New structural properties of (\(s,S\)) policies for inventory models with lost sales. (English) Zbl 1217.90027
Authors’ abstract: “We revisit the classical inventory model for which \((s,S)\) policies are optimal. We consider the finite and infinite horizon versions of the lost sales problem. New structural properties are developed for the optimal policy and cost function. These properties are then used to develop computational schemes for the lost sales problem with Erlang demands.”
Reviewer: Liang-Yuh Ouyang (Tamsui)
MSC:
| 90B05 | Inventory, storage, reservoirs |
References:
| [1] | Archibald, B. C., Continuous review \((s, S)\) policies with lost sales, Management Science, 27, 1171-1177 (1981) · Zbl 0465.90021 |
| [2] | Arrow, K.; Harris, T.; Marschak, J., Optimal inventory policy, Econometrica, 19, 250-272 (1951) · Zbl 0045.23205 |
| [3] | Bensoussan, A.; Crouhy, M.; Proth, J., Mathematical Theory of Production Planning (1983), North Holland · Zbl 0564.90010 |
| [4] | Bertsekas, D., Dynamic Programming and Stochastic Control (1976), Academic Press · Zbl 0549.93064 |
| [5] | Bertsekas, D., Dynamic Programming and Optimal Control (2000), Athena Scientific: Athena Scientific Belmont, MA |
| [6] | Beyer, D.; Sethi, S., The classical average-cost inventory models of Iglehart and Veinott-Wagner revisited, Journal of Optimization Theory and Applications, 101, 523-555 (1999) · Zbl 0943.90003 |
| [7] | Federgruen, A.; Zipkin, P., An efficient algorithm for computing optimal \((s, S)\) policies, Operations Research, 34, 1268-1285 (1984) · Zbl 0553.90031 |
| [8] | Feng, Y.; Xiao, B., A new algorithm for computing optimal \((s, S)\) policies in a stochastic single item/location inventory system, IIE Transactions, 32, 1081-1090 (2000) |
| [9] | Iglehart, D., Optimality of \((s, S)\) policies in the infinite horizon dynamic inventory problems, Management Science, 9, 259-267 (1963) |
| [10] | Karlin, S., Steady state solutions, (Studies in the Mathematical Theory of Inventory and Production (1958), Stanford University: Stanford University Stanford, CA), (Chapter 14) |
| [11] | Porteus, E., On the optimality of generalized \((s, S)\) policies, Management Science, 17, 411-426 (1971) · Zbl 0221.90011 |
| [12] | Scarf, H., The optimality of \((S, s)\) policies in dynamic inventory problems, (Mathematical Methods in the Social Sciences (1960), Stanford University: Stanford University Stanford, CA) · Zbl 0203.22102 |
| [13] | Shreve, S. E., Abbreviated proof [in the lost sales case], (Bertsekas, D. P., Dynamic Programming and Stochastic Control (1976), Academic Press: Academic Press New York), 105-1-6 |
| [14] | Veinott, A., On the optimality of \((s, S)\) inventory policies: new conditions and a new proof, SIAM Journal on Applied Mathematics, 14, 1067-1083 (1966) · Zbl 0173.47603 |
| [15] | Veinott, A.; Wagner, H., Computing optimal \((s, S)\) inventory policies, Management Science, 11, 525-552 (1965) · Zbl 0137.14102 |
| [16] | Zheng, Y.; Federgruen, A., Finding optimal \((s, S)\) policies is about as simple as evaluating a single policy, Operations Research, 39, 654-665 (1991) · Zbl 0749.90024 |
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