Abstract
This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the environment of utility function approach. MCMTP is converted to multi-objective transportation problems (MOTP) by transforming the multi-choice parameters like cost, demand, and supply to real-valued parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTP are solved by goal programming (GP) approach. Using GP, the solution of MOTP may not be satisfied all the time by the decision maker (DM) when the proposed problem contains interval-valued aspiration level. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and utility function into the MOTP and then compared the solution between them. Finally, numerical examples are presented to show the feasibility and usefulness of our paper.
Highlights
The transportation problem is the central nerve system to keep the balance in economical world from ancient day until today
The main motivation of this paper is to investigate the better solution of multi-choice multi-objective transportation problem (MCMTP) by using utility function approach and compare the solutions to other methods such as goal programming (GP) and revised multi-choice goal programming (RMCGP)
Results and discussion for problem given in case 1 Using LINGO software, we solved Models 3A, 3B, and 3C and reported the solution as follows: The optimal solution of Model 3A is reported as x11 = 0, x12 = 9, x13 = 1, x21 = 0, x22 = 0, x23 = 9, x31 = 6, x32 = 0, x33 = 0; Z1 = 209.1, Z2 = 1559, Z3 = 214.5
Summary
The transportation problem is the central nerve system to keep the balance in economical world from ancient day until today. In real-life applications, all the parameters of the transportation problem are not generally defined precisely Keeping this point of view, in this paper, we have incorporated with multi-choice multi-objective transportation problem (MCMTP) considering the parameters of transportation problem as multi-choice type. If there may be several choices involved associated with the transportation parameters like cost, supply, or demand, the decision maker is confused to select the proper choice for these parameters. In this circumstances, the study of transportation problem creates a new direction which is called multi-choice multiobjective transportation problem. Though the multi-choice concept discussed in both the papers of Chang [1,2] is totally related to the goals of objective functions, recently, Mahapatra et al [3] and Roy et al [4] discussed the multi-choice stochastic transportation problem involving extreme value distribution and exponential distribution in which the multi-choice concept involved only in the cost parameters
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