Multiobjective Interval Transportation Problems: A Short Review
The conventional transportation problem usually involves the transportation of goods from several supply points to different demand points and considers the minimization of the total transportation costs. The transportation problem is a special case of li
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Abstract The conventional transportation problem usually involves the transportation of goods from several supply points to different demand points and considers the minimization of the total transportation costs. The transportation problem is a special case of linear programming models, following a particular mathematical structure, which has a wide range of potential practical applications, namely in logistic systems, manpower planning, personnel allocation, inventory control, production planning and location of new facilities. However, in reality, the transportation problem usually involves multiple, conflicting, and incommensurable objective functions, being called the multiobjective transportation problem. Several methods have been developed for solving this sort of problems with the assumption of precise information regarding sources, destinations and crisp coefficients for the objective function coefficients. Nevertheless, when dealing with real-life transportation problems, these circumstances may not be verified, since the transportation costs may vary as well as supply and demand requirements. Therefore, different approaches for dealing with inexact coefficients in transportation problems have been proposed in scientific literature, namely with the help of fuzzy and interval programming techniques. This paper is aimed at providing a short critical review of some interval programming techniques for solving this particular type of problems.
C. Oliveira Henriques (&) Polytechnic Institute of Coimbra - ISCAC Business School, Quinta Agrícola, Bencanta, 3040-316 Coimbra, Portugal e-mail: [email protected] URL: http://www.iscac.pt D. Coelho Polytechnic Institute of Coimbra - ISEC, Rua Pedro Nunes, Quinta da Nora, 3030-199 Coimbra, Portugal e-mail: [email protected] URL: http://www.isec.pt C. Oliveira Henriques D. Coelho INESC Coimbra, Coimbra, Portugal © Springer International Publishing Switzerland 2017 A.P. Barbosa-Póvoa et al. (eds.), Optimization and Decision Support Systems for Supply Chains, Lecture Notes in Logistics, DOI 10.1007/978-3-319-42421-7_7
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C. Oliveira Henriques and D. Coelho
Keywords Multiobjective transportation problems gramming Interval order relations
Multiobjective interval pro-
1 Introduction The transportation problem (TP) might be seen as a particular case of linear programming (LP) models which is generally used to determine the optimal solution for the distribution of certain goods, from different supply points (sources—e.g. production facilities, warehouses) to different demand points (destinations—e.g. warehouses, sales, outlet), considering that there is a certain distance between these points. The objective function in the TP usually represents the total transportation costs, while the constraints are defined by the supply capacity and demand requirements of certain sources or destinations, respectively. However, in real-life situations the TP usually encompasses multiple, conflicting and incommensurate objective functions (e.g. transportation cost, average delivery
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