Abstract: Equipment maintenance material is important resource for conducting equipment maintenance and support tasks in wartime, and maintaining the combat effectiveness of the army. The supply of wartime equipment maintenance material has the features of multi-subjects, multi-ways, multi-phases, and multi-optimization problems. Multi-subject represents the demand side (the army), transportation side, and supply side including the rear and field warehouses. Multi mode means that the supply of equipment maintenance material can be fulfilled by multiples ways, such as direct supply from the rear warehouses, supply from the field warehouses, and lateral transshipment. Multi-phase means the supply task usually has multiple phases since the military operation generally includes more than one phase. Multi-optimization problem means that a complete equipment maintenance material supply plan needs to solve various typical optimization problems such as field warehouse location selection, demand allocation, supply mode selection, warehouse inventory control, transportation vehicle route planning, etc.
   Therefore, the paper describes the above-mentioned equipment maintenance material supply problem from the overall perspective and define it as a combinatorial location-inventory-routing problem that simultaneously make decisions on field warehouse location selection, demand allocation, inventory control, and vehicle route planning. A multi-stage and multi-level material supply mode was built considering direct supply from the rare warehouse, hierarchical supply from field warehouses, and lateral transshipment between troops. A mixed integer linear programming model with the goal of minimizing the total supply cost is then formulated. Specifically, the total cost includes four parts, i.e., the of ordering cost of material from the rear warehouse, the opening cost of field warehouses, inventory costs, and transportation costs. The model considers lateral transshipment under limited transportation capacity between troops and will evaluate its impact on the objective function value in the numerical experiment.
   In terms of algorithm design, the problem studied in the paper is NP-hard, which has high complexity and difficulty in solving, and requires the development of efficient heuristic algorithms. Therefore, the paper introduces the simulated annealing into the logic-based Benders decomposition algorithm to form an efficient heuristic algorithm. The basic principle is to decompose the original problem into a main problem and a subproblem and solve them iteratively. The main problem is to determine the location selection of field warehouses, demand allocation, and inventory control. The solution obtained after solving the main problem is used as the lower bound of the original problem, and the solution of the relevant variables is transmitted to the subproblem, so that the subproblem can be described as a series of classical traveling salesman problems. The simulated annealing method is used to quickly solve the subproblem, and the complete solution of the original problem is obtained as the upper bound of the original problem. The optimality Benders cuts based on the upper bound value are then generated and returned to the main problem for the next iteration. As the number of iterations increases, the difference between the upper and lower bounds gradually decreases. When the upper and lower bounds are equal or other predetermined termination conditions are reached, the iteration process stops and the final solution to the problem is obtained.
   In order to verify the effectiveness of the algorithm proposed in the paper, numerical experiments were conducted using sample data. The experimental results showed that: 1)The LBBD algorithm proposed in this paper can effectively reduce problem complexity and improve solution quality. The total cost of the supply solution obtained by the LBBD algorithm is 41.62% lower than that obtained by the CPLEX solver. 2)Considering lateral transshipment can effectively reduce total cost by 6.24%, and can improve the flexibility of the supply system.

Key words: equipment maintenance material, location-inventory-routing, combinatorial optimization, lateral transshipment, logic-based Benders decomposition

摘要： 装备维修器材的精确、定量和快速供应是部队遂行作战、训练等任务的重要物质保证。针对多阶段装备维修器材供应问题,考虑多种器材供应方式,构建装备维修器材多级供应模式。为提升器材供应方案的全局最优性,将野战仓库选址、器材库存控制及运输车辆路径规划等关键问题融合为一类选址-库存-路径组合优化问题,以总成本最小为目标,考虑部队级仓库间的横向供应方式,构建混合整数线性规划模型。设计一种基于逻辑的Benders分解算法,将原问题分解为主问题和子问题,通过生成Benders切割迭代求解。通过示例分析证明:①本文所提出的LBBD算法能够有效降低问题复杂度,提升求解质量,LBBD算法得出的供应方案总成本比CPLEX求解器得出方案成本低41.62%;②考虑横向供应能够有效降低保障费用,考虑横向供应能够使总成本降低6.24%,同时,考虑横向供应可提高装备维修器材供应系统的灵活性。

关键词: 装备维修器材, 选址-库存-路径, 组合优化, 横向供应, 基于逻辑的Benders分解