1. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 1 A framework for financial supply chain optimization Pierre Féniès a,b, Philippe Lacomme a, Nikolay Tchernev a a LIMOS UMR CNRS 6158 b CRCGM

2. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 2 1.Problem description 2.A genetic algorithm based framework 3.Numerical experiments 4.Conclusion

3. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 3 1. Problem description

4. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 4 Problem description A supply chain is a coalition of autonomous entities coordonated by the same logistic process... An opened set crossed by flows…; A system with physical entities and autonomous organization… An activities set which could be modelled as a value chain … 1

5. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 5 Information flow Goods and Services flows Financial Flows Planning budgeting 1 Coordonate physical and financial flows in decision tools and models for supply chain mangement

6. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 6 Inclusion of cash flow in scheduling problem: -) the Resource Investment Problem (RIP) (Najafi, 2006) -) the Payment Scheduling Problem (PSP) (Ulusoy, 2000). based on cash flows in networks structure, defined by (Russell, 1970, 1986). Depending on the objective: -)Net present value (NPV) (Elmaghraby and Herroelen, 1990); -)NPV and extra restrictions as bonus-penalty structure (Russell, 1986) (Zhengwen and Xu, 2007) -)Discounted cash-flows (Najafi, 2006) (Icmeli, 1996). 1

7. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 7 Financial Flows Optimization and Supply Chain Management Decisional level Objective function Operational levelMaximization of cash position (Badell et al., 2005) (Bertel et al., 2008) ; Few links with physical flows; financial papers focus on payment term and interest rate, not on the impact of physical flow in financial flows. Tactical levelNet present value maximization under cash position constraints (Russel., 1970) (Comelli et al., 2008). Links are proposed for a single company, not for a supply chain. Strategic levelNet present value maximization is a classical approach in network design in supply chain management (Vidal et al., 2001) Few works at operational level; Supply chain is always modeled as a flow- shop or an hybrid flow shop. 1

8. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 8 Physical flows optimization at operational level financial flows optimization at operational level MakespanCash Position (Comelli et al., 2008) Cash Flows (Bertel et al., 2008) 1 reveals the cash which is available at the end of a specific period reveals the cash generation during a specific period

9. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 9 We propose to model Supply Chain as a « Job shop » and to take into account cash management constraints: - allows to extend financial constraints on physical flows - allows to take into account phenomena such as reverse logistics - allows different routing in Supply Chain 1 A machine represents a Supply Chain entity (factory, warehouse…) A job represents a manufacturing batch.

10. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 10 1

11. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 11 J1 : M1 (10), M2 (20), M3 (10) J2 : M2 (5), M1 (20), M3(10) J3 : M3 (10), M1 (10), M2 (5) 1

12. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 12 Mach.Processing time PriceTime payment delay Op1 Job 1M110122 Op2 Job 1M220243 Op3 Job 1M31040*8 Op1 Job 2M2518 Op2 Job 2M120402 Op3 Job 2M31066*12 Op1 Job 3M31023 Op2 Job 3M110155 Op3 Job 3M2520*3 1

13. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 13 R1R2 QPriceQ Op1 Job 13241 Op2 Job 11111 Op3 Job 12341 Op1 Job 24111 Op2 Job 28253 Op3 Job 22341 Op1 Job 22342 Op2 Job 23245 Op3 Job 21111 1

14. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 14 Delay R1Delay R2 Machine 121 Machine 211 Machine 351 1

15. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 15 CashP0CashMin Machine 124-40 Machine 220-40 Machine 324-40 Supply Chain 680 1

16. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 16 J1 : M1 (10), M2 (20), M3 (10) J2 : M2 (5), M1 (20), M3(10) J3 : M3 (10), M1 (10), M2 (5) 1

17. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 17 1

18. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 18 1

19. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 19 Job Shop semi active solution Cash position evaluationCash Time Job shop non semi active solution

20. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 20 Problem formulation: Min Maxespan with CashP>Cashmin Cash position evaluation Cash Time

21. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 21 A LINEAR MODEL FOR THE JOB SHOP SCHEDULING PROBLEM WITH CASH FLOW (JSPCF) -extends the classical mathematical model of the job-shop scheduling problem; - is written by extension of both classical linear formulations of the job- shop and of the AON-flow formulation of the RCPSP (Artigues et al., 2003). -Financial constraints are added: CashPosition Cash Min -A flow network model is therefore defined and takes into account financial flows constraints. 1

22. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 22 2. A genetic algorithm based framework 21

23. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 23

24. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 24

25. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 25 Non oriented disjunctive graph G defining a job-shop problem Oriented disjunctive graph representing a solution of makespan 70 21

26. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 26 Overdraft: unacceptable solution, in a financial point of view

27. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 27

28. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 28 Example of fully oriented disjunctive graph Finding a flow in a graph is not straightforward and could be time consuming… Our proposals - computing a flow - in the graph complies with the Bierwith sequence since arcs are introduced from : any node to any node Financial flows constraints

29. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 29 Heuristic resolution of the flow problem (HRFP) Financial flows constraints Such a flow could be denoted and could be computed by any max flow algorithm (Dinic, 1970), (Edmonds and Karp, 1972), (Cheriyan et al., 1999) (Goldberg and Tarjan, 1988)…

30. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 30

31. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 31 The flow fully: - defined the extra arcs denoted DFA (Disjunctive Financial Arcs) - permits to define the fully oriented graph which encompasses both job-shop constraints (including job precedence constraints and machines precedence constraints) and financial constraints. 21

32. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 32 The graph : a solution of the problem 21

33. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 33 The graph : a solution of the problem 21

34. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 34

35. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 35

36. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 36 The memetic algorithm based framework is quite conventional including well known refinement for optimization: chromosome representation and evaluation A local search procedure which takes advantage of the critical path analysis. Details are given in the paper 21

37. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 37 Note the critical path is composed either of disjunctive arcs from machines (Job-Shop constraints) or of disjunctive cash flow arcs 21

38. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 38 III. Numerical experiments

39. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 39 312 Implementations and benchmarks - All procedures are implemented under Delphi 6.0 package - Experiments were carried out on a 1.8 GHz computer under Windows XP with 1 GO of memory. -The benchmark is concerned with instances based on the OR-library which instances concern classical shop problems (job-shop, flow-shop). -The instances with financial consideration can be downloaded at: http://www.isima.fr/lacomme/Job_Shop_Financial.html http://www.isima.fr/lacomme/Job_Shop_Financial.html -The framework performance is studied over experiments including both flow- shop and job-shop instances and 30 instances with financial consideration.

40. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 40 -the objective is to underline, the capabilities of the framework to provide new solutions for job-shop instances with both inflow and outflow. -The results presented below push us into accepting that the framework encompasses a wide range of problems: Experiments objectives -) with some merits in both job-shop and flow-shop instances; -) with new results in job-shop instances with financial consideration. 312

41. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 41 n j :number of jobs n m :number of machines n:total number of operations to schedule OPT:denotes the optimal solution LB:denotes a lower bound BKS:Best Known Solution (asterisk denotes optimal solution) S*:the best solution Dev.%:deviation in percentage from S* to OPT or BKS Avg.: average I*:iteration number where S* has been found T*:computational time (in seconds) to found S* TT:total computational time (in seconds) 312

42. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 42 312

43. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 43 312

44. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 44 Typical cash flow profile solving job-shop (La01 instance)

45. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 45 Typical cash flow profile solving JSPCF (La01 instance)

46. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 46 Job shop makespan JSPCF makespan Typical cash flow profile solving JSPCF and Job shop (La03 instance)

47. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 47 4. CONCLUSION

48. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 48 IV. Conclusion 4312 This work is a step forward definition of wide-ranging methods for shop problem, supply chain management and cash management. The key features of this current study are to define the JSPCF for simultaneously addressing during optimization: physical metrics (makespan) financial metrics (cash position, cash flow) Our proposal is relevant for a company supply chain

49. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 49 A framework based on modeling the problem as a disjunctive graph with flow consideration is introduced; A memetic algorithm based approach is proposed; The memetic algorithm encompasses features including min cost max flow resolution for financial consideration, local search based on analysis of the critical path; The framework permits to address a wide range of job-shop problems including the classical one; The numerical experiment proves that our framework obtain almost optimal solutions in a rather short computational time for classical shop problem in terms of quality of results. The proposed framework is more time consuming than dedicated methods, this is not surprising since the framework has a wide range class of application. 4312

50. P. Féniès, P. Lacomme, N.Tchernev LIMOS UMR CNRS 6158 CRCGM 5 décembre 2006 June, 15 MONTREAL – IESM09 50 Perspectives Simultaneous financial consideration of all financial machines; (each machine has a cash position) Stochastic delays in payment allowing to determine robust solutions from the financial point of view (Hinderer et Waldmann, 2001); Splitting in machine operation depending on the financial resource units; Exchange and interest rates in cash flow. 4312 Future works will be relevant for a global supply chain, and will give supply chain manager the possibility to share value (cash flows) between supply chain entities