The continuous-time single-sourcing problem with capacity expansion opportunities

This paper develops a new model for allocating demand from retailers (or customers) to a set of production/storage facilities. A producer manufactures a product in multiple production facilities, and faces demand from a set of retailers. The objective is to decide which of the production facilities should satisfy each retailer's demand, in order to minimize total production, inventory holding, and assignment costs (where the latter may include, for instance, variable production costs and transportation costs). Demand occurs continuously in time at a deterministic rate at each retailer, while each production facility faces fixed-charge production costs and linear holding costs. We first consider an uncapacitated model, which we generalize to allow for production or storage capacities. We then explore situations with capacity expansion opportunities. Our solution approach employs a column generation procedure, as well as greedy and local improvement heuristic approaches. A broad class of randomly generated test problems demonstrates that these heuristics find high quality solutions for this large-scale cross-facility planning problem using a modest amount of computation time.