Abstract:
Transportation models are of multidisciplinary fields of interest. Mainly in the business
arena, it is common to encounter the problem of transportation of some products/goods
from source/origin to sink/destination so that cost of transportation is minimal and also
satisfy the constraints related to demand and the supply. A huge number of physical
problems are modeled as Transportation problem (TP) which includes inventory problem,
assignment problem, traffic problem and so on. TPs are required for analyzing and
formulating such models. In order to minimize the transportation cost satisfying all
constraint, transportation model first provides the Initial Basic Feasible Solution (IBFS)
and then IBFS be optimized by some related optimization algorithm if IBFS is not
optimized. So the primary objective of transportation model is to find out a good IBFS of
TPs.
In classical transportation approaches, the flow of allocation is controlled by the cost
entries such as West Corner Method (WCM), Least Cost Method (LCM) etc. and/or
manipulation of cost entries, so called Distribution Indicator (DI) or Total Opportunity
Cost (TOC) like Vogel’s Approximation Method (VAM) and its variations. In LCM, the
flow of allocation is directly controlled by the cost entries i.e. lowest cost prefers first. On
the other hand, for examples, on VAM, its variants and some other methods, the flow of
allocations is controlled by the DI or TOC tables. But these DI or TOC tables are
formulated by the manipulation of cost entries only. None of them considers demand
and/or supply entry to formulate the DI/ TOC table.
In this thesis, we have first developed a new procedure of control of allocation named
Weighted Opportunity Cost (WOC) matrix by incorporating supply/demand entries. At
first, weight factors are formulated by using demand and supply entries which is off-course
statistically valid. Then virtual weighted cost entries are formulated by manipulation of
cost entries along with weight factors. Finally WOC matrix is formulated in which
supply/demand entries acts as weight factor upon corresponding cost entries. Several
examples are provided to demonstrate the concept of WOC matrix.
After successfully development of WOC, our intension is go upon the development of an
algorithm to find out IBFS of TPs. It is known that, in Least Cost Matrix method, the flows
of allocations are controlled by the cost entries only. The flows of allocations are
predefined according to the cost entries i.e the ascending order of cell cost and the
whenever identical costs are encountered whatever be the structure of demand/supply
entries. So, the algorithm does not need to update allocation direction in subsequent steps.
On the other hand in VAM, the flow of allocation is controlled by the DI table rather than
directly cost matrix. By incorporating these two ideas, we have proposed a Weighted
Opportunity Cost based on LCM (WOC-LCM) approach. In this proposed approach, the
flow of allocation is controlled by the WOC matrix rather than cost matrix as in LCM
approach. But WOC matrix is invariant through all over the allocation procedures like cost
matrix in LCM method whereas DI table is updated after each step of allocations. Some
experiments have been carried out to justify the validity and the effectiveness of the
proposed WOC-LCM approach. Experimental results have shown that the WOC-LCM
approach outperforms LCM. Moreover, sometime this approach is able to find out optimal
solution too.
Description:
This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, July 2018.
Cataloged from PDF Version of Thesis.
Includes bibliographical references (pages 45-47).