there is also a task v _i in the ^j, also means a v _i ∈L _cp ^j. If it is simply the total number of tasks v _{j in} the range 0 ≦ j ≦ n + 1, the same is true even if the radix of task v _i is counted. Therefore, (Equation 3) can be further transformed into (Equation 4). Here, the characteristic function χ is defined as in (Equation 5).

However, the deformation of the (Equation 4) is a modification to be made from the started task v ₀ on the assumption that parts critical path to task v _i is present only one. If there are a plurality of partial critical paths, the last transformation to (Equation 4) is denied. For this reason, the calculated superimposed path score s _i can be used as an evaluation value for comparison with the peripheral task, but the superimposed path score s _i of any task v _{i is} the number of nets on the subsequent partial critical path. The feature of the same number is lost. Therefore, when the critical path calculation unit 3 detects a plurality of partial critical paths, the fact may be displayed on the display device 30 as a warning.

Based on the above-described modification to (Equation 4), the superimposed path score S corresponding to the entire set L _all can be obtained by the following algorithm.
(1) First, all elements s _i of the superimposed path score S satisfying 0 ≦ i ≦ n + 1 are initialized to zero. Also, the set L _cp for storing the partial critical path is initialized to φ.
(2) Next, i = 0 is set, and 1 is substituted into the superimposed path score s ₀ corresponding to the start task v ₀ .

(3) i is incremented by 1, a partial critical path is searched retroactively from task v _i, and the task set L _cp ⁱ on the obtained path is stored in L _cp . However, if L _cp ^k corresponding to the task v _k exists in the set L _cp during the search for the partial critical path, no further search is performed, and the task that is an element of L _cp ^k is also L with the searched task. Add as element of _cp ⁱ .
(4) Increment path score S is incremented by 1 for all elements s _i corresponding to task set L _cp ⁱ .
(5) The above steps (3) to (4) are repeated, and when i = n + 1 is reached, the value of the superimposed path score S at that time is set as the superimposed path score corresponding to the entire set L _all .

  In this way, by superimposing the calculation of the superimposed path score S into a form suitable for the critical path search of the superimposed path score map, the superimposed path score S can be easily obtained.

  In addition, each of the above-described embodiments is merely an example of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed in a limited manner. In other words, the present invention can be implemented in various forms without departing from the spirit or main features thereof.

1 Task information input part 2 Task temporary setting part 3 Critical path calculation part 4 Evaluation value calculation part 5 Map display part

Claims (4)

A task graph analysis device that analyzes a task graph composed of _n tasks (n is an integer of 1 or more) {v ₁ , v ₂ ,.
Task identification information including task identification information for identifying the n tasks, order information indicating the processing order of the n tasks on the schedule, and load information indicating the load size of the n tasks. A task information input section to be input;
The 0th task information is temporarily set as the start task v _{0 at} the beginning of the n tasks to which the task information is input by the task information input unit, and the end task v _{n + 1} is set at the end of the _n tasks. a temporary task setting unit for temporarily setting the (n + 1) th task information;
Based on the task information of the n tasks input by the task information input unit and the task information of the start task and the end task temporarily set by the task temporary setting unit, the task v _i (i = 0, 1,..., N, n + 1) to task v _j (j = 0, 1,..., N, n + 1) are calculated, and each critical path is included in the path. A critical path calculation unit for obtaining a task;
The task _{v i (i = 0,1, ··} , n, n + 1) for each, to calculate the total number of tasks included on each critical path that starts from the task _{v i} as the evaluation value of the task _{v i} A task graph analysis device comprising an evaluation value calculation unit. Based on the task identification information and the order information included in the task information, further comprising a map display unit that displays the preceding and succeeding relationship of each task as a task graph on a display device,
The map display section, in accordance with the magnitude of the evaluation value calculated by the evaluation value calculation unit, that it has to vary the display mode of the line representing the prior Follows output from the task v _i The task graph analysis apparatus according to claim 1, wherein A computer readable program for analyzing a task graph comprising _n (n is an integer of 1 or more) tasks {v ₁ , v ₂ ,..., V _n } constituting a schedule,
Task identification information including task identification information for identifying the n tasks, order information indicating the processing order of the n tasks on the schedule, and load information indicating the load size of the n tasks. Task information input means to input,
Together temporarily sets the 0 th task information as a starting task v ₀ at the beginning of the task information the n-number of input task by the task information input means, as the end task v _{n + 1} to the end of the n-number of tasks temporary task setting means for temporarily setting the (n + 1) th task information;
Based on the task information of the n tasks input by the task information input unit and the task information of the start task and the end task temporarily set by the task temporary setting unit, the task v _i (i = 0, 1,..., N, n + 1) to task v _j (j = 0, 1,..., N, n + 1) are calculated, and each critical path is included in the path. For each of the critical path calculation means for obtaining a task and the tasks v _i (i = 0, 1,..., N, n + 1), the total number of tasks included in each critical path starting from the task v _i is described above. evaluation value calculating means for calculating an evaluation value of the task v _i,
A computer-readable task graph analysis program for making a computer function as a computer. Based on the task identification information and the order information included in the task information, map display means for displaying a predecessor / success relationship of each task as a task graph on a display device, the evaluation calculated by the evaluation value calculation unit 4. The computer according to claim 3, wherein the computer further functions as map display means for displaying the lines representing the preceding and succeeding relationships output from the task v _i in different manners according to the magnitude of the value. Computer-readable task graph analysis program.

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