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### Ecec09presentation

1. 1. inspection optimization for MSPS Soﬁe Van Volsem Joint optimization of all inspection Introduction parameters for multi-stage processes: MSPS Inspection algorithm, simulation and test set Cost Process model Method Finding solutions Part 1: TIC Soﬁe Van Volsem Part 2: EA Conclusion Department of Industrial Management Ghent University Bruges, April 15, 2009
2. 2. Overview inspection optimization for MSPS Introduction 1 Soﬁe Van Volsem Multistage production systems Inspection strategy Introduction MSPS Cost-efﬁcient inspection Inspection Cost Process model Process model Method Finding solutions Method 2 Part 1: TIC Part 2: EA Finding solutions Conclusion First problem: calculating inspection costs Second problem: an intelligent solution space search Conclusion 3
3. 3. Sequential linear multistage production system (MSPS) inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
4. 4. Sequential linear multistage production system (MSPS) inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost example: Production of chocolate cookies Process model production stage 1: preparation of dough Method Finding solutions production stage 2: baking of cookies Part 1: TIC Part 2: EA production stage 3: ﬁnishing with chocolate Conclusion
5. 5. Inspection strategies for MSPS inspection optimization for MSPS Soﬁe Van Volsem An inspection strategy for MSPS is Introduction MSPS a set of decisions Inspection Cost WHERE to inspect: 1 Process model after which of the production stages? Method HOW STRINGENT to inspect: Finding solutions 2 Part 1: TIC what are the acceptance limits? Part 2: EA HOW MUCH to inspect: 3 Conclusion all products or only a sample?
6. 6. Inspection strategies for MSPS inspection optimization for MSPS Soﬁe Van Volsem An inspection strategy for MSPS is Introduction MSPS a set of decisions Inspection Cost WHERE to inspect: 1 Process model after which of the production stages? Method HOW STRINGENT to inspect: Finding solutions 2 Part 1: TIC what are the acceptance limits? Part 2: EA HOW MUCH to inspect: 3 Conclusion all products or only a sample?
7. 7. Inspection strategies for MSPS inspection optimization for MSPS Soﬁe Van Volsem An inspection strategy for MSPS is Introduction MSPS a set of decisions Inspection Cost WHERE to inspect: 1 Process model after which of the production stages? Method HOW STRINGENT to inspect: Finding solutions 2 Part 1: TIC what are the acceptance limits? Part 2: EA HOW MUCH to inspect: 3 Conclusion all products or only a sample?
8. 8. Inspection strategies for MSPS inspection optimization for MSPS Soﬁe Van Volsem An inspection strategy for MSPS is Introduction MSPS a set of decisions Inspection Cost WHERE to inspect: 1 Process model after which of the production stages? Method HOW STRINGENT to inspect: Finding solutions 2 Part 1: TIC what are the acceptance limits? Part 2: EA HOW MUCH to inspect: 3 Conclusion all products or only a sample?
9. 9. Inspection costs inspection optimization for MSPS Soﬁe Van Costs associated with a selected inspection strategy: Volsem execute inspection 1 Introduction (test cost, TC) MSPS Inspection repair or replace faulty products internally 2 Cost (rework cost, RC) Process model Method repair or replace faulty products externally 3 Finding solutions (penalty cost, PC) Part 1: TIC Part 2: EA Total costs also includes (loss of) production time, Conclusion capacity, product image, ... Simpliﬁed: more and tighter inspection will lead to higher quality, but will also induce higher costs.
10. 10. Inspection costs inspection optimization for MSPS Soﬁe Van Costs associated with a selected inspection strategy: Volsem execute inspection 1 Introduction (test cost, TC) MSPS Inspection repair or replace faulty products internally 2 Cost (rework cost, RC) Process model Method repair or replace faulty products externally 3 Finding solutions (penalty cost, PC) Part 1: TIC Part 2: EA Total costs also includes (loss of) production time, Conclusion capacity, product image, ... Simpliﬁed: more and tighter inspection will lead to higher quality, but will also induce higher costs.
11. 11. Inspection costs inspection optimization for MSPS Soﬁe Van Costs associated with a selected inspection strategy: Volsem execute inspection 1 Introduction (test cost, TC) MSPS Inspection repair or replace faulty products internally 2 Cost (rework cost, RC) Process model Method repair or replace faulty products externally 3 Finding solutions (penalty cost, PC) Part 1: TIC Part 2: EA Total costs also includes (loss of) production time, Conclusion capacity, product image, ... Simpliﬁed: more and tighter inspection will lead to higher quality, but will also induce higher costs.
