Study of two stage transportation problems

Abstract

In this thesis, a class of time minimization transportation problems has been studied where the transportation is done in two stages. Two problems in this regard have been discussed. The First problem focused on the study of two stage bottleneck transportation problem wherein certain situation like storage capacity limitations or lack of maintenance facilities at the production floor the shipment of goods is done in two stages. In the first stage, the minimum requirement of each destination is met and in the second stage the left over the quantities are shipped to destinations. The objective is to find that schedule which minimizes the sum of Stage I and Stage II shipment times. A polynomial time algorithm is discussed to obtain the optimal schedule by investigating the lexicographic feasible solutions of a related standard (TMTP). This problem was first discussed by Sonia and Puri (2002) and later on generalized by Sharma et al. (2010). Another two stage transportation problem has been discussed in the form of a two stage interval time minimization transportation problem, where total availability of a homogeneous product at various sources is known to lie in a specified interval. A polynomial time algorithm is discussed to solve the problem to optimality, where at various steps of the algorithm lexicographic optimal solutions of the restricted versions of a related standard time minimizing transportation problem are examined and finally the global optimal solution is determined. Two different approaches of this problem, one given by Sonia and Puri (2004) and the second approach suggested by Sharma et al. (2008) have been studied.