Mean-Risk Analysis of Multiperiod Inventory Problems

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 178)


In this chapter, we carry out mean-risk analysis of multiperiod inventory problems. We select the well-known (R, nQ) multiperiod inventory replenishment model (see Chen and Zheng 1994, 1998; Larsen and Kiesmüller 2007; Li and Sridharan 2008; Shang and Zhou 2010; Lagodimos et al. 2012 and the references therein for more details of the recent developments and extensions of this model) as an example to demonstrate how to perform a mean-risk analysis for multiperiod inventory problems. As shown later on in this chapter, the mean-risk analysis of multiperiod inventory problems is very different from the mean-risk analysis of single-period analysis, in terms of problem formulations and methodology applied. In particular, the (R, nQ) model considers an infinite-horizon replenishment problem under which the total profit/cost is infinite, too. Therefore, the expected (total) profit and the variance of (total) profit cannot be used directly as the “mean” and the “risk,” respectively, in the mean-risk analysis of the (R, nQ) model. To perform the mean-risk analysis, we take the long-run average profit as the “mean,” and propose the variance of on-hand inventory and the variance of one-period profit as “risk” of the (R, nQ) model. We first derive the closed form expressions of the long-run average profit, the variance of on-hand inventory, and the variance of one-period profit. Then, we apply the numerical analysis to demonstrate how to construct the efficient frontier, in the mean-risk sense.


Mean-risk Analysis Efficient Frontier Single-period Analysis Reorder Point Backorder Cost 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Institute of Textiles and ClothingThe Hong Kong Polytechnic UniversityHung Hom, KowloonHong Kong
  2. 2.Department of Management SciencesCity University of Hong KongKowloon Tong, KowloonHong Kong

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