Multi-plant manufacturing assortment planning in the presence of transshipments

Abstract

In this study, we consider the assortment planning problem of a manufacturing firm with multiple plants. Making a plant capable of producing a product is costly, therefore the firm cannot manufacture every product in every plant. In case a customer's order in a particular region is not available in the closest plant, another plant can ship the product using transshipment, but at an extra transportation cost. If a demanded product is not produced in any plant, substitution from first choice to a second choice is also considered, which can be either satisfied by the closest plant, or by transshipment. The problem is to jointly determine assortments in all plants such that total profit after assortment and transshipment costs is maximized. The resulting problem is complex as transshipments and substitutions are intertwined to affect assortment decisions. We show that the optimal assortments are nested, i.e., the assortment of a plant with a smaller market share is a subset of the assortment of a plant with a larger share. The common assortment of all locations is shown to be in the popular set (i.e., no leapfrogging in product popularities), and a sufficient condition on substitution rate is derived for each individual assortment to be in the popular set. We conduct an extensive numerical study to understand the effects of allowing transshipments on resulting assortments. Moreover, we introduce approximate assortment planning algorithms that benefit from the derived structural properties, which are shown to generate near-optimal assortments in a broad range of instances tested.