Mathematical programming approaches for multi-objective optimization in operations research

Abstract

This study investigates mathematical programming approaches for multi-objective optimization in operations research, specifically addressing trade-offs among cost, efficiency, and time. A structured framework is proposed, formulating problems through decision variables, constraints, and objective functions, and applying Linear Programming (LP), Nonlinear Programming (NLP), and Integer Programming (IP) models. Solution techniques including Weighted Sum, Goal Programming, ε-Constraint, and Evolutionary Algorithms are employed to generate Pareto-optimal solutions. Results indicate that LP achieved a feasible solution of Z = 31.5 with high computational efficiency (0.45 s), NLP attained the highest objective value of Z = 91.4 at the cost of increased computation time (1.25 s), and IP provided a practical discrete solution of Z = 29.0 in 0.95 s. Pareto front analysis demonstrated efficient trade-offs between objectives, while sensitivity analysis revealed that small parameter changes beyond critical thresholds significantly affect outcomes. The study provides a clear methodology for multi-objective decision-making and highlights the strengths and limitations of each approach, offering guidance for future hybrid and robust optimization strategies in complex real-world applications.