Title: On a class of capacitated transshipment problems with bounds on rim conditions

Authors: Archana Khurana; Tripti Verma

Addresses: School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Dwarka Sector-16C, Delhi 110075, India ' School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Dwarka Sector-16C, Delhi 110075, India

Abstract: The transshipment technique is used to find the shortest route from one point in a network to another point and is useful to truncate the cost of transportation. Inspired by dead mileage problem evaluated in terms of running empty buses from various depots to starting points, in this paper we study capacitated transshipment problems with bounds on total availabilities at sources and total destination requirements. Sometimes because of the budget/political constraints, the total flow of transportation is stipulated by some external decision maker which thereby results in impaired or enhanced flow in the market. This motivated us to explore such problems as a particular case of the original problem. The optimal solution of the specified problem is obtained by transforming it into an equivalent capacitated transportation problem. We have also discussed various situations emerging out of unbalanced capacitated transshipment problems in the form of inequalities and numerical examples are also given to illustrate the theory.

Keywords: dead mileage; capacitated transshipment problem; impaired flow; enhanced flow; bounds; rim conditions; transport costs; empty buses.

DOI: 10.1504/IJMOR.2015.069142

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.3, pp.251 - 280

Received: 03 Jan 2013
Accepted: 26 Oct 2013
Published online: 30 Apr 2015 *

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