A Hybrid Heuristic for a Two-Agent Multi-Skill Resource-Constrained Scheduling Problem

Abstract

This paper addresses an industrial case of the two-agent scheduling problem with a global objective function. Each agent manages one or several projects and competes with another agent for the use of common multi-skilled employees. There is a pool of employees, each of which can perform a set of skills with heterogeneous performance levels. The objectives of the two agents are both to minimize the total weighted tardiness of its tasks. Furthermore, We assume that some constraints (soft constraints) can be violated when there is no feasible schedule for the problem. Thus, the global objective function minimizes the constraint violations by reducing the undesirable deviations in the soft constraints from their respective goals. The overall objective is to find a schedule that minimizes both agents objective functions (local objectives) and the global objective function. We provide a mixed-integer goal programming (MIGP) formulation for the problem. In addition, we present a hybrid algorithm combining an exact procedure, a greedy heuristic, and a genetic algorithm to find an approximate Pareto solution set. We compare the performance of the hybrid algorithm against the corresponding MIGP formulation with simulated instances derived from real-world instances.