An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion

作者: A. Federgruen , P. Zipkin

DOI: 10.1287/MOOR.11.2.208

关键词: Stationary processMathematical economicsFunction (mathematics)MathematicsMathematical optimizationProduction (economics)Distribution (mathematics)Discounted cost

摘要: This paper considers a single-item, periodic-review inventory model with uncertain demands. We assume finite production capacity in each period. With stationary data, convex one-period cost function and continuous demand distribution, we show under few additional unrestrictive assumptions that modified basic-stock policy is optimal the discounted criterion, both for infinite planning horizons. In addition characterize base-stock levels several ways.

参考文章(18)
J. Wijngaard, An inventory problem with constrained ordercapacity EUT report. WSK, Dept. of Mathematics and Computing Science. ,(1972)
Matthew J. Sobel, Daniel P. Heyman, Stochastic models in operations research ,(1982)
Steven E. Shreve, Dimitri P. Bertsekas, Stochastic optimal control : the discrete time case ,(2007)
Michael Florian, Morton Klein, Erratum: Deterministic Production Planning with Concave Costs and Capacity Constraints Management Science. ,vol. 18, pp. 721- 721 ,(1972) , 10.1287/MNSC.18.11.721
Gabriel R. Bitran, Horacio H. Yanasse, Computational Complexity of the Capacitated Lot Size Problem Management Science. ,vol. 28, pp. 1174- 1186 ,(1982) , 10.1287/MNSC.28.10.1174
A. Federgruen, A. Hordijk, H.C. Tijms, Denumerable state semi-Markov decision processes with unbounded costs, average cost criterion Stochastic Processes and their Applications. ,vol. 9, pp. 223- 235 ,(1979) , 10.1016/0304-4149(79)90034-6
M. Florian, J. K. Lenstra, A. H. G. Rinnooy Kan, Deterministic Production Planning: Algorithms and Complexity Management Science. ,vol. 26, pp. 669- 679 ,(1980) , 10.1287/MNSC.26.7.669
A. G. De kok, H. C. Tijms, F. A. Van der Duyn Schouten, Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints Advances in Applied Probability. ,vol. 16, pp. 378- 401 ,(1984) , 10.1017/S0001867800022588
A. Federgruen, P. J. Schweitzer, H. C. Tijms, Denumerable Undiscounted Semi-Markov Decision Processes with Unbounded Rewards Mathematics of Operations Research. ,vol. 8, pp. 298- 313 ,(1983) , 10.1287/MOOR.8.2.298