Research on scheduling and planning problems based on simulated annealing algorithm and penalty function approach

Abstract

This paper investigates the scheduling and planning problem within a warehouse allocation framework using a combination of Simulated Annealing (SA) algorithm and penalty function approaches. Initially, a one-to-one warehouse allocation scheme is formulated by considering multiple objectives: minimizing costs, maximizing correlation, utilization rates, and capacity utilization. Each objective is equally weighted (0.25) within a linear programming model, subject to warehouse capacity, production capacity, and allocation count constraints. Penalty terms are introduced for unmet constraints to prevent infeasible solutions. The SA algorithm is then applied to iteratively approach optimal solutions, yielding an objective function value of 299.59. Subsequently, a one-to-many warehouse allocation scheme is explored based on product category correlation. An integer linear programming model rooted in game theory is developed, where product categories act as players deciding on warehouse placements as their strategies. By adjusting weights to prioritize higher correlation and applying stricter penalty terms for constraint violations, the combined SA-penalty function approach is utilized. This results in an objective function value of −31.8113 for the one-to-many scenario.