TITLE:
Linear Plus Linear Fractional Capacitated Transportation Problem with Restricted Flow
AUTHORS:
Kavita Gupta, Shri Ram Arora
KEYWORDS:
Transportation Problem; Linear Plus Linear Fractional; Restricted Flow; Corner Feasible Solution
JOURNAL NAME:
American Journal of Operations Research,
Vol.3 No.6,
November
27,
2013
ABSTRACT: In this paper, a transportation problem with
an objective function as the sum of a linear and fractional function is considered. The linear function
represents the total transportation cost incurred when the goods