Coordinated Capacitated Lot‐Sizing Problem with Dynamic Demand: A Lagrangian Heuristic
研究了多产品共享有限资源时的协调补货问题，提出混合整数规划模型和拉格朗日松弛求解方法，实验显示启发式解平均仅比最优高2.52%，并在行业测试中降低总成本22.5%。
ABSTRACT Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed‐integer programming formulation and Lagrangian relaxation solution procedure for the single‐family coordinated capacitated lot‐sizing problem with dynamic demand. The problem extends both the multi‐item capacitated dynamic demand lot‐sizing problem and the uncapacitated coordinated dynamic demand lot‐sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual‐based heuristic over linear programming‐based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs.