Mixed-integer programming formulations for resource scheduling and operational planning in industrial networks

Abstract

Problems related to mixed-integer programming with respect to resource scheduling and operational planning need mathematical models that can incorporate both discreteness, continuity and conflicting objective functions. Traditional methods of mixed-integer programming are effective in expressing feasibility constraints and combinatorial structures of the decision process; but they do not have explicit ways of balancing worst-case objective behavior when the objective function is multi-objective. In this research, a framework of mixed-integer minimax optimization that utilizes minimax robustness with mixed-integer decision process modeling is introduced as an approach for balanced optimization in a constrained environment. The proposed formulation is an amalgam of continuous resource variables, discrete scheduling variables, logic constraints, and multi-objective functions expressed as a minimax objective. Existence of optimal solutions and relaxations-based bounds that enable the implementation of the branch-and-bound optimization method are analyzed theoretically. The computational model is tested numerically by using 50 decision variables, 120 constraints, and different optimization cases. The proposed Minimax-MIP model resulted in an objective function value of 118.7 with a minimized optimality gap of 1.9% compared with the other methods, including linear programming relaxation, genetic optimization, and traditional MIP optimization methods. The convergence and sensitivity analysis show the efficiency of the model.