Optimal Control of Supply Chain Systems with Multiple Products

Chapter
Part of the Advances in Industrial Control book series (AIC)

Abstract

This chapter considers the supply chain systems producing multiple types of products serving different customers. We consider two problems as examples. The first is the joint optimal control problem for ordering and production decisions by extending the basic supply chain system in  Chap. 2 to multiple products. The optimal control problem for raw material ordering and production capacity allocation over multiple types of products is formulated. Its optimal control structure is then investigated. The second problem is the optimal production capacity allocation in a failure-prone manufacturing supply chain producing two-type products. The structural characteristics of the optimal control policy are established explicitly. It is shown that the optimal policy can be characterized by three monotonic switching curves, which divide the state space into three control regions to determine the optimal production capacity allocation.

References

  1. Arruda, E.F., Do Val, J.B.R.: Stability and optimality of a multi-product production and storage system under demand uncertainty. Eur. J. Oper. Res. 188(2), 406–427 (2008)MathSciNetCrossRefMATHGoogle Scholar
  2. Benjaafar, S., ElHafsi, M.: Production and inventory control of a single product assemble-to-order system with multiple customer classes. Manage. Sci. 52(12), 1896–1912 (2006)CrossRefMATHGoogle Scholar
  3. Benjaafar, S., ElHafsi, M., Huang, T.: Optimal control of a production-inventory system with both backorders and lost sales. Nav. Res. Logist. 57(3), 252–265 (2010)MathSciNetMATHGoogle Scholar
  4. Benjaafar, S., ElHafsi, M., Lee, C.Y., Zhou, W.H.: Optimal control of an assembly system with multiple stages and multiple demand classes. Oper. Res. 59(2), 522–529 (2011)MathSciNetCrossRefMATHGoogle Scholar
  5. Bertsekas, D.P.: Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs (1987)MATHGoogle Scholar
  6. Carr, S., Duenyas, I.: Optimal admission control and sequencing in a make-to-stock/make-to-order production system. Oper. Res. 48(5), 709–720 (2000)CrossRefGoogle Scholar
  7. Choia, J., Caob, J.J., Romeijnb, H.E., Geunesb, J., Baib, S.X.: A stochastic multi-item inventory model with unequal replenishment intervals and limited warehouse capacity. IIE Trans. 37(12), 1129–1141 (2005)CrossRefGoogle Scholar
  8. Cohen, M.A., Kleindorfer, P.R., Lee, H.L.: Service constrained (s, S) inventory systems with priority demand classes and lost sales. Manage. Sci. 34(4), 482–499 (1988)CrossRefMATHGoogle Scholar
  9. De Vericourt, F., Karaesmen, F., Dallery, Y.: Dynamic scheduling in a make-to-stock system: a partial characterization of optimal policies. Oper. Res. 48(5), 811–819 (2000)CrossRefGoogle Scholar
  10. De Vericourt, F., Karaesmen, F., Dallery, Y.: Optimal stock allocation for a capacitated supply system. Manage. Sci. 48(11), 1486–1501 (2002)CrossRefMATHGoogle Scholar
  11. Frank, K.C., Zhang, R.Q., Duenyas, I.: Optimal policies for inventory systems with priority demand classes. Oper. Res. 51(6), 993–1002 (2003)MathSciNetCrossRefMATHGoogle Scholar
  12. Graves, S.C.: The multi-product production cycling problem. AIIE Trans. 12(3), 233–240 (1980)CrossRefGoogle Scholar
  13. Ha, A.: Inventory rationing in a make-to-stock production system with several demand classes and lost sales. Manage. Sci. 43(8), 1093–1103 (1997a)CrossRefMATHGoogle Scholar
  14. Ha, A.: Stock-rationing policy for a make-to-stock production system with two priority classes and backordering. Nav. Res. Logist. 44(5), 458–472 (1997b)CrossRefGoogle Scholar
  15. Ha, A.: Optimal dynamic scheduling policy for a make-to-stock production system. Oper. Res. 45(1), 42–53 (1997c)CrossRefMATHGoogle Scholar
  16. Ha, A.: Stock-rationing in an M/Ek/1 make-to-stock queue. Manage. Sci. 46(1), 77–87 (2000)CrossRefMATHGoogle Scholar
  17. Huang, B., Iravani, S.M.R.: Technical note—A make-to-stock system with multiple customer classes and batch ordering. Oper. Res. 56(5), 1312–1320 (2008)MathSciNetCrossRefMATHGoogle Scholar
  18. Iravani, S.M.R., Liu, T., Luangkesorn, K.L., Simchi-Levi, D.: A produce-to-stock system with advance demand information and secondary customers. Nav. Res. Logist. 54(3), 331–345 (2007)MathSciNetCrossRefMATHGoogle Scholar
  19. Iravani, S.M.R., Liu, T., Simchi-Levi, D.: Optimal production and admission policies in make-to-stock/make-to-order manufacturing systems. Prod. Oper. Manage. 21(2), 224–235 (2012)CrossRefGoogle Scholar
  20. Isotupa, K.P.S.: An Markovian inventory system with lost sales and two demand classes. Math. Comput. Model. 43(7–8), 687–694 (2006)MathSciNetCrossRefMATHGoogle Scholar
  21. Melchiors, P., Dekker, R., Kleijn, M.J.: Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes. J. Oper. Res. Soc. 51(1), 111–122 (2000)MATHGoogle Scholar
  22. Mollering, K.T., Thonemann, U.W.: An optimal critical level policy for inventory systems with two demand classes. Nav. Res. Logist. 55(7), 632–642 (2008)MathSciNetCrossRefGoogle Scholar
  23. Nahmias, S., Demmy, W.S.: Operating characteristics of an inventory system with rationing. Manage. Sci. 27(11), 1236–1245 (1981)CrossRefMATHGoogle Scholar
  24. Pena-Perez, A., Zipkin, P.: Dynamic scheduling rules for a multi-product make-to-stock queue. Oper. Res. 45(6), 919–930 (1997)CrossRefMATHGoogle Scholar
  25. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)MATHGoogle Scholar
  26. Song, D.P.: Stability and optimization of a production inventory system under prioritized base-stock control. IMA J. Manage. Math. 20(1), 59–79 (2009)CrossRefGoogle Scholar
  27. Song, D.P., Sun, Y.X.: Optimal control structure of an unreliable manufacturing system with random demands. IEEE Trans. Autom. Control. 44(3), 619–622 (1999)MathSciNetCrossRefMATHGoogle Scholar
  28. Teunter, R.H., Haneveld, W.K.K.: Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering. Eur. J. Oper. Res. 190(1), 156–178 (2008)CrossRefMATHGoogle Scholar
  29. Topkis, D.M.: Optimal ordering and rationing policies in a nonstationary dynamic inventory model with n demand classes. Manage. Sci. 15(3), 160–176 (1968)CrossRefGoogle Scholar
  30. Wein, L.M.: Dynamic scheduling of a multiclass make-to-stock queue. Oper. Res. 40(4), 724–735 (1992)MathSciNetCrossRefMATHGoogle Scholar
  31. Zhao, N., Lian, Z.T.: A queueing-inventory system with two classes of customers. Int. J. Prod. Econ. 129(1), 225–231 (2011)MathSciNetCrossRefGoogle Scholar
  32. Zheng, Y., Zipkin, P.: A queueing model to analyze the value of centralized inventory information. Oper. Res. 38(2), 296–307 (1990)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.School of ManagementUniversity of PlymouthPlymouthUK

Personalised recommendations