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

The multi-period single-sourcing problem (MPSSP) is the problem of finding an assignment, over time, of customers to warehouses such that each custome r is assigned to exactly one warehouse in each period, subject to capacity constraints, such that the total transportation and inventory costs are min imized. We propose a general stochastic model for the MPSSP, and derive a t ight condition on this stochastic model under which the MPSSP is feasible w ith probability I when the number of customers goes to infinity. This resul t can be used to generate suitable experimental data. Moreover, we show tha t 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. ( C) 2001 Elsevier Science B.V. All rights reserved.