A Lexicographic Approach to Sustainable Multi-Objective Assignment Optimization

Abstract

The classical assignment problem allocates jobs to agents while optimizing a single performance criterion. Modern allocation decisions often require simultaneous consideration of economic, operational, resource, and environmental consequences. This paper formulates a four-objective multi-objective assignment problem in which total cost, total completion time, resource consumption, and environmental impact are minimized simultaneously. Binary integer programming is developed for assigning (n) tasks to (n) agents subject to one-to-one assignment constraints. Each task-agent combination is characterized by four coefficients representing cost, time, resource consumption, and environmental burden. Since these objectives may conflict, a single solution that independently minimizes all criteria generally does not exist. The Lexicographic Method is adopted to incorporate explicit priority information from the decision maker. The model provides a transparent framework for sustainable task allocation and can be applied to workforce, machine, logistics, project, and service assignment environments. A numerical instance demonstrates the sequential optimization procedure and resulting trade-offs.