{"title":"Modification of the Clarke and Wright Algorithm with a Dynamic Savings Matrix","authors":"Jan Fikejz, Markéta Brázdová, Ľudmila Jánošíková","doi":"10.1155/2024/8753106","DOIUrl":null,"url":null,"abstract":"<p>The goods collection and delivery process often relates to distribution logistics problems. The task is to deliver goods from warehouses to customers under specific circumstances. Efforts to optimize the process are largely aimed at reducing overall costs of goods transportation. Among the prominent algorithms for solving the basic type of the delivery (or collection) problem, which includes a single depot and a homogeneous vehicle fleet, is the algorithm developed by Clarke and Wright in 1964. This algorithm minimizes transportation costs by maximizing the savings achieved through merging multiple routes into one. This paper primarily aims to solve the pickup and delivery problem where the goods must be delivered and empty packaging collected in a single process. The request of a customer can be routed from the depot or from another customer. Similarly, the destination of the request may be the depot or another customer. Unlike the original version of the Clarke and Wright algorithm, the initial routes are created to satisfy delivery orders, and therefore, the same customer can occur in multiple routes. Consequently, a situation may arise in which two routes containing one or more common vertices must be combined during the calculation. Furthermore, these vertices need not be the outermost vertices of the routes. This situation cannot be addressed by using the original version of the Clarke and Wright algorithm, and that is why we propose its modification. Merging routes through inner vertices means that the cost savings depend on the configurations of the routes, and therefore, they cannot be calculated a priori. Instead, the dynamic savings matrix must be used.</p>","PeriodicalId":50259,"journal":{"name":"Journal of Advanced Transportation","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Advanced Transportation","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2024/8753106","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CIVIL","Score":null,"Total":0}
引用次数: 0
Abstract
The goods collection and delivery process often relates to distribution logistics problems. The task is to deliver goods from warehouses to customers under specific circumstances. Efforts to optimize the process are largely aimed at reducing overall costs of goods transportation. Among the prominent algorithms for solving the basic type of the delivery (or collection) problem, which includes a single depot and a homogeneous vehicle fleet, is the algorithm developed by Clarke and Wright in 1964. This algorithm minimizes transportation costs by maximizing the savings achieved through merging multiple routes into one. This paper primarily aims to solve the pickup and delivery problem where the goods must be delivered and empty packaging collected in a single process. The request of a customer can be routed from the depot or from another customer. Similarly, the destination of the request may be the depot or another customer. Unlike the original version of the Clarke and Wright algorithm, the initial routes are created to satisfy delivery orders, and therefore, the same customer can occur in multiple routes. Consequently, a situation may arise in which two routes containing one or more common vertices must be combined during the calculation. Furthermore, these vertices need not be the outermost vertices of the routes. This situation cannot be addressed by using the original version of the Clarke and Wright algorithm, and that is why we propose its modification. Merging routes through inner vertices means that the cost savings depend on the configurations of the routes, and therefore, they cannot be calculated a priori. Instead, the dynamic savings matrix must be used.
期刊介绍:
The Journal of Advanced Transportation (JAT) is a fully peer reviewed international journal in transportation research areas related to public transit, road traffic, transport networks and air transport.
It publishes theoretical and innovative papers on analysis, design, operations, optimization and planning of multi-modal transport networks, transit & traffic systems, transport technology and traffic safety. Urban rail and bus systems, Pedestrian studies, traffic flow theory and control, Intelligent Transport Systems (ITS) and automated and/or connected vehicles are some topics of interest.
Highway engineering, railway engineering and logistics do not fall within the aims and scope of JAT.