A heuristic for a special case of the generalized assignment problem with additional conditions

Abstract

We consider the following variant of the generalized assignment problem (GAP). There are a set of agents and a set of jobs for which a single resource use. Each job is to assign to one and only one agent subject to the constraints on the capacity and loading of agents. The resource expense for executing any job is independent of the agents choice unlike the profit from the job. Each job has a certain type (or color). For every agent, the maximum possible number of the job types given. It is necessary to find a feasible assignment of agents to jobs so that all jobs were completed and total profit was maximized. Finding a feasible solution to this problem is NP-hard. We present a heuristic algorithm based on the ideas of random search and local improvement of solutions. Used the mixed-integer programming (MIP) relaxation and variables fixing, we construct a set of integer linear programming (ILP) subproblems similar to the original problem and solve them by the general MIP solver. The results of a computational experiment for tasks with random initial data are presented.