12. 12. Inspection costs inspection optimization for MSPS Soﬁe Van Costs associated with a selected inspection strategy: Volsem execute inspection 1 Introduction (test cost, TC) MSPS Inspection repair or replace faulty products internally 2 Cost (rework cost, RC) Process model Method repair or replace faulty products externally 3 Finding solutions (penalty cost, PC) Part 1: TIC Part 2: EA Total costs also includes (loss of) production time, Conclusion capacity, product image, ... Simpliﬁed: more and tighter inspection will lead to higher quality, but will also induce higher costs.
13. 13. Inspection optimization for MSPS: process model inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model For each production stage: Method Finding solutions Cost parameters Part 1: TIC Part 2: EA (test cost TC, rework cost RC, Conclusion penalty cost, PC (only after ﬁnal production stage)) Process parameters (process characteristics: mean and variance) Inspection parameters (where, how much and how stringent to inspect?)
14. 14. Optimization: what are the decision variables? inspection optimization for MSPS Soﬁe Van Volsem Cost and process parameters are given. Introduction Only the inspection parameters are decision variables. MSPS Inspection In multistage systems three types of inspection Cost parameters can be distinguished, namely Process model Method inspection type 1 Finding solutions Part 1: TIC 100% inspection (F) Part 2: EA sampling inspection (S) Conclusion no inspection (N) inspection (acceptance) limits 2 sampling parameters 3
15. 15. Optimization: what are the decision variables? inspection optimization for MSPS Soﬁe Van Volsem Cost and process parameters are given. Introduction Only the inspection parameters are decision variables. MSPS Inspection In multistage systems three types of inspection Cost parameters can be distinguished, namely Process model Method inspection type 1 Finding solutions Part 1: TIC 100% inspection (F) Part 2: EA sampling inspection (S) Conclusion no inspection (N) inspection (acceptance) limits 2 sampling parameters 3
16. 16. Decision variables: illustration inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
17. 17. Finding solutions inspection optimization for MSPS Soﬁe Van Volsem Solution = cost-efﬁcient inspection strategy for MSPS Introduction Best solution => lowest total inspection cost (TIC) MSPS Inspection Cost For every possible solution we need to be able to 1 Process model Method calculate TIC Finding solutions Part 1: TIC Number of possible solutions is inﬁnite 2 Part 2: EA => naive heuristic = calculate every possibility to ﬁnd Conclusion the best = impossible => development of an intelligent search method = metaheuristic
18. 18. Finding solutions inspection optimization for MSPS Soﬁe Van Volsem Solution = cost-efﬁcient inspection strategy for MSPS Introduction Best solution => lowest total inspection cost (TIC) MSPS Inspection Cost For every possible solution we need to be able to 1 Process model Method calculate TIC Finding solutions Part 1: TIC Number of possible solutions is inﬁnite 2 Part 2: EA => naive heuristic = calculate every possibility to ﬁnd Conclusion the best = impossible => development of an intelligent search method = metaheuristic
19. 19. Finding solutions inspection optimization for MSPS Soﬁe Van Volsem Solution = cost-efﬁcient inspection strategy for MSPS Introduction Best solution => lowest total inspection cost (TIC) MSPS Inspection Cost For every possible solution we need to be able to 1 Process model Method calculate TIC Finding solutions Part 1: TIC Number of possible solutions is inﬁnite 2 Part 2: EA => naive heuristic = calculate every possibility to ﬁnd Conclusion the best = impossible => development of an intelligent search method = metaheuristic
20. 20. Calculating TIC: formula inspection optimization for MSPS Soﬁe Van TIC TTC + TRC + TPC (1) = Volsem with Introduction n MSPS Inspection TTC TCi (2) = Cost Process model i=1 Method n Finding solutions Part 1: TIC TRC RCi (3) = Part 2: EA i=1 Conclusion TPC cP .dn (4) = and with TCi cT ,i .(αF ,i .K + αS,i .si ) (5) = RCi cR,i .pi .αF ,i .K (6) =
21. 21. Calculating TIC: illustration inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
22. 22. Calculating TIC: method inspection optimization for MSPS Soﬁe Van Volsem With known defect rates pi , analytical calculation of TIC is straightforward. Introduction MSPS Alas, no closed analytical formula for pi available for Inspection Cost non-trivial cases. Process model Method Deﬁnition: Finding solutions Part 1: TIC Part 2: EA pi = P [Xi ∈ [LILi , UILi ]] = 1 − P[LILi ≤ Xi ≤ UILi ] / Conclusion => TIC is therefore calculated (approximated) through Monte Carlo simulation.
