A Joint Production and Delivery Problem in Multi‐Factory Multi‐Distribution‐Center Multiproduct Systems With Limited Capacities
研究了多工厂多配送中心多产品系统中有限产能下的联合生产与配送问题，提出一种拉格朗日松弛启发式算法，数值实验表明该算法比短视启发式算法损失更小、更稳定。
ABSTRACT We consider a joint production and delivery problem in multi‐factory multi‐DC (distribution center) multiproduct systems with limited production and delivery capacities over a finite horizon. The objective is to minimize the system's expected total cost. Since the structure of the optimal policy is hard to find, we propose a Lagrangian relaxation heuristic to solve the problem. The proposed heuristic is based on solving a Lagrangian relaxation of the original problem. Although the Lagrangian relaxation problem remains challenging due to the joint production and delivery decisions, we identify a zero‐inventory policy that enables further decomposition into independent single‐product, single‐DC subproblems, each of which can be solved independently. We evaluate the heuristic's performance by deriving a theoretical upper bound on its expected loss. In numerical experiments, we compare the Lagrangian relaxation heuristic with a benchmark myopic heuristic. The results consistently show that the Lagrangian relaxation heuristic achieves a significantly smaller expected relative loss and exhibits greater stability than the myopic heuristic.