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pp 1–32 | Cite as

Dual-mode inventory management under a chance credit constraint

  • Qiushi Chen
  • Lei ZhaoEmail author
  • Jan C. Fransoo
  • Zhe Li
Regular Article
  • 67 Downloads

Abstract

We study a dual-mode inventory management problem of a high-value component where the customer demand and the regular transportation lead time are stochastic, and the review periods of the two modes are different. The manufacturer is subject to a chance credit constraint that bounds the working capital. To solve the resulting chance-constrained stochastic optimization problem, we develop a hybrid simulation optimization algorithm that combines the modified nested partitions method as the global search framework, a feasibility detection procedure for chance constraint verification, and a \(\hbox {KN}{++}\) procedure as the final “cleanup” procedure to ensure solution quality. We are then able to analyze the impact of the chance credit constraint on the inventory policies and operational cost. Our numerical study shows that the effects of the reduction in mean or variance of the regular transportation lead time depend on whether the chance credit constraint is loose or tight. We show in this way that this tightness may lead to different mechanisms dominating the observed behavior. Further, we show that substantially extending the deterministic credit limit is less effective than having a slight increase in the probability parameter of the chance credit constraint.

Keywords

Supply chain management Dual-sourcing inventory management Stochastic lead time Chance-constrained program Simulation optimization 

Notes

Acknowledgements

The research is partially funded by the National Natural Science Foundation of China under Projects No. 70771053.

