A hybrid heuristic algorithm for the sequencing generalized assignment problem in an assembly line

Abstract

The generalized assignment problem (GAP) is an enlarged version of the classical assignment problem in which the assignment of several tasks to an agent is possible. The only restriction that can limit the assignment of the tasks to the agents is the capacity of the agent. In this study, a manpower planning is modeled as a GAP in an assembly line. The considered assembly line consists of a number of workstations in series where each workstation contains several jobs in parallel. The present research seeks to assign the best operator to the jobs in order to minimize the processing time in each workstation and in the whole of the system. The generalized assignment formulation is adapted to this case. A mixed-integer mathematical model is proposed for this problem and proved that the considered problem is NP-complete. The model is solved in various sizes by employing Gurobi mixed-integer solver. This paper presents a greedy heuristic combined with a local search for the generalized assignment problem. The slight deviation from the optimal solutions and the computational times which is extremely reduced, validate the efficiency of the proposed heuristic approach for solving such problems.