The Effect of Customer Patience on Multiple-Location Inventory Systems

  • Michael Dreyfuss
  • Yahel GiatEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 152)


This chapter considers the optimization of spares for various multiple-location inventory systems. The systems’ performance level is the window fill rate, which generalizes the fill rate by taking into account customer patience, that is, that customers may tolerate a certain wait. Formally, the window fill rate of a particular location is the percent of customers that will receive service within the tolerable wait. At the system’s level, the window fill rate is the weighted average of the locations’ window fill rates weighted by the arrival rates to the locations. A near-optimal algorithm that solves the spares allocation problem efficiently (e.g., running time is linear with the number of spares) is described with the conditions for which the solution is optimal. The algorithm’s a priori and a posteriori distances from optimum are decreasing with the system’s size (e.g., number of locations) and therefore it is particularly useful for large scale inventory systems. The chapter concludes with a numerical example that demonstrates that customer patience affects performance and budget profoundly, and neglecting to account for it results with overstocking. Moreover, it is very beneficial to encourage customer patience and, depending on the cost of spares, managers should consider incentives to increase it.


Inventory optimization Customer patience Multiple location inventory Greedy optimization Waiting time 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Jerusalem College of TechnologyJerusalemIsrael

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