Supplementary material

References

  1. Alrefaei M, Andradóttir S (2005) Discrete stochastic optimization using variants of the stochastic ruler method. Nav Res Logist 52(4):344–360CrossRefGoogle Scholar
  2. Andradóttir S (1995) A method for discrete stochastic optimization. Manag Sci 41(12):1946–1961CrossRefGoogle Scholar
  3. Andradóttir S, Kim S (2010) Fully sequential procedures for comparing constrained systems via simulation. Nav Res Logist 57(5):403–421Google Scholar
  4. Bashyam S, Fu M (1998) Optimization of \((s, S)\) inventory systems with random lead times and a service constraint. Manag Sci 44(12):243–256CrossRefGoogle Scholar
  5. Batur D, Kim S (2005) Procedures for feasibility detection in the presence of multiple constraints. In: Proceedings of the 2005 winter simulation conference, pp 692–698Google Scholar
  6. Bendavid I, Herer Y, Yücesan E (2016) Inventory management under working capital constraints. J Simul.  https://doi.org/10.1057/s41273-016-0030-0 CrossRefGoogle Scholar
  7. Blancard S, Boussemart JP, Briec W, Kerstens K (2006) Short- and long-run credit constraints in French agriculture: a directional distance function framework using expenditure-constrained profit functions. Am J Agric Econ 88(2):351–364CrossRefGoogle Scholar
  8. Buzacott J, Zhang R (2004) Inventory management with asset-based financing. Manag Sci 50(9):1274–1292CrossRefGoogle Scholar
  9. Charnes A, Cooper W (1959) Chance-constrained programming. Manag Sci 6(1):73–79CrossRefGoogle Scholar
  10. Charnes A, Cooper W (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Oper Res 11(1):18–39CrossRefGoogle Scholar
  11. Chen C (1995) An effective approach to smartly allocate computing budget for discrete event simulation. In: Proceedings of the 34th IEEE conference on decision and control, vol 3, pp 2598–2603Google Scholar
  12. Chen C (1996) A lower bound for the correct subset-selection probability and its application to discrete-event system simulations. IEEE Trans Autom Control 41(8):1227–1231CrossRefGoogle Scholar
  13. Chen C, He D, Fu M (2006) Efficient dynamic simulation allocation in ordinal optimization. IEEE Trans Autom Control 51(12):2005–2009CrossRefGoogle Scholar
  14. Chen C, He D, Fu M, Lee L (2008) Efficient simulation budget allocation for selecting an optimal subset. INFORMS J Comput 20(4):579–595CrossRefGoogle Scholar
  15. Chen C, Yücesan E, Dai L, Chen H (2010) Optimal budget allocation for discrete-event simulation experiments. IIE Trans 42(1):60–70CrossRefGoogle Scholar
  16. Feder G (1985) The relation between farm size and farm productivity. J Dev Econ 18:297–313CrossRefGoogle Scholar
  17. Fu M (2002) Optimization for simulation: theory vs. practice. INFORMS J Comput 14(3):192–215CrossRefGoogle Scholar
  18. Fu M, Hu J (1997) Conditional Monte Carlo: gradient estimation and optimization applications. Kluwer, NorwellCrossRefGoogle Scholar
  19. Glasserman P, Tayur S (1995) Sensitivity analysis for base-stock levels in multiechelon production–inventory systems. Manag Sci 41(2):263–281CrossRefGoogle Scholar
  20. Guariglia A, Mateut S (2016) External finance and trade credit extension in china: does political affiliation make a difference? Eur J Finance 22(4–6):319–344CrossRefGoogle Scholar
  21. Hartmann S, Briskorn D (2010) A survey of variants and extensions of the resource-constrained project scheduling problem. Eur J Oper Res 207(1):1–14CrossRefGoogle Scholar
  22. Hillier FS (1967) Chance-constrained programming with 0–1 or bounded continuous decision variabes. Manag Sci 14(1):34–57CrossRefGoogle Scholar
  23. Hong L, Nelson B (2006) Discrete optimization via simulation using COMPASS. Oper Res 54(1):115–129CrossRefGoogle Scholar
  24. Hong L, Nelson B (2007) A framework for locally convergent random-search algorithms for discrete optimization via simulation. ACM Trans Model Comput Simul 17(4):19:1–22CrossRefGoogle Scholar
  25. Janakiraman G, Roundy R (2004) Lost-sales problems with stochastic lead times: convexity results for base-stock policies. Oper Res 52(5):795–803CrossRefGoogle Scholar
  26. Kim S, Nelson B (2001) A fully sequential procedure for indifference-zone selection in simulation. ACM Trans Model Comput Simul 11(3):251–273CrossRefGoogle Scholar
  27. Kim S, Nelson B (2006a) On the asymptotic validity of fully sequential selection procedures for steady-state simulation. Oper Res 54(3):475–488CrossRefGoogle Scholar
  28. Kim S, Nelson B (2006b) Selecting the best system. In: Henderson S, Nelson B (eds) Handbooks in operations research and management science: simulation. Elsevier, Amsterdam, pp 501–534 (Chap. 13)Google Scholar
  29. Kim S, Nelson B (2007) Recent advances in ranking and selection. In: Proceedings of the 2007 winter simulation conference, pp 692–698Google Scholar
  30. Law AM, Kelton WD (2000) Simulation modeling and analysis. McGraw-Hill series in industrial engineering and management science. McGraw-Hill, New YorkGoogle Scholar
  31. Lejeune M, Ruszczyński A (2007) An efficient trajectory method for probabilistic production–inventory–distribution problems. Oper Res 55(2):378–394CrossRefGoogle Scholar
  32. Liu S, Wang C (2009) Two-stage profit optimization model for linear scheduling problems considering cash flow. Constr Manag Econ 27(11):1023–1037CrossRefGoogle Scholar
  33. Luedtke J (2013) A branch-and-cut decomposition algorithm for solving general chance-constrained mathematical programs with finite support. Math Program 138:223–251CrossRefGoogle Scholar
  34. Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J Optim 19(2):674–699CrossRefGoogle Scholar
  35. Luedtke J, Ahmed S, Nemhauser G (2010) An integer programming approach for linear programs with probabilistic constraints. Math Program 122(2):247–272CrossRefGoogle Scholar
  36. Malone G, Kim S, Goldsman D, Batur D (2005) Performance of variance updating ranking and selection procedures. In: Proceedings of the 2005 winter simulation conference, pp 825–832Google Scholar
