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We present an optimisation model for supply chain network design under risk of failure. The design parameters include a finite set of potential warehouse locations, a finite set of potential warehouse capacities, a set of branches with known demand for multiple products, a list of products available from each warehouse, and costs of land, building, processing and transportation. Each branch-product pair is assigned a primary and a secondary warehouse. If the primary warehouse fails, some portion of the demand will be supplied by a secondary warehouse. The major contribution of this paper is a novel  method of scenarios  and an algorithm to determine those scenarios, for the solution of instances of the optimisation model. The scenarios are novel in that they do not specify a subset of warehouses to be built, but rather they specify the number of warehouses of each capacity that are to be built. We give an upper bound on the number of scenarios, and the bound is linear in the difference between the largest and smallest failure probabilities. The effectiveness of the  method of scenarios  is demonstrated with its application to a case study of a Canadian company and to a fabricated example based in Europe.

Optimal warehouse location and size under risk of failure