AT16849U1 - Method and system for the production of a product by means of an optimal process chain through a given amount of resources - Google Patents

Abstract

Method (100) for generating a product (101) by means of an optimal process chain (102) using a predetermined amount of resources, the following steps being carried out: a) First determination (110) of a first process chain (111) based on a product description (103 ), which describes the product (101) and its generation, b) second determination (120) of at least one available input material (121-124) from the specified amount of input material with the aid of the first process chain (111), c) third determination (130 ) an execution time (131) of the resource (121-124) with the aid of the first process chain (111), d) estimation (140) of an occupancy (141) of the resource (121-124) taking into account the execution time (131), e) Check (150) whether the occupancy is within a predefined value range and, if applicable (151), continue with step f), if not applicable (152), mark the resource (121-124) as "not available" for the duration he the execution time and proceeding with step b), f) assigning (160) the first process chain (111) to the resource (121-124) taking into account the highest occupancy as the optimal process chain (102), g) executing (170) the optimal one Process chain (102) and production of the product (101).

Description

description

PROCESS AND SYSTEM FOR GENERATING A PRODUCT USING AN OPTIMAL PROCESS CHAIN THROUGH A SPECIFIED QUANTITY OF INPUT RESOURCES

The invention relates to a method and a system for producing a product by means of an optimal process chain through a predetermined amount of resources.

Advances in manufacturing technologies today are moving toward automation and flexibility in intelligent manufacturing ecosystems. The needs of customers increasingly require these ecosystems to be able to handle product variability quickly, reliably and cost-effectively while guaranteeing a high degree of flexibility.

A critical bottleneck in coping with product variability in a factory is the design of manufacturing processes for products that do not always optimally utilize the production facilities in factories due to very different production chains.

Sequential tasks for the execution of processes, ie the creation of process chains, are often "NP-hard / NP-difficult" problems. The NP severity describes a property of an algorithmic problem.

Complexity theory, a branch of theoretical computer science, deals with the classification of problems with regard to their complexity. An important problem class is the complexity class NP, the class of all decision problems for which a found L6 solution can be efficiently checked. NP stands for nondeterministic polynomial time. An NP-hard problem is at least as "difficult" as all problems in NP. This means that an algorithm that solves an NP-hard problem can be used by means of a reduction to solve all problems in NP.

Problems with NPs that are difficult to solve can be very time-consuming and costly due to very complex combinatorial optimization tasks.

Most known methods for process planning do not take into account error models, alternative execution paths for individual processes, uncertainties in the execution time and the interaction of different process chains. A large number of identical process chains are also required for planning.

It is the object of the invention to overcome the disadvantages mentioned in the prior art and to provide a method and a system which improve the production of new products, in particular by determining an optimal process chain for a production plant.

The object is achieved by a method of the type mentioned at the beginning, the following steps being carried out:

a) First determination of a first process chain based on an order that describes the product and its creation,

b) Second determination of at least one available resource from the specified amount of resource with the help of the first process chain,

c) Thirdly determining an execution time of the at least one resource with the help of the first process chain,

d) Estimating the occupancy of the at least one resource taking into account the execution time,

e) Check whether the assignment is within a predefined value range and, if applicable, continue with an assignment in step f),

if not applicable, marking the at least one resource as "not available" for the duration of the execution time and continuing with the second determination in step b),

f) Assigning the first process chain to the at least one resource taking into account the highest occupancy as the optimal process chain,

g) Execution of the optimal process chain and creation of the product.

The invention enables an optimal selection of resources from a predetermined amount of resources, for example automatic production machines in a factory, for generating the product with regard to the optimal utilization of available resources.

Furthermore, the invention allows fewer restrictions on the type of process chain and the type of input probability density functions than in previously known solutions, and allows a higher level of detail in the results.

This higher level of detail allows more precise metrics and better information about future executions of process chains or about the use of resources.

Under resources are, for example, automatic processing machines such as CNC machines, robots for the automatic assembly of individual components, but also manual processing steps by humans, as well as operating and input resources such as starting materials, lubricants, electricity or gas for performing individual work steps.

A process chain is understood to mean, for example, a sequential sequence of processing steps, with individual steps also being able to take place in parallel.

The duration of the execution time is the time span between a start time and an end time of a job.

