Geodesic
Pickup and delivery problem with split demand and transfers
Kybernetika, Tome 49 (2013) no. 5, pp. 755-764 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We deal with a logistic problem motivated by a case study from a company dealing with inland transportation of piece goods in regular cycles. The problem consists in transportation of goods among regional centres – hubs of a network. Demands on transportation are contained in a matrix of flows of goods between pairs of hubs. The transport is performed by vehicles covering the shipping demands and the task is to design a cyclical route and to place a depot for each vehicle. The route depot can be placed in any hub of the route. Goods can be transferred from one route and vehicle to another route and vehicle. The aim is to minimize the total transportation cost. The task is classified as a new case of the pickup and delivery problem with split demand and transfers (SDPDPT). We propose a mathematical model and prove NP-hardness of the problem. We study demand reducibility. We also deal with skip pickup and delivery problem as a special case and show its complexity.
We deal with a logistic problem motivated by a case study from a company dealing with inland transportation of piece goods in regular cycles. The problem consists in transportation of goods among regional centres – hubs of a network. Demands on transportation are contained in a matrix of flows of goods between pairs of hubs. The transport is performed by vehicles covering the shipping demands and the task is to design a cyclical route and to place a depot for each vehicle. The route depot can be placed in any hub of the route. Goods can be transferred from one route and vehicle to another route and vehicle. The aim is to minimize the total transportation cost. The task is classified as a new case of the pickup and delivery problem with split demand and transfers (SDPDPT). We propose a mathematical model and prove NP-hardness of the problem. We study demand reducibility. We also deal with skip pickup and delivery problem as a special case and show its complexity.
Classification : 90B06, 90B35, 90B90, 90C10
Keywords: pickup and delivery problem; case study; integer programming; skip transportation 
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     author = {Pelik\'an, Jan},
     title = {Pickup and delivery problem with split demand and transfers},
     journal = {Kybernetika},
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Pelikán, Jan. Pickup and delivery problem with split demand and transfers. Kybernetika, Tome 49 (2013) no. 5, pp. 755-764. http://geodesic.mathdoc.fr/item/KYB_2013_49_5_a5/

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