A new approach for the stochastic cash balance problem with fixed costs

Xin Chen, David Simchi-Levi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)545-562
Number of pages18
JournalProbability in the Engineering and Informational Sciences
Issue number4
StatePublished - Oct 2009

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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