Price Discount and Stochastic Initial Inventory in the Newsboy Problem

Document Type : Research Paper

Authors

1 1Dept. of Mech. and Ind. Eng. University of Illinois at Chicago, Chicago, IL, 60607, USA

2 Dept. of Ind. Eng. Sharif University of Technology, Tehran, Iran

3 Dept. of Mech. and Ind. Eng. University of Illinois at Chicago, Chicago, IL, 60607, USA

Abstract

Many extension of the newsboy problem have been solved in the literature. One of those extensions solves a newsboy problem with stochastic initial inventory, earlier extensions have focused on quantity discounts offered by suppliers. An important practical extension would address a combination of the two pervious extensions. In this paper we consider a newsboy problem in which the suppliers offer quantity discount and the initial inventory at the beginning of the period is a random variable. We obtain the optimal value of the order quantity which maximizes the total profit and then present the results for some practical distributions of both random variables, demand and initial inventory.

Keywords

Main Subjects


[1] Anvari M. (1987), Optimality criteria and risk in inventory models: The case of the newsboy problem;
Journal of the Operational Research Society 38; 625-632.
[2] Bijari M., Haji R. (2004), The single-period (news-vendor) problem with stochastic initial inventory;
International Journal of Engineering Science 15(2); 47-54.
[3] Ehrhardt R., Taube L. (1987), An inventory model with random replenishment quantity; Int. J. Prod.
Res. 25; 1795-1803.
[4] Hadley G., Whitin T. M. (1963), Analysis of inventory systems; Prentice-Hall, Englewood Cliffs, NJ.
[5] Haji R., Bijari M. (2003), The newsboy problem with stochastic initial inventory; Proceedings of the
8th Annual International Conference on Industrial Engineering, Nov. 10-12, 822-827.
[6] Henig M., Gerchak Y. (1990), The structure of periodic review policies in the presence of random
yield; Opr. Res. 38; 634-643.
[7] Ismail B., Louderback J. (1979), Optimizing and satisfying in stochastic cost-volume-profit analysis;
Decision Sciences 10; 205-217.
[8] Jain K., Silver E.A. (1995), The single period procurement problem where dedicated supplier capacity
can be reserved, Naval Res. Logist 42; 915-934.
[9] Johnson L.A., Montgomery D.C. (1974), Operations research in production planning, scheduling and
inventory control; John Wiley, New York.
[10] Jucker J.V., Rosenblatt M.J. (1985), Single-period inventory models with demand uncertainty and
quantity discounts; Behavioral implications and a new solution Procedure, Naval Research Logistics
Quarterly 32; 537-550.
[11] Kabak I., Weinberg C. (1972), The generalized newsboy problem, contract negotiations and
secondary vendors; IIE Transactions 4; 154-157.
[12] Khouja M. (1995), The newsboy problem under progressive multiple discounts, Eur. J. Op. Res. 84;
458-466.
[13] Khouja M. (1996), The newsboy problem with progressive retailer discounts and supplier quantity
discounts, Decis. Sci. 27; 589-599.
[14] Lau H. (1980), The newsboy problem under alternative optimization objective, Journal of the
Operational Research Society 31; 525-535.
[15] Lau, A., Lau, H. (1988), The newsboy problem with price-dependent demand
Distribution; IIE Transaction 20, 168-175.
[16] Lin C., Kroll D.E. (1997), The single-item newsboy problem with dual performance measures and
quantity discounts; European Journal. of Operations Research August; 562-565.
[17] Love S. (1979), Inventory control; McGraw-Hill, New York.
[18] Magee R.P. (1975), Cost-volume-profit analysis, uncertainty and capital market equilibrium, Journal
of Accounting Research 13; 257-266.
[19] Moon I. Choi S. (1995), The distribution free newsboy problem with balking, J. Opl. Res. Soc. 46;
537-542.
[20] Nahmias S. (2005), Production and Operations Analysis, 5th ed.; McGraw-Hill, New York.
[21] Noori A.H., Keller G. (1986), One-period order quantity strategy with uncertain mach between the
amount received and quantity requisitioned, INFOR, 24; 1-11.
[22] Pantumsinchai P., Knowles T.W. (1991), Standard container size discounts and the single-period
inventory problem, Decision Sciences 22; 612-619.
[23] Polatoglu L.H. (1991), Optimal order quantity and pricing decisions in single-period inventory
systems, Int. J. Prod. Econ. 23; 175-185.
[24] Reyniers D. (1991), A high-low search for a newsboy problem with delayed information feedback,
Oper. Res. 38; 838-846.
[25] Ross S.M. (1983), Stochastic processes, John Wiley, New York.
[26] Sankarasubramanian E., Kumaraswamy S. (1983), Optimal order quantity for pre-determined level of
profit, Management Science 29; 512-514.
[27] Shih W. (1979), A general decision model for cost-volume-profit analysis under uncertainty, The
Accounting Review 54; 687-706.
[28] Shih W. (1980), Optimal inventory policies when stockouts result from defective products, Int. J.
Prod. Res. 18; 677-686.