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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: [email protected]
David Simchi-Levi
Affiliation:
Department of Civil and Environmental Engineering, and The Engineering System Division Massachusetts Institute of Technology, Cambridge, MA 02139USA E-mail: [email protected]
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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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