A process chain can be described, for example, by BPMN ("Business Process Management Notation"), in which:

° A probability density function for the duration of each job, and

° The probability for each output node of an XOR passage in process mode is determined.

A process model can be described as a directed and connected graph (N, E):

N = AUGU {Nssart, NEnde} with EZNxN where N is a finite set of nodes, A is a set of orders / activities (English "activities"), G a set of passages (or also gates; English "gateways"), Nstar Job start (event), NeEnd is a job end (event), and E is a set of edges connecting the nodes.

1 shows a start node, FIG. 2 an end node, FIG. 3 an order a, FIG. 4 an AND passage (AND gate), FIG. 5 an XOR passage (XOR- Gate) and FIG. 6 shows a loop according to a simplified BPMN.

A capability of a resource is SpaiR * VreEeR, vaeA where R is a set of resources (English "resources‘ "), and Sea is a multiplication factor of a resource" for the duration of an order a.

For example, s .., <1 means that a resource r can probably carry out an order a faster than the average.

For example, s ..,> 1 means that a resource r can probably carry out an order a more slowly than the average.

For example, s ...> 10, that is to say greater than a predetermined limit value, can mean that a resource r cannot be used for an order a.

A resource-order assignment WA »[0,1] vr ER

[0024] is a proportion of the time that a resource is used to execute an order a. Examples are given in Table 1.

Resources—> Order! . rn | description

The order a: is only assigned to the resource 5 and will fully utilize r

ar 1 0 The order az is only assigned to resource 5 »and 7 will be half full

a2 0 0.5 The order az is assigned to resources 5 and r »and will use half and« »full capacity

a3 0.5 | 1

Table 1: Examples of resource-order assignment

In a further development of the invention it is provided that in the third determination step a probability density function is determined for the execution time of the assigned at least one resource.

This ensures that the probability is taken into account with which an order a is carried out by means of resources with the assignment w and the duration £

required, and the optimal process chain can therefore be determined more precisely. A probability density function for a duration of an order a € A Da (OR *> [0,1] VaER

Represents the probability that the order a takes a duration t on average.

The order durations D, (t) are estimated or determined by means of methods that are based on the principle of machine learning and assigned to the process model.

An order duration with respect to an assignment can be described by a probability density function for an order a € A and an assignment w € W, which denotes the probability that an order a is carried out using resources with the assignment w and requires the duration for this .

Dy.a (OR *> [0.1] vw EW, Va € A

t Dial) = Da (;) w, a

Swa = ZrerSr, aWr (a); ZrerW; (a) The probability density function D, "(£) is the probability density function Dqa (t) expanded by the factor sa.

The factor s "" 4 is the weighted average of the factor for the capability of a resource s, "according to the explanations above.

For example, sa = 0.5, based on an input resource r ”, and D“ (£) as a normal distribution with N (5.1), that is, an order a has an average duration of 5 with a variance of 1, and the resource r is faster than the average by a factor of 0.5 when executing order a. The probability density function D, “(£) for a duration of the order a then results in N (2.5,0.25).

As is known, for normal distributions, the product of a scalar and a random variable k * X results in a new random variable with a mean value of k * mean value (X) and a variance of k? * Variance (X).

In a further development of the invention it is provided that an edge transition probability function is determined in the step of estimating.

What is achieved thereby is that the optimal process chain can be determined in a simple manner.

The edge transition probability function used in the following takes the following properties into account:

* Edge transition probability times are used, not just job durations,

* process loops can be integrated, and * capabilities of resources are used.

An edge transition probability function describes the probability with which an edge (English "edge") e € E is traversed at a point in time £ € R *:

fR *> [0.1] VeEE

As is known, the edge transition probability function of a first edge of a process which leaves the order start nsaz is an input value which designates the start time of the respective process instance.

As is known, f £ (t £) is not necessarily a probability density function, but if the process does not have any XOR passes, the condition Ve € E: | is met f £ (t) dt = 1 always closed and all f £ (t) are probability density functions.

In a further development of the invention it is provided that in the step of estimating an edge passage probability function is determined.

This means that the optimal process chain can be determined in a particularly simple manner.

An edge passing probability function fo. : (t) for an order a € A with an incoming edge / n, an outgoing edge out and a probability density function for the duration D "" "(t) is given by:

Fout (t) = fin® * Diva (©)

7 symbolically shows a probability density function for the duration of an order a.

