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A NEW APPROACH FOR THE STOCHASTIC CASH BALANCE PROBLEM WITH FIXED COSTS

Published online by Cambridge University Press:  28 August 2009

Xin Chen  and
David Simchi-Levi
Xin Chen
Affiliation:
Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Champaign, IL E-mail: xinchen@uiuc.edu
David Simchi-Levi
Affiliation:
Department of Civil and Environmental Engineering, and The Engineering System Division Massachusetts Institute of Technology, Cambridge, MA 02139USA E-mail: dslevi@mit.edu
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Abstract

The stochastic cash balance problem is a periodic review inventory problem faced by a firm in which the customer demands might be positive or negative. At the beginning of each time period, the firm may decide to replenish the inventory or return excess stock. Both the ordering cost and the return cost include a fixed component and a variable component. A holding or penalty cost is charged depending on whether the inventory level is positive or negative. The objective of the firm is to find an ordering and return policy so as to minimize the total expected cost over the entire planning horizon. We show how the concept of symmetric K-convexity introduced by Chen and Simchi-Levi [2,3] and the concept of (K, Q)-convexity introduced by Ye and Duenyas [13] can be used to characterize the optimal policy for this problem.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 4 , October 2009 , pp. 545 - 562
Copyright
Copyright © Cambridge University Press 2009

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References

1.Chen, X. (2003). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost. Ph.D. dissertation, Massechusetts Institute of Technology, Cambridge, MA.Google Scholar
2.Chen, X. & Simchi-Levi, D. (2004). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon Case. Operations Research 29: 698–723.Google Scholar
3.Chen, X. & Simchi-Levi, D. (2004). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case. Mathematics of Operations Research 52: 887–896.CrossRefGoogle Scholar
4.Eppen, G.D. & Fama, E.F. (1999). Cash balance and simple dynamic portofolio problems with proportional costs. International Econmomics Review 10: 119–133.CrossRefGoogle Scholar
5.Feinberg, E. & Lewis, M. (2005). Optimality of four-threshold policies inventory systems with customer returns and borrowing/storage options. Probability in the Engineering and Informational Sciences 19(1):45–71.CrossRefGoogle Scholar
6.Feinberg, E. & Lewis, M. (2007). Optimality inequalities for average cost markov decision processes and the stochastic cash balance problem. Mathematics of Operations Research 32(4): 769–783.Google Scholar
7.Fleischmann, M., Bloemhof-Ruwaarda, J., Dekker, R., van der Laana, E., van Nunena, J., & Van Wassenhove, L., (1997). Quantitative models for reverse logistics: A review. European Journal on Operational Research 103(1): 1–47.Google Scholar
8.Girgis, N.M. (1968). Optimal cash balance levels. Management Science 15: 130–140.CrossRefGoogle Scholar
9.Neave, E.H. (1970). The stochastic cash balance problem with fixed costs for increases and decreases. Management Science 16: 472–490.Google Scholar
10.Scarf, H. (1960). The optimality of (s, S) policies for the dynamic inventory problem. In Arrow, K., Karlin, S. & Suppes, P. (eds.), Proceedings of the 1st Stanford symposium on mathematical methods in the social sciences. Stanford University Press, Stanford, CA.Google Scholar
11.Simchi-Levi, D., Chen, X. & Bramel, J. (2004). The logic of logistics: Theory, algorithms, and applications for logistics and supply chain management, 2nd ed.New York: Springer-Verlag.Google Scholar
12.Whisler, W.D. (1967). A stochastic inventory model for rented equipment. Management Science 13: 640–647.CrossRefGoogle Scholar
13.Ye, Q. & Duenyas, I. (2003). Optimal joint capacity investment and pricing/production quantity decisions with random and fixed capacity adjustment costs. Working paper, University of Michigan.Google Scholar
14.Ye, Q. & Duenyas, I. (2007). Optimal capacity investment decisions with two-sided fixed-capacity adjustment costs. Operations Research 55(2): 272–283.CrossRefGoogle Scholar