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A priority based time minimization transportation problem

This paper discusses a priority based time minimizing transporation problem in which destinations are prioritized so that the material is supplied, based upon the priorities of the destinations. All the destinations, which are at priority, are served first in Stage-I while the demands of the secondary destinations are met in Stage-II. It is assumed that secondary transportation can not take place until the primary transportation is done. | Yugoslav Journal of Operations Research 28 (2018), Number 2, 219–235 DOI: https://doi.org/10.2298/YJOR170512008K A PRIORITY BASED TIME MINIMIZATION TRANSPORTATION PROBLEM Bindu KAUSHAL Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University For Women, Kashmere Gate, Delhi, INDIA bindukaushal27@gmail.com Shalini ARORA Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University For Women, Kashmere Gate, Delhi, INDIA shaliniarora@igdtuw.ac.in Received: May 2017 / Accepted: February 2018 Abstract: This paper discusses a priority based time minimizing transporation problem in which destinations are prioritized so that the material is supplied, based upon the priorities of the destinations. All the destinations, which are at priority, are served first in Stage-I while the demands of the secondary destinations are met in Stage-II. It is assumed that secondary transportation can not take place until the primary transportation is done. The purpose is to transport in such a manner that the sum of the transportation time of primary and secondary destinations is minimum. To achieve this, two approaches are proposed. In the first approach, primary destinations are served optimally by giving weights while in the second approach, lexicographic optimization is used. From the generated pairs, the minimum sum of times corressponding to Stage-I and Stage-II times is picked up as the optimal solution. It is also shown, through Computational Details, that the lexicographic optimization converges to the optimal solution faster than the first approach as reported in Table 4. Keywords: Time Minimizing Transportation Problem(TMTP), Non Linear Programming(NLP) , Lexicographic Solution. MSC: 90B85, 90C26. 1. INTRODUCTION Time minimizing transportation is an important class of transportation problem. In this, concave function is optimized over a convex polytope and for this 220 B.Kaushal and S.Arora / Priority Based Time .