Exact algorithms for integrated facility location and production planning problems

We consider a class of facility location problems with a time dimension, which requires assigning every customer to a supply facility in each of a finite number of periods. Each facility must meet all assigned customer demand in every period at a minimum cost via its production and inventory decisions. We provide exact branch-and-price algorithms for this class of problems and several important variants. The corresponding pricing problem takes the form of an interesting class of production planning and order selection problems. This problem class requires selecting a set of orders that maximizes profit, defined as the revenue from selected orders minus production-planning-related costs incurred in fulfilling the selected orders. We provide polynomial-time dynamic programming algorithms for this class of pricing problems, as well as for generalizations thereof. Computational testing indicates the advantage of our branch-and-price algorithm over various approaches that use commercial software packages. These tests also highlight the significant cost savings possible from integrating location with production and inventory decisions and demonstrate that the problem is rather insensitive to forecast errors associated with the demand streams.