A three-phase matheuristic algorithm for the multi-day task assignment problem

This paper considers a multi-day task assignment model that introduces several features of practical relevance into the widely-studied generalized assignment problem. This model includes a significantly increased number of variables and constraints compared to the task assignment models investigated in the literature and thus is computationally challenging. For solving this problem, we propose an innovative three-phase matheuristic algorithm that first employs a construction phase to quickly produce a reasonable quality solution and then alternates between an intensification phase to reach local optima and a diversification phase to drive the search into new regions. The construction phase decomposes the original problem into a sequence of smaller subproblems, solves each subproblem with the Gurobi optimizer, and aggregates the solutions from the subproblems to produce a feasible solution. The intensification phase executes an iterative variable fixing heuristic that divides the solution space into different neighborhoods and iteratively explores each neighborhood by solving the reduced model. The diversification phase solves a modified model that adds a distance component into the original objective function. Computational experiments demonstrate that our proposed algorithm outperforms Gurobi, LocalSolver and Tabu Search in terms of both solution quality and computational time. The best solutions found by our algorithm have percentage gaps to the upper bounds (attained by Gurobi and LocalSolver) ranging from 0.82% to 2.79%, indicating that they are very close to the optimal solutions. In addition, experimental analysis has been carried out to identify the impact of some of the key components of the proposed algorithm which are contributing to its superior performance. The benchmark instances generated for our study are made available to the public for future research works on this problem.