tailieunhanh - Time minimizing transportation problem with fractional bottleneck objective function

This paper is aimed at studying the Time Minimizing Transportation Problem with Fractional Bottleneck Objective Function (TMTP-FBOF). TMTP-FBOF is related to a Lexicographic Fractional Time Minimizing Transportation Problem (LFTMTP), which will be solved by a lexicographic primal code. An algorithm is also developed to determine an initial efficient basic solution to this TMTP-FBOF. The developed TMTPFBOF Algorithm is supported by a real life example of Military Transportation Problem of Indian Army. | Yugoslav Journal of Operations Research 22 (2012), Number 1, 115-129 DOI: TIME MINIMIZING TRANSPORTATION PROBLEM WITH FRACTIONAL BOTTLENECK OBJECTIVE FUNCTION M. JAIN Department of Mathematics, . Institute of Technology, Mathura, India madhuridayalbagh@ . SAKSENA Faculty of Engineering, Dayalbagh Educational Institute, Dayalbagh, Agra, India premkumarsaksena@ Received: August 2010 / Accepted: January 2012 Abstract: This paper is aimed at studying the Time Minimizing Transportation Problem with Fractional Bottleneck Objective Function (TMTP-FBOF). TMTP-FBOF is related to a Lexicographic Fractional Time Minimizing Transportation Problem (LFTMTP), which will be solved by a lexicographic primal code. An algorithm is also developed to determine an initial efficient basic solution to this TMTP-FBOF. The developed TMTPFBOF Algorithm is supported by a real life example of Military Transportation Problem of Indian Army. Keywords: Time transportation, lexicographic, optimization, fractional programming. MSC: 90C08, 90C05. 1. INTRODUCTION Transportation Problem with a bottleneck objective function is generally known as time minimizing transportation problem or bottleneck transportation problem, where a feasible transportation schedule is to be found, which minimizes the maximum of transportation time needed between a supply point and a demand point such that the distribution between the two points is positive. Seshan and Tikekar [4] presented a time 116 M. Jain, . Saksena / Time Minimizing Transportation minimizing transportation problem to determine the set S hk of all non basic cells which when introduced into the basis either eliminate a given basic cell (h, k ) from the basis or reduce their amount. Achary and Seshan [1] discuss a time minimizing transportation problem based on a more general and realistic assumption that the time tij ( xij ) required for transporting xij units from the i th source to the j th .