双目标两阶段运输问题
Bi-objective Two Phase Transportation Problem
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- University Institute of Engineering and Technology, Panjab University（潘杰布大学工程技术学院）
- Department of Mathematics, Panjab University（潘杰布大学数学系）
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中文总结 AI 辅助
本文研究双目标两阶段运输问题，开发多项式时间迭代算法BTPTP-Algorithm，可求得其所有非支配解，且通过数值示例验证了算法的理论与计算性能。
中文摘要 AI 辅助
本文讨论一种双目标两阶段运输问题（Bi-objective two-phase transportation problem，BTPTP），其中运输分为两个阶段进行：全部源-汇链路被划分为两个不相交集合，即阶段I和阶段II；仅当阶段I的源-汇链路运输完成后，才会开展阶段II的源-汇链路运输，且各阶段内的源-汇链路运输并行进行。本文研究的问题旨在同时最小化两个目标：两个阶段的总运输时间与总运输成本。由于目标具有冲突性，本文开发了一种多项式时间迭代算法，命名为BTPTP-Algorithm，该算法可求得问题的所有非支配解。在每次迭代中，BTPTP-Algorithm求解若干特定的受限成本最小化运输问题，得到对应的最优可行解；各问题中对阶段I和阶段II源-汇链路施加的限制，取决于前一步骤得到的对应阶段I和阶段II的运输时间。该算法的设计可系统地剔除所有支配解并记录问题的所有非支配解，本文提供了BTPTP-Algorithm能记录所有非支配点的证明。此外，本文针对不同规模的多个BTPTP实例，以CPU时间为指标，给出了数值示例以支撑BTPTP-Algorithm的理论与计算性能。
英文摘要
This paper discusses a bi-objective two-phase transportation problem (BTPTP) in which transportation takes place in two phases. The whole set of source-destination links is partitioned into two disjoint sets namely, Phase-I and Phase-II. The transportation among the source-destination links of Phase-II set is done only after the transportation among the source-destination links of Phase-I set is complete. The transportation among the source-destination links in each phase is done in parallel. The problem discussed in this paper concentrates on minimizing two objectives viz., sum of transportation times and sum of transportation costs of both the phases, simultaneously. Due to conflicting nature of the objectives, a polynomial time iterative algorithm named as BTPTP-Algorithm is developed that finds all of its non-dominated solutions. At each iteration, the BTPTP-Algorithm solves some specific restricted cost minimizing transportation problems and finds corresponding optimal feasible solutions. The restrictions imposed on the source-destination links of Phase-I and Phase-II sets, in each of these problems, depend upon their corresponding Phase-I and Phase-II transportation times obtained at the previous step. The algorithm is developed in such a way that it expels all the dominated solutions and records all the non-dominated solutions of the problem, systematically. A proof of the BTPTP-Algorithm's capability of recording all the non-dominated points is provided. Further, a numerical illustration is given in support of the theory and computational behavior of the BTPTP-Algorithm for various BTPTP instances of different sizes, is provided in terms of CPU time.
