An analysis of Weighted Sum Scalarization Approach for Bi-Objective Resource-Constrained Assignment Problems: Special Focus on Balancing Cost Minimization and Profit Maximization with Numerical Case Studies
DOI:
https://doi.org/10.29070/jt3g8t51Keywords:
Multi-Objective Assignment Problem, Weighted Sum Scalarization, Resource-Constrained Optimization, Pareto Efficiency, Cost-Profit Trade-offAbstract
This Study presents the practical implementation and computational validation of a multi-objective assignment framework designed to simultaneously minimize total assignment cost and maximize total profit under realistic operational constraints. Building on the theoretical foundations established in prior Studys, the study formulates a bi-objective assignment model incorporating standard assignment constraints alongside resource limitations such as worker availability, job demand requirements, machine capacities, skill compatibility, and budget restrictions.
A weighted sum scalarization technique is employed to transform the multi-objective problem into a series of single-objective optimization problems, enabling the systematic generation of Pareto-efficient solutions. Interval programming extensions are discussed to handle parameter uncertainty. Detailed numerical experiments on balanced 3×3 and resource-constrained 4×4 assignment problems demonstrate the methodology’s effectiveness, including full enumeration for small instances, dominance analysis, lower-bound heuristics for computational acceleration, and performance comparisons showing significant reductions in solving time for larger instances (n=10 to 30).
The results highlight the trade-offs between conflicting objectives, the impact of resource constraints on feasible assignments, and the robustness of solutions through sensitivity considerations. This work bridges theoretical multi-objective optimization with managerial decision-making, offering a flexible and computationally efficient tool for real-world resource allocation in manufacturing, logistics, and service environments.
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