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A bimodal scheme for multi-stage production and inventory control. (English) Zbl 1033.90028

Summary: This study considers a multi-stage multi-item production plant with its supply chain and customer environment. The production, supply and inventory plan is optimized on a dual-mode basis, under two different information patterns. The short-term plan relies on firm orders received from customers. On the contrary, the long-term plan is based on predicted demands represented by random sequences. In this study, the role of the long-term plan is mainly to impose a final condition set to the short-term plan.

MSC:

90B30 Production models
90B05 Inventory, storage, reservoirs
90C05 Linear programming
Full Text: DOI

References:

[1] Bitran, G. R., & Tirupati, D. (1993). Hierarchical production planning. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Handbooks in operations research and management science; Bitran, G. R., & Tirupati, D. (1993). Hierarchical production planning. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Handbooks in operations research and management science
[2] Bitsoris, G., Positively invariant polyhedral sets of discrete-time linear systems, International Journal of Control, 47, 1713-1726 (1988) · Zbl 0646.93041
[3] Clarke, A. J.; Scarf, H., Optimal policies for a multiechelon inventory problem, Management Science, 6, 475-490 (1960)
[4] Ehrhardt, R., (s,s) policies for a dynamic inventory model with stochastic lead-times, Operations Research, 32, 121-132 (1984) · Zbl 0531.90024
[5] Federgruen, A. (1993). Centralized planning models for multi-echelon inventory systems under uncertainty. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Handbooks in operations research and management science; Federgruen, A. (1993). Centralized planning models for multi-echelon inventory systems under uncertainty. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Handbooks in operations research and management science
[6] Federgruen, A.; Zipkin, P., Computational issues in an infinite-horizon, multi-echelon inventory model, Operations Research, 32, 818-836 (1984) · Zbl 0546.90026
[7] Fogarty, D. W.; Hoffmann, T. R., Production and inventory management. Cincinnati, Ohio (1983), South-Western Publishing Company
[8] Grubbström, R. W.; Ovrin, P., Intertemporal generalization of the relationship between material requirement planning and input-output analysis, International Journal of Production Economics, 26, 311-318 (1992)
[9] Hennet, J.-C., Une extension du lemme de farkas et son application au problème de régulation linéaire sous contraintes, Comptes Rendus de Academie des Sciences, t.308, I, 415-419 (1989) · Zbl 0850.93336
[10] Hennet, J. C., & Barthès, I. (1998). Closed-loop planning of multi-level production under resource constraints. In Proceedings of the IFAC symposium INCOM98; Hennet, J. C., & Barthès, I. (1998). Closed-loop planning of multi-level production under resource constraints. In Proceedings of the IFAC symposium INCOM98
[11] Hennet, J.-C., & Dórea, C. E. T. (1994). Invariant regulators for linear systems under combined input and state constraints. In Proceedings of the 33th IEEE conference and decision and control; Hennet, J.-C., & Dórea, C. E. T. (1994). Invariant regulators for linear systems under combined input and state constraints. In Proceedings of the 33th IEEE conference and decision and control
[12] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scockaert, P. O.M., Constrained model predictive controlStability and optimality, Automatica, 36, 789-814 (2000) · Zbl 0949.93003
[13] Nahmias, S., Simple approximations for a variety of dynamic lead-time lost sales inventory models, Operations Research, 27, 904-924 (1979) · Zbl 0426.90027
[14] Porteus, E. L. (1991). Stochastic inventory theory. In D. P. Heyman, M. J. Sobel (Eds.), Handbooks in operations research and management science; Porteus, E. L. (1991). Stochastic inventory theory. In D. P. Heyman, M. J. Sobel (Eds.), Handbooks in operations research and management science · Zbl 0736.90026
[15] Rosling, K., Optimal inventory policies for assembly systems under random demand, Operations Research, 37, 4, 565-579 (1989) · Zbl 0677.90025
[16] Thomas, L. J., & McClain, J. O. (1993). An overview of production planning. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Handbooks in operations research and management science; Thomas, L. J., & McClain, J. O. (1993). An overview of production planning. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Handbooks in operations research and management science
[17] Vassilaki, M.; Hennet, J. C.; Bitsoris, G., Feedback control of linear discrete-time systems under state and control constraints, International Journal of Control, 47, 1727-1735 (1988) · Zbl 0644.93046
[18] Veinott, A. F., Minimum concave-cost solution of leontief substitution models of multi-facility inventory systems, Operations Research, 17, 2, 262-291 (1969) · Zbl 0175.17602
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