As is known, the convolution operator * for two functions f and g is defined as:

(F + 9) ® = | FeDgC- Ede

For example, the convolution of two Gaussian-distributed probability density functions yields:

N (107) * N (u203) = N (M1 + H2,0? + 03) [0047] An edge transition probability function for AND passes is for passages

ggang g € Gayp with incoming edges {in ,, ..., in "} = EN (N x g) and outgoing edges {out; ,, ..., out} = EN (g x N) defined as:

n t d fout® = | | ] [fm a ') A [0048] FIG. 8 symbolically shows an edge transition probability function for an AND passage. An edge transition probability function for XOR passes is for passes g € Gxor with incoming edges {in ,, ..., in "} = EN (N xg) and outgoing edges {out ,, ..., out} = EN (gx N) defined as: Fout; (€) - Pour; Din: (1sjs = m) i = 1 FIG. 9 symbolically shows an edge transition probability function for an XOR passage. With a given process model P and a set of XOR passes g € Gxor from P, where each edge e € E, which starts from a pass, can have an edge probability p. € [0.1] must be specified. All edge probabilities must be greater than zero and meet the condition: Pe = 1 (VgE Gxor) eEN (gxN) An edge transition probability function for loops is with an edge probability p for exiting a loop, where a loop body fpoay is computed by treating the contents of the loop as a separate process, defined as:

An edge transition probability function for XOR passes is for passes g € Gxor with incoming edges {in ,, ..., in "} = EN (N xg) and outgoing edges {out ,, ..., out} = EN (gx N) defined as:

Fout; (€) - Pour; Din: (1sjs = m) i = 1

FIG. 9 symbolically shows an edge transition probability function for an XOR pass.

With a given process model P and a set of XOR passes g € Gxor from P, where each edge e € E, which starts from a pass, can have an edge probability p. € [0.1] must be specified. All edge probabilities must be greater than zero and meet the condition:

Pe = 1 (VgE Gxor) eEN (gxN)

An edge transition probability function for loops is defined as having an edge probability p for exiting a loop, where a loop body fpoay is calculated by treating the contents of the loop as a separate process:

fout (€) = fin (t) * & pA-— p) '* (fooay®) X ... froay (O)) i = 1

Fig. 10 symbolically shows an edge transition probability function for a loop.

In a development of the invention it is provided that in the step of estimating the occupancy is determined from an execution time probability function.

What is achieved thereby is that the optimal process chain takes into account an allocation of resources and this can be determined in a particularly simple manner.

[0056] Over-allocation of an input resource can undesirably delay the manufacture of a product. The timely identification of an over-occupancy can thus reduce the risk during production.

It is advantageous if values in the form of probabilities and stochastic variables are estimated with a predetermined probability-density function for various parameters of a process chain, instead of using scalars.

The risk, in particular in the case of resource allocation, can be described by how many resources are likely to be overutilized when a process chain is carried out taking into account uncertainties.

The execution time probability function F, denotes the probability that an order a € A is executed at a point in time t € R *, with each order a having exactly one incoming edge:

FAR *> [0.1] UaeA

The order is executed at time £, that is, the order is started before time £ and ended after time}:

t t = | fin (E Dat ’- | fin (E ') * Dr.a (Yes

The assignment is always used in connection with a resource. An occupancy with occupancy values o € R *, o> 1 is referred to as over-occupancy.

As is known, compared to f2 or F ,, the occupancy is never a probability density function (e € E, a € A).

The total occupancy probability density function 0 over the time of a resource r € R at a time t € R * is defined with {a ,, ..., an} as:

0 ,: (R * X R *)> R * O, - (t, o) = ö (0o, 0) + (5C0. Wa) Faz (+ 500.0) (1 - Fa, (8)

+0 (800, Wa,) Far (D + 600.0) (1 - Fa, (D))

Where *, is the convolution over the parameter 0.

As is known, when t is fixed, 0- (t, o) is always a probability density function over 0.

As is known, the Dirac delta function δ (x, xo) can be used as a probability density function for the occupancy, which expresses a complete certainty of the unavailability. The Dirac delta function is defined by

0 x = X © X = X

Ö (x, xo) = | 1 = [_5004x

11 shows an example of the total occupancy probability density function 0 as a function of a parameter 0 and the time. An execution probability 1 and a probability density function 2 for resource occupancy can be seen. The edge probability p can be read on the z-axis.

