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

Abstract

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.

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

“…These results are far better than other published metaheuristic results for the MKP. Dellinger et al (2021) employed SSIT to quickly (average of 63 seconds on a standard PC) generate solutions guaranteed to be within 0.08% of the optimum on 51 generalized assignment problem (GAP) instances commonly used in the literature. These results are very competitive with the best published solution methods for the GAP.…”

“…These results are very competitive with the best published solution methods for the GAP. Additionally, in Dellinger et al (2021), both Gurobi and CPLEX were used to solve the GAP instances, and there was no statistically significant difference in solution quality or execution times between Gurobi and CPLEX. Using classification tree analysis, Song et al (2021) classify multi-demand MKPs (MDMKPs) as either easy, moderate, or difficult to solve based on predicted execution time to solve the MDMKP on a standard PC.…”

“…Additionally, in Dellinger et al. (2021), both Gurobi and CPLEX were used to solve the GAP instances, and there was no statistically significant difference in solution quality or execution times between Gurobi and CPLEX. Using classification tree analysis, Song et al.…”

A Feasible Flow-based Algorithm for Solving Classic Assignment Problem with Bottleneck

“…Among the variations of AP presented by researchers were ones to the bottleneck AP [1], the generalized AP, the semi-AP, the quadratic AP, and a variety of others. Also, there were some papers combining two or more of these basic variations [2][3][4].…”