A demand-shifting feasibility algorithm for Benders decomposition

Abstract

Benders decomposition is a popular method for solving problems by resource-directive decomposition. Often, the resource allocations from the master problem lead to infeasible subproblems, as resources are insufficient to meet demand. This generally requires the use of feasibility cuts to reach a feasible solution, which can be computationally expensive. For problems in which subproblems have limited capacity, we propose an efficient algorithm which shifts excess demand to other sources of capacity. The advantages of the algorithm are that it is quick, requires only one solution of each subproblem in each Benders iteration, and does not add any feasibility cuts into the master problem. A computational study is performed on a fleet sizing problem to illustrate the algorithm’s efficiency when compared to the traditional feasibility cut method.