Abstract
We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity (sales quantity) under random yield is more (less) than that under certain yield.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arrow, K.J., Karlin, S., Scarf, H. Studies in the Mathematical Theory of Inventory and Production. Stanford University Press, Stanford, CA., 1958
Bassok, Y., Yano, C.A. Optimal finite and infinite horizon policies for a single stage production system with variable yields. Working paper, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI., 1992
Chan, L.M.A., Simchi-Levi, D., Swann, J. Pricing, production, and inventory policies for manufacturing with stochastic demand and discretionary sales. Manufacturing and Service Operations Research, 8: 149–168 (2006)
Chen, K.K., Chang, C.-T. A seasonal demand inventory model with variable lead time and resource constraints. Applied Mathematical Modelling, 31: 2433–2445 (2007)
Ciarallo, F.W., Akella, R., Morton, T.E. A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies. Management Science, 40: 320–332 (1994)
Gerchak, Y., Vickson, R.G., Parlar, M. Periodic review production models with variable yield and uncertain demand. IIE Transactions, 20: 144–150 (1988)
Henig, M., Gerchak, Y. The structure of periodic review policies in the presence of random yield. Operations Research, 38: 634–643 (1990)
Heyman, D., Sobel, M.J. Stochastic Models in Operations Research Volume II: Stochastic Optimization, McGraw-Hill Book Company, New York, 1984
Kalro, A.H., Gohil, M.M. A lot size model with backlogging when the amout ordered is uncertain. International Journal of Production Research, 20: 775–786 (1982)
Khang, D.B., Fujiwara, O. Optimality of myopic ordering policies for inventory model with stochastic supply. Operations Research, 48: 181–184 (2000)
Lee, H.L., Yano, C.A. Production control in multistage systems with variable yield losses. Operations Research, 36: 269–278 (1988)
Li, Q., Zheng, S.-H. Joint inventory replenishment and pricing control for systems with uncertain yield and demand. Operations Research, 54: 696–705 (2006)
Lou, S., Sethi, S.P., Sorger, G. Stability of real-time lot scheduling policies for an unreliable machine. IEEE Transactions on Automatic Control, 37: 1966–1970 (1992)
Mazzola, J.B., Mccoy, W.F., Wagner, H.M. Algorithm and heuristics for variable yield lot sizing. Naval Research Logistics Quarterly, 34: 67–86 (1987)
Parlar, M., Wang, D. Diversification under yield randomness in inventory models. European Journal of Operational Research, 66: 52–64 (1993)
Parlar, M., Wang, Y.Z., Gerchak, Y. A periodic review inventory model with markovian supply availability. International Journal of Production Economics, 42: 131–136 (1995)
Presman, E., Sethi, S.P., Zhang, H., Zhang, Q. Optimality of zero-inventory policies for an unreliable manufacturing system producing two part types. Dynamics of Continuous, Discrete and Impulsive Systems, 4: 485–496 (1998)
Rezaei, J., Davoodi, M. A deterministic, multi-item inventory model with supplier selection and imperfect quality. Forthcoming in Applied Mathematical Modelling, 2007
Scarf, H.E. Optimal inventory policies when sales are discretionary. International Journal of Production Economics, 93–94: 111–119 (2005)
Sethi, S.P., Zhang, H. Average-cost optimal policies for a unreliable flexible multiproduct machine. International Journal of Flexible Manufacturing Systems, 11: 147–157 (1999)
Shih, W. Optimal inventory policies when stockouts result from defective products. International Journal of Production Research, 18: 677–686 (1980)
Silver, E.A. Establishing the order quantity when the amount received is uncertain. INFOR, 14: 32–39 (1976)
Wang, Y.Z., Gerchak, Y. Periodic review production models with variable capacity, random yield, and uncertain demand. Management Science, 42: 130–137 (1996)
Wang, J., Cao, J., Liu, B. Unreliable production-inventory system with superposition of k Poisson demand arrival processes. Acta Mathematicae Applicatae Sinica (Chinese Series), 26: 47–55 (2003)
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially Supported by the National Natural Science Foundation of China under Grants (No. 606740852, No. 70731003, No. 70221001).
Rights and permissions
About this article
Cite this article
Yan, Xm., Liu, K. Optimal policies for inventory systems with discretionary sales, random yield and lost sales. Acta Math. Appl. Sin. Engl. Ser. 26, 41–54 (2010). https://doi.org/10.1007/s10255-009-8824-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-009-8824-8