  37. Miller B, Wagner H (1965) Chance constrained programming with joint constraints. Oper Res 13(6):930–945CrossRefGoogle Scholar
  38. Minner S (2003) Multiple-supplier inventory models in supply chain management: a review. Int J Prod Econ 81–82:265–279CrossRefGoogle Scholar
  39. Moinzadeh K, Nahmias S (1988) A continuous review model for an inventory system with two supply modes. Manag Sci 34(6):761–773CrossRefGoogle Scholar
  40. Murr M, Prekopa A (2000) Solution of a product substitution problem using stochastic programming. Nonconv Optim Appl 49:252–271CrossRefGoogle Scholar
  41. Nelson B, Swann J, Goldsman D, Song W (2001) Simple procedures for selecting the best simulated system when the number of alternatives is large. Oper Res 49(6):950–963CrossRefGoogle Scholar
  42. Nemirovski A, Shapiro A (2006a) Convex approximations of chance constrained programs. SIAM J Optim 17(4):969–996CrossRefGoogle Scholar
  43. Nemirovski A, Shapiro A (2006b) Scenario approximations of chance constraints. In: Calafiore G, Dabbene F (eds) Probabilistic and randomized methods for design under uncertainty. Springer, Berlin, pp 3–47 (Chap. 1)CrossRefGoogle Scholar
  44. Ólafsson S, Yang J (2005) Intelligent partitioning for feature selection. INFORMS J Comput 17(3):339–355CrossRefGoogle Scholar
  45. Olson D, Swenseth S (1987) A linear approximation for chance-constrained programming. J Oper Res Soc 38(3):261–267CrossRefGoogle Scholar
  46. Pagnoncelli B, Ahmed S, Shapiro A (2009) Sample average approximation method for chance constrained programming: theory and applications. J Optim Theory Appl 41(2):263–281Google Scholar
  47. Pichitlamken J, Nelson B (2003) A combined procedure for optimization via simulation. ACM Trans Model Comput Simul 13(2):155–179CrossRefGoogle Scholar
  48. Poojari C, Varghese B (2008) Genetic algorithms based technique for solving chance constraint problems. Eur J Oper Res 185(3):1128–1154CrossRefGoogle Scholar
  49. Ramasesh RV, Ord JK, Hayya JC, Pan A (1991) Sole versus dual sourcing in stochastic lead-time \((s, q)\) inventory models. Manag Sci 37(4):428–443CrossRefGoogle Scholar
  50. Reindorp M, Lange A, Tanrisever F (2013) Pre-shipment financing: credit capacities and supply chain consequences. Technical report, Eindhoven University of Technology, EindhovenGoogle Scholar
  51. Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat 22(3):400–407CrossRefGoogle Scholar
  52. Scheller-Wolf A, Veeraraghavan S, van Houtun G (2007) Effective dual sourcing with a single index policy. Technical report, Carnegie-Mellon University, PittsburghGoogle Scholar
  53. Sculli D, Wu S (1981) Stock control with two suppliers and normal lead times. Int J Oper Res Soc 32(11):1003–1009CrossRefGoogle Scholar
  54. Seppala Y (1971) Constructing sets of uniformly tighter linear approximations for a chance constraint. Manag Sci 17(11):736–749CrossRefGoogle Scholar
  55. Sheopuri A, Janakiraman G, Seshadri S (2010) New policies for the stochastic inventory control problem with two supply sources. Oper Res 58(3):734–745CrossRefGoogle Scholar
  56. Shi L, Ólafsson S (2000a) Nested partitions method for global optimization. Oper Res 48(3):390–407CrossRefGoogle Scholar
  57. Shi L, Ólafsson S (2000b) Nested partitions method for stochastic optimization. Methodol Comput Appl Probab 2(3):271–291CrossRefGoogle Scholar
  58. Shi L, Olafsson S (2007) Nested partitions optimization. Tutor Oper Res 29:1–22Google Scholar
  59. Shi L, Ólafsson S (2008) Nested partitions method, theory and applications. Springer, BerlinGoogle Scholar
  60. Shi L, Ólafsson S, Sun N (1999) New parallel randomized algorithms for the traveling salesman problem. Comput Oper Res 26(4):371–394CrossRefGoogle Scholar
  61. Swenson D (2011) The influence of Chinese trade policy on automobile assembly and parts (October 25, 2011). CESifo working paper series no. 3615. http://ssrn.com/abstract=1949070
  62. Swisher J, Jacobson S, Yücesan E (2003) Discrete-event simulation optimization using ranking, selection, and multiple comparison procedures: a survey. ACM Trans Model Comput Simul 13(2):134–154CrossRefGoogle Scholar
  63. Swisher J, Hyden P, Jacobson S, Schruben L (2004) A survey of recent advances in discrete input parameter discrete-event simulation optimization. IIE Trans 36(6):591–600CrossRefGoogle Scholar
  64. Talluri S, Narasimhan R, Nair A (2006) Vendor performance with supply risk: a chance-constrained DEA approach. Int J Prod Econ 100(2):212–222CrossRefGoogle Scholar
  65. Tanrisever F, Cetinay H, Reidorp M, Fransoo J (2012) The value of reverse factoring in multi-stage supply chains. Technical report, Eindhoven University of Technology, EindhovenGoogle Scholar
  66. Veeraraghavan S, Scheller-Wolf A (2008) Now or later: a simple policy for effective dual sourcing in capacitated systems. Oper Res 56(4):850–864CrossRefGoogle Scholar
  67. Vlachos D, Tagaras G (2001) An inventory system with two supply modes and capacity constraints. Int J Prod Econ 72(1):41–58CrossRefGoogle Scholar
  68. Wu D, Olson D (2008) Supply chain risk, simulation, and vendor selection. Int J Prod Econ 114(2):646–655CrossRefGoogle Scholar
  69. Xu J, Nelson B, Hong J (2010) Industrial strength COMPASS: a comprehensive algorithm and software for optimization via simulation. ACM Trans Model Comput Simul 20(1):3CrossRefGoogle Scholar
  70. Zhang H, Shi L, Meyer R, Nazareth D, D’Souza W (2009) Solving beam-angle selection and dose optimization simultaneously via high-throughput computing. INFORMS J Comput 21(3):427–444CrossRefGoogle Scholar
  71. Zhao L, Langendoen F, Fransoo J (2012) Supply management of high-value components with a credit constraint. Flex Serv Manuf J 24(2):100–118CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringTsinghua UniversityBeijingChina
  2. 2.Kuehne Logistics UniversityHamburgGermany

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