• capacity planning;
  • generalized assignment problem;
  • supply chain management;
  • algorithm;
  • heuristic


We consider a generalization of the well-known generalized assignment problem (GAP) over discrete time periods encompassed within a finite planning horizon. The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single-period assignment costs and agent-capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent. As is the case for its single-period antecedent, MultiGAP offers a robust tool for modeling a wide range of capacity planning problems occurring within supply chain management. We provide two formulations for MultiGAP and establish that the second (alternative) formulation provides a tighter bound. We define a Lagrangian relaxation-based heuristic as well as a branch-and-bound algorithm for MultiGAP. Computational experience with the heuristic and branch-and-bound algorithm on over 2500 test problems is reported. The Lagrangian heuristic consistently generates high-quality and in many cases near-optimal solutions. The branch-and-bound algorithm is also seen to constitute an effective means for solving to optimality MultiGAP problems of reasonable size. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012