Optimization Methods for Multi-phase Equipment Maintenance Material Supply Considering Lateral Transshipment
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 prob-lems.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 gener-ally 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 intro-duces 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.
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