Inventory and Facility Location Models with Market Selection

We consider important generalizations of a wide class of traditional deterministic inventory and facility location models that we call inventory/facility location models with market selection. Instead of the traditional setting, we are given a set of markets, each specified by a sequence of demands and associated with a revenue. Decisions are made in two stages. We first make a decision of what markets to select, where all other markets are rejected. Next we have to construct a minimum-cost production plan (facility layout) to satisfy all of the demands of all the selected markets. The goal is to minimize the overall lost revenues of rejected markets and the production (facility openings and connection) costs. We show how to leverage existing approximation results for the traditional models to corresponding results for the counterpart models with market selection. More specifically, any LP based α–approximation for the traditional model can be leveraged to a $\frac{1}{_{1-e}-\frac{1}{\alpha}}$- approximation algorithm for the counterpart model with market selection. Our techniques are also applicable to an important class of covering problems.