A Simple and Efficient Technique to Generate Bounded Solutions for the Generalized Assignment Problem: A Guide for OR Practitioners

The generalized assignment problem (GAP) is a NP-hard problem that has a large and varied number of important applications in business and industry. Approximate solution approaches for the GAP do not require excessive computation time, but typically there are no guarantees on solution quality. In this article, a methodology called the simple sequential increasing tolerance (SSIT) matheuristic that iteratively uses any general-purpose integer programming software is discussed. This methodology uses a sequence of increasing tolerances in conjunction with optimization software to generate a solution that is guaranteed to be within a specified percentage of the optimum in a short time. SSIT requires no problem-specific coding and can be used with any commercial optimization software to generate bounded solutions in a timely manner. Empirically, SSIT is tested on 51 GAP instances (24 medium and 27 large) in the literature. The performance of CPLEX versus Gurobi on these 51 GAP test instances is also statistically analyzed.