ABSTRACT

This paper studies an interval data min–max regret (IDMR) version of the packing-delivery problem, in which a 0-1 knapsack problem is for parcel packing and a capacitated travelling salesman problem is for parcel delivery. The parcel profits for the courier and the tour costs are uncertain and they can take any value from a specific interval with lower and upper bound values. The problem is how to select and deliver a subset of parcels to minimise the maximum regret of net profit which is the difference between the total profits of the selected parcels and the total delivery costs, to deal with the trade-off of the solution robustness and performance. To tackle the problem effectively, we first prove the worst-case scenario of a solution to the problem, based on which, a mixed integer linear programming is formulated. A Benders-like decomposition algorithm is then developed to solve small-scale problems to optimality within the manageable computation time. For medium- and large-scale problems, a simulated-annealing-based heuristic method with a local search procedure is designed. Extensive computational experiments show the efficiency and effectiveness of the proposed methods.

摘要

本文研究了包装递送问题的区间数据最小-最大遗憾 (IDMR) 版本，其中 0-1 背包问题用于包裹包装，而有能力的旅行商问题用于包裹递送。快递员的包裹利润和旅行成本是不确定的，它们可以从具有下限和上限值的特定区间中取任何值。问题是如何选择和投递包裹的子集，以最小化净利润的最大遗憾，即所选包裹的总利润与总投递成本的差值，以处理解决方案鲁棒性和投递成本的权衡。表现。为了有效地解决问题，我们首先证明了问题解决方案的最坏情况，并在此基础上制定了混合整数线性规划。然后开发了类 Benders 分解算法，以在可管理的计算时间内将小规模问题解决到最优。针对大中型问题，设计了一种基于模拟退火的启发式方法和局部搜索程序。大量的计算实验表明了所提出方法的效率和有效性。