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A review on fuzzy and stochastic extensions of the multi index transportation problem

The classical transportation problem (having source and destination as indices) deals with the objective of minimizing a single criterion, i.e. cost of transporting a commodity. Additional indices such as commodities and modes of transport led to the Multi Index transportation problem. | Yugoslav Journal of Operations Research 27 (2017), Number 1, 3-29 DOI: 10.2298/YJOR150417007S A REVIEW ON FUZZY AND STOCHASTIC EXTENSIONS OF THE MULTI INDEX TRANSPORTATION PROBLEM Sungeeta SINGH Department of Mathematics, Amity University, Gurgaon, Haryana, India, ssingh1@ggn.amity.edu Renu TULI Department of Mathematics, Amity School of Engineering and Technology, Bijwasan, New Delhi, India, rtuli@amity.edu Deepali SARODE Department of Mathematics, Amity University, Gurgaon, Haryana, India, dimple1579@gmail.com Received: April 2015 / Accepted: January 2016 Abstract: The classical transportation problem (having source and destination as indices) deals with the objective of minimizing a single criterion, i.e. cost of transporting a commodity. Additional indices such as commodities and modes of transport led to the Multi Index transportation problem. An additional fixed cost, independent of the units transported, led to the Multi Index Fixed Charge transportation problem. Criteria other than cost (such as time, profit etc.) led to the Multi Index Bi-criteria transportation problem. The application of fuzzy and stochastic concept in the above transportation problems would enable researchers not only to introduce real life uncertainties but also to obtain solutions of these transportation problems. The review article presents an organized study of the Multi Index transportation problem and its fuzzy and stochastic extensions till today, and aims to help researchers working with complex transportation problems. Keywords: Multi Index Transportation Problem, Fixed Charge, Bi-Criteria, Fuzzy Numbers, Stochastic Concept. MSC: 90B06, 03E72. 4 S.Singh,R.Tuli,D.Sarode / A Review on Fuzzy and Stochastic Extensions 1. INTRODUCTION The classical transportation problem (TP) with the objective of minimizing cost of transportation of a single commodity from m sources to n destinations is well studied in literature. The classical TP considered two indices, source and .