In a further development of the invention, it is provided that in the checking step, an occupancy of the at least one resource is determined from a process execution probability.

It is thereby achieved that the optimal process chain takes into account over-allocation of resources and this can be determined in a particularly simple manner.

A resource over-allocation m, (r € R) is the extent of allocations> 1:

m, R m. = | | 0. (, 0) dt do 10

A process over-allocation m is the sum of all resource over-allocations:

m: R m => m,

A process execution function Fe at a point in time t € R * is: Fp: R *> R *

t t BC) | fear (Ede - f femaltDdt 0 0

In a further development of the invention it is provided that a resource usage discrepancy is determined from the process execution probability.

This means that the optimal process chain takes into account a deviation from the optimal use of resources and this can be determined in a particularly simple manner.

Input resource usage deviations u, with (r € R) are the accumulated distances from the optimal resource usage:

ur: R u, = | FC | 11- 0 - (, 0) 1do dt 0 0

In a further development of the invention, it is provided that a process usage discrepancy is determined from the resource usage discrepancy.

What is achieved thereby is that the optimal process chain takes a process usage deviation into account and this can be determined in a particularly simple manner.

A process usage deviation u is the sum of all resource usage deviations:

71717

u: R

us Yu

reR

In a further development of the invention it is provided that the optimal process chain comprises at least one process that can be carried out on an automatic device.

This means that parameters which describe the optimal process chain are recorded particularly precisely, for example by machine learning, and the optimal process chain can thus be determined particularly precisely.

The object according to the invention is also achieved by a system of the type mentioned at the beginning, further comprising a computing device which is set up to carry out the method according to the invention.

The invention is explained in more detail below with reference to an exemplary embodiment shown in the accompanying drawings. In the drawings shows:

1 shows a start node in a simplified BPMN, FIG. 2 shows an end node in a simplified BPMN, FIG. 3 shows an order in a simplified BPMN,

Fig. 4 shows an AND pass in a simplified BPMN, Fig. 5 shows an XOR pass in a simplified BPMN, Fig. 6 shows a loop in a simplified BPMN,

7 symbolically shows a probability density function for the duration of an order,

8 symbolically shows an edge transition probability function for an AND passage,

9 symbolically shows an edge transition probability function for an XOR passage,

10 symbolically shows an edge transition probability function for a loop,

11 shows an example of the total occupancy probability density function,

12 shows a schematic representation of an exemplary embodiment for the method according to the invention,

13 shows a schematic representation of an exemplary embodiment for the system according to the invention,

14 shows a schematic representation of the assignment of sub-processes of a process chain and resources for manufacturing a product.

FIG. 12 schematically shows an exemplary embodiment of the method 100 according to the invention for producing a product 101 by means of an optimal process chain 102 using a predetermined amount of input resources. The following steps are carried out:

a) First determination 110 of a first process chain 111 based on a product description 103, which describes the product 101 and its creation,

b) Second determination 120 of at least one available resource 121 from the predetermined amount of resource with the aid of the first process chain 111,

c) Third determination 130 of an execution time 131 of the at least one resource 121 with the aid of the first process chain 111,

d) estimating 140 an occupancy 141 of the at least one resource 121 taking into account the execution time 131,

e) Check 150 whether the assignment is within a predefined value range and, if applicable 151, continue with an assignment 160 in step f),

if not applicable 152, marking the at least one resource 121 as “not available” for the duration of the execution time and continuing with the second determination 120 in step b),

f) Assigning 160 the first process chain 111 to the at least one resource 121, taking into account the highest occupancy as the optimal process chain 102,

g) Executing 170 the optimal process chain 102 and generating the product 101.

In the step of the third determination 130, a density function for the execution time 131 of the assigned at least one resource 121 is optionally determined.

In the step of estimating 140, an edge transition probability function is optionally determined.

[00101] In the step of estimating 140, an edge-passage probability function is optionally determined.

In step of estimating 140, occupancy 141 is optionally determined from an execution time probability function.

In the step of checking 150, an occupancy of the at least one resource 121 is optionally determined from a process execution probability.

[00104] A resource usage discrepancy is optionally determined from the process execution probability.

A process usage discrepancy is optionally determined from the resource usage discrepancy.

It is clear that in the optional determination of the aforementioned parameters, a further parameter is required for its determination and must therefore also be determined.

The mentioned optional steps can be combined with one another.

In general, loops, for example, can form an infinite sum. Numerical integration methods can be used for process chains that have loops.

The method can be implemented, for example, by the Monte Carlo method, which simulates a random process execution repeatedly and generates probability density functions from it, but leads to a correspondingly high effort with a desired accuracy.

13 shows schematically an exemplary embodiment for the system according to the invention for generating a product 101 based on product description 103 by means of the optimal process chain 102 through a predetermined amount of resources and a computing device which is set up to carry out the method 100.

14 shows a schematic BPMN representation of the assignment of sub-processes 112, 210, 211, 220-222, 230, a process chain 111 and resources 121-124 for producing the product 101 by means of an assignment matrix 50.

The BPMN graph shows activities or orders 210, 211, 220-222, 230, AND gates, an XOR gate and a loop.

[00113] Associations of a resource 122 in the form of a welding robot 122 with an order 211 or in the form of manual work 123 by people with a are exemplary

Order 220 shown and marked with dashed lines.

It can also be seen whether a particular resource is available (check mark) or not (cross), the allocation being stored in a memory.

Utilization means 121 can be, for example, welding robots 122, manual work 123 by humans or a CNC milling machine 124.

REFERENCE CHARACTERISTICS LIST:

1 Probability of execution 2 Probability density function for a resource allocation 10 Calculation system 20 Production system 50 Allocation matrix (process vs. resource) 100 Process 101 Product 102, 111 Process chain 112, 210, 211, 220-222, 230 (partial) Process 103 Product description 110, 120, 130 Determine 121 Resources 122 Welding robot 123 Manual work by humans 124 CNC milling machine 131 Probability density function for the execution time 140 Estimate 141 Allocation 150 Check 151 Applicable 152 Not applicable 160 Assign 170 Execute aı, a2 Order Da (t) probability density function for the duration of an order a fin, ©, finm ©) Edge transition probability function for incoming edges Fout, ©), Foutm Ct) Edge transition probability function for outgoing edges fooay (® ) Loop body 0 parameter pP edge probability t time

Claims (9)

Expectations 1. A method (100) for producing a product (101) by means of an optimal process chain (102) using a predetermined amount of resources, the following steps being carried out: a) First determination (110) of a first process chain (111) based on a product description (103), which describes the product (101) and its generation, b) Second determination (120) of at least one available resource (121-124) from the specified amount of resource with the aid of the first process chain (111), c) third determination (130) of an execution time (131) of the at least one resource (121-124) with the aid of the first process chain (111), d) estimating (140) an occupancy (141) of the at least one resource (121-124) taking into account the execution time (131), e) Checking (150) whether the occupancy is within a predefined range of values and, if applicable (151), continuing with step f), if not applicable (152), marking the at least one resource (121-124) as “Not available "For the duration of the execution time and continue with step b), f) assigning (160) the first process chain (111) to the at least one resource (121-124) taking into account the highest occupancy as the optimal process chain (102), g) executing (170) the optimal process chain (102) and generating the product (101). 2. The method (100) according to the preceding claim, wherein in the step of the third determination (130) a probability density function for the execution time (131) of the assigned at least one resource (121-124) is determined. 3. The method (100) according to the preceding claim, wherein in the step of estimating (140) an edge-transition probability function is determined. 4. The method (100) according to any one of the preceding claims, wherein in the step of estimating an edge-passage probability function is determined. 5. The method (100) according to any one of the preceding claims, wherein in the step of estimating (140) the occupancy (141) is determined from an execution time probability function. 6. The method (100) according to any one of the preceding claims, wherein in the step of checking (150) an occupancy of the at least one resource (121-124) is determined from a process execution probability. 7. The method (100) according to the preceding claim, wherein a resource usage deviation is determined from the process execution probability. 8. The method (100) according to the preceding claim, wherein a process usage discrepancy is determined from the resource usage discrepancy. 9. System for generating a product (101) by means of an optimal process chain (102) by a predetermined amount of resources and a computing device which is set up to carry out the method (100) according to one of the preceding claims. In addition 5 sheets of drawings