23. 23. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
24. 24. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
25. 25. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
26. 26. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
27. 27. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
28. 28. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
29. 29. Search strategy: evolutionary algorithm Applied metaheuristic search method: Evolutionary inspection optimization Algorithm (EA) for MSPS Soﬁe Van based on Darwin’s theory on biological evolution: Volsem desirable characteristics => better chance of survival Introduction MSPS => better chance of transferral to next generation. Inspection Cost characteristics quot;storedquot; in genes; genes are transferred Process model through reproduction/breeding. Method Finding solutions principles evolutionary algorithm: Part 1: TIC Part 2: EA encoding of candidate solutions; 1 Conclusion creation of an intital population evaluating and ordering candidate solutions 2 creating a new generation of candidate solutions from 3 promising (parts of) candidate solutions of the previous generation iterating steps 2 and 3 until stopping criterium; 4 decoding of quot;bestquot; solution
30. 30. Evolutionary algorithm: example inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
31. 31. Evolutionary algorithm: example inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
32. 32. Evolutionary algorithm: example inspection optimization for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
33. 33. Does the method work? inspection optimization 1◦ EA’s convergence is established for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
34. 34. Does the method work? inspection optimization 1◦ EA’s convergence is established for MSPS Soﬁe Van Volsem Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
35. 35. Does the method work? inspection optimization for MSPS Soﬁe Van Volsem 2◦ EA’s capability to ﬁnd meaningful solutions is established Introduction MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
36. 36. Does the method work? inspection optimization for MSPS Soﬁe Van Volsem 2◦ EA’s capability to ﬁnd meaningful solutions is established Introduction 10 processes (A through J) were analyzed and compared MSPS Inspection Cost Process model Method Finding solutions Part 1: TIC Part 2: EA Conclusion
37. 37. Does the method work? inspection optimization for MSPS Soﬁe Van Volsem 2◦ EA’s capability to ﬁnd meaningful solutions is established Introduction 10 processes (A through J) were analyzed and compared MSPS Inspection Cost cases A through J process mean exp. value Process model Method step 1 normal µ = 10 10 Finding solutions Part 1: TIC step 2 + normal µ = 10 20 Part 2: EA step 3 + normal µ = 10 30 Conclusion step 4 + normal µ = 10 40
38. 38. Does the method work? inspection optimization for MSPS Soﬁe Van Volsem Introduction case A B C D E MSPS Inspection all steps σ = 0.1 σ = 0.1 σ = 0.1 σ = 0.2 σ = 0.2 Cost Process model penalty 1 000 10 000 100 000 1 000 10 000 Method Finding solutions case F G H I J Part 1: TIC Part 2: EA steps 1&3 σ = 0.2 σ = 0.2 σ = 0.2 σ = 0.1 σ = 0.01 Conclusion steps 2&4 σ = 0.1 σ = 0.1 σ = 0.01 σ = 0.2 σ = 0.2 penalty 1 000 10 000 1 000 1 000 1 000
39. 39. Solutions from the case study inspection optimization case winner solution vector TIC for MSPS Soﬁe Van A N N N N 45 900 Volsem 10.060 25 40.405 B S9.940 0 N N F39.595 67 255 Introduction MSPS 10.012 40.405 C F9.988 N N F39.595 102 590 Inspection Cost 10.210 100 40.402 50 D S9.790 1 N N S39.592 1 133 450 Process model Method 10.071 31.434 40.403 E F9.929 N F28.566 F39.5957 178 940 Finding solutions Part 1: TIC 40.417 25 Part 2: EA 10.166 F F9.834 N N S39.583 0 102 935 Conclusion 10.034 25 40.406 G S9.966 0 N N F39.594 138 015 10.165 100 30.425 H S9.835 1 N F29.575 N 72 550 40.418 I N N N F39.582 73 520 40.411 J N N N F39.589 58 840
40. 40. Further research inspection optimization for MSPS Soﬁe Van Volsem Suggestions: Introduction MSPS Extensions to the current EA Inspection Cost non-sequential MSPS Process model imperfect inspection Method Finding solutions variable number of simulation runs Part 1: TIC Part 2: EA further development of standard test sets Conclusion validation through real life case studies
41. 41. inspection optimization for MSPS Soﬁe Van Volsem Joint optimization of all inspection Introduction parameters for multi-stage processes: MSPS Inspection algorithm, simulation and test set Cost Process model Method Finding solutions Part 1: TIC Soﬁe Van Volsem Part 2: EA Conclusion Department of Industrial Management Ghent University Bruges, April 15, 2009