A probablistic analysis of the multi-period single-sourcing problem

Romeijn, H. Edwin and Romero-Morales, Dolores (2001) A probablistic analysis of the multi-period single-sourcing problem. Discrete Applied Mathematics, 112 (1-3). pp. 301-328.

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Abstract

The multi-period single-sourcing problem (MPSSP) is the problem of finding an assignment, over time, of customers to warehouses such that each customer is assigned to exactly one warehouse in each period, subject to capacity constraints, such that the total transportation and inventory costs are minimized. We propose a general stochastic model for the MPSSP, and derive a tight condition on this stochastic model under which the MPSSP is feasible with probability 1 when the number of customers goes to infinity. This result can be used to generate suitable experimental data. Moreover, we show that the normalized optimal value of the problem converges almost surely to a constant, for which we provide an explicit expression; this property can be useful in constructing asymptotically optimal heuristics for the problem. The rate of convergence to the limiting value is illustrated empirically.

Item Type: Article
Keywords: Probabilistic analysis; Generalized Assignment Problem; Dynamic assignments
Subject(s): Management science
Centre: Faculty of Management Science
Date Deposited: 09 Sep 2010 14:25
Last Modified: 23 Oct 2015 14:05
URI: http://eureka.sbs.ox.ac.uk/id/eprint/436

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