Planned lead time optimization in material requirement planning environment for multilevel production systems

Abstract

This paper deals with the problem of planned lead time calculation in a Material Requirement Planning (MRP) environment under stochastic lead times. The objective is to minimize the sum of holding and backlogging costs. The proposed approach is based on discrete time inventory control where the decision variables are integer. Two types of systems are considered: multi-level serial-production and assembly systems. For the serial production systems (one type of component at each level), a mathematical model is suggested. Then, it is proven that this model is equivalent to the well known discrete Newsboy Model. This directly provides the optimal values for the planned lead times. For multilevel assembly systems, a dedicated model is proposed and some properties of the decision variables and objective function are proven. These properties are used to calculate lower and upper limits on the decision variables and lower and upper bounds on the objective function. The obtained limits and bounds open the possibility to develop an efficient optimization algorithm using, for example, a Branch and Bound approach. The paper presents the proposed models in detail with corresponding proofs and several numerical examples. Some advantages of the suggested models and perspectives of this research are discussed.

Keywords

Multilevel assembly and production systems / MRP / random lead times / discrete inventory control model / planned lead time optimization

References

[1] Banks J., Carson J.S., Nelson B.L., Nicol D.M.. Discrete-event System Simulation, 2001, New Jersey: Prentice-Hall

[2] Chatfield D., Kim J., Harrison T., Hayya J.. The bullwhip effect in supply chains — impact of stochastic lead times, information quality, and information sharing: a simulation study. Production and Operations Management, 2004, 13(4): 340-353.

[3] Chen F., Drezner Z., Ryan J., Simchi-Levi D.. Quantifying the bullwhip effect in assembly supply chain: the impact of forecasting, lead times and information. Management Science, 2000, 46(3): 436-443.

[4] Chu C., Proth J.M., Xie X.. Supply management in assembly systems. Naval Research Logistics, 1993, 40: 933-949.

[5] Dolgui A.. On a model of joint control of reserves in automatic control systems of production. Automation and Remote Control, 2001, 62(12): 2020-2026.

[6] Dolgui A., Portmann M.C., Proth J.M.. Planification de systèmes d’assemblage avec approvisionnement al’eatoire en composants. Journal of Decision Systems, 1995, 4(4): 255-279.

[7] Dolgui, A., Portmann, M.C. & Proth, J.M. (1996). A control model of the assembly manufacturing. In: Dolezal, J., Fidler, J. (Eds.), System Modeling and Optimization. Proceedings of the 17th IFIP TC7 Conference, 519–526, Chapman and Hall

[8] Elhafsi M.. Optimal leadtimes planning in serial production systems with earliness and tardiness costs. IIE Transactions, 2002, 34: 233-243.

[9] Kaplan R.. Dynamic inventory model with stochastic lead times. Management Science, 1970, 16: 491-507.

[10] Kim J.G., Chatfield D., Harrison T.P., Hayya J.C.. Quantifying the bullwhip effect in a supply chain with stochastic lead time. European Journal of Operational Research, 2006, 173(2): 617-636.

[11] Ould Louly, M.A., Dolgui, A. & Hnaien, F. (2008). Optimal supply planning in MRP environments for assembly systems with random component procurement times. International Journal of Production Research, (Accepted, in Press)

[12] Ould Louly M.A., Dolgui A.. Generalized newsboy model to compute the optimal planned lead times in assembly systems. International Journal of Production Research, 2002, 40(17): 4401-4414.

[13] Ould Louly M.A., Dolgui A.. The MPS parameterization under lead time uncertainty. International Journal Production Economics, 2004, 90: 369-376.

[14] Porteus, E.L. (1990). Stochastic inventory theory. In: Heyman D.P., Sobel M.J. (eds.), Hand-book in OR and MS, Vol 2, pp. 605–652. Elsevier Science Publishers

[15] Proth J.M., Mauroy G., Wardi Y., Chu C., Xie X.. Supply management for cost minimization in assembly systems with random components yield times. Journal of Intelligent Manufacturing, 1997, 8: 385-403.

[16] Tang O., Grubbström R.W.. The detailed coordination problem in a two-level assembly system with stochastic lead times. International Journal Production Economics, 2003, 81–82: 415-429.

[17] Yano C.A.. Setting planned leadtimes in serial production systems with tardiness costs. Management Science, 1987, 33(1): 95-106.

[18] Yano C.A.. Planned leadtimes for serial production systems. IIE Transactions, 1987, 19(3): 300-307.

[19] Yano C.A.. Stochastic leadtimes in two-level assembly systems. IIE Transactions, 1987, 19(4): 95-106.