A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases with uncapacitated facilities, capacitated facilities, correlated retailer demand, stochastic lead times, and multicommodities. We show how to formulate these problems as conic quadratic mixed-integer problems. Valid inequalities, including extended polymatroid and extended cover cuts, are added to strengthen the formulations and improve the computational results. Compared to the existing modeling and solution methods, the new conic integer programming approach not only provides a more general modeling framework but also leads to fast solution times in general.