Stochastic capacity planning in a Global Mining Supply Chain

Abstract

The strategic planning problem, when applied to a Global Mining Supply Chain, aims at developing the necessary capacity — through either incrementing capacity on existing assets (facilities or logistics channels), or establishing new capacity in the form of new assets — in order to satisfy increasing demand. Hence, throughout the planning horizon, decisions about which new assets to establish and where to increment capacity must be taken at minimal cost (or minimal risk) and in a timely manner. However, when demand varies non-monotonically, decisions about which assets to temporarily shut down in times of decreasing demand and which of those to reopen when market conditions improve must also be taken into account. In order to respond to the risky nature of commodity markets, we propose a multi-stage stochastic programming approach to deal with the capacity planning problem in a realistic Global Mining Supply Chain. A discrete probability scenario tree defines a large-scale integer program which is hard to solve even for modern optimization software and powerful workstations. An analysis of specific software configurations indicates a series of alternative solution approaches — from exact methods such as cutting planes to approximate methods such as local search — that can be further explored in order to develop more efficient algorithms.