Two-phase time minimization transportation problem with the restricted flow

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-09-27 DOI:10.1016/j.matcom.2024.09.030

Supinder Kaur , Kalpana Dahiya , Anuj Sharma

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引用次数: 0

Abstract

Motivated by the hierarchical structure within transportation systems, this paper explores a two-phase time minimization transportation problem with restricted flow (

2 p - T P_{F}

). In this problem, the transportation of products occurs in two distinct phases due to the partition of source–destination links into two separate levels: Level-1 and Level-2 links, with a specified amount of commodity being transported in each phase. For the transportation of a specific quantity of goods during the first phase, only Level-1 links are utilized. Following this, during the second phase of transportation, only Level-2 links are utilized. Transportation is carried out concurrently via numerous source–destination links relevant to each phase. This paper proposes an iterative algorithm (Algorithm-

T P_{F}

) to find an optimal solution for a two-phase time minimization transportation problem that minimizes the sum of Phase-1 and Phase-2 transportation times. The proposed algorithm solves a solid time minimization transportation problem

∖

its restricted version at each iteration. Various theoretical results are proven to support the convergence of the algorithm. Numerical examples of various sizes are provided to support the theoretical results. Computational experiments conducted on randomly generated instances demonstrate the algorithm’s efficiency and convergence. The proposed algorithm offers an alternative method for solving two-phase time minimization transportation problems.

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限制流量的两阶段时间最小化运输问题

受运输系统内部分层结构的启发，本文探讨了限制流量的两阶段时间最小化运输问题（2p-TPF）。在这个问题中，由于源-目的链路被划分为两个不同的层次，产品的运输被分为两个不同的阶段：第 1 层和第 2 层链路，每个阶段运输指定数量的商品。在第一阶段运输特定数量的商品时，只使用一级链接。之后，在第二阶段的运输中，只使用二级链接。运输是通过与每个阶段相关的众多源-目的链路同时进行的。本文提出了一种迭代算法（Algorithm-TPF），用于寻找两阶段时间最小化运输问题的最优解，使第一阶段和第二阶段运输时间之和最小化。所提出的算法每次迭代都会求解一个固态时间最小化运输问题∖其限制版本。各种理论结果证明了算法的收敛性。提供了各种规模的数值示例来支持理论结果。在随机生成的实例上进行的计算实验证明了算法的效率和收敛性。所提出的算法为解决两阶段时间最小化运输问题提供了另一种方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.