Determining inventory allocation policies in a one-warehouse R identical retailer distribution system
Abstract
Much of the recent literature in the area of multi-echelon inventory theory has addressed the issue of risk-pooling as a motive for using a warehouse to allocating stock to retailers in a distribution system with stochastic demand. In this paper we construct a model for determining risk-pooling allocation policies for distributing warehouse stock to R identical retailers during the order cycle in such a way as to minimize system lost sales. An allocation policy is specified by: (1) the time intervals between warehouse-to-retailer allocations; (2) the amount of warehouse stock to allocate at the beginning of each interval; and (3) the policy for distributing stock among the retailers. Due to the difficulty of analyzing the R-retailer case, we develop an infinite-retailer approximation of our model which effectively removes much of the difficulty associated with the stochastic demand element of the problem. We use this approximation and the concept of inventory probability distributions to show that (1) stock allotted in each interval is distributed in such a way as to "balance" retailer inventories, (2) there exists an optimal allocation policy where the post-allotment balanced inventory levels each interval are non-increasing from interval to interval, (3) there exists an optimal allocation policy where the interval lengths are non-increasing, and (4) minimizing lost sales two consecutive intervals is convex. Numerical tests over a two-interval version of our model indicate that the risk-pooling benefits of well-chosen allocation policies with two unequal intervals are roughly comparable to the benefits of base-stock policies with four equal intervals. Simulation results suggest that the policies prescribed by optimizing the infinite-retailer approximation are near optimal for as few as two retailers.
Degree
Ph.D.
Advisors
Schwarz, Purdue University.
Subject Area
Marketing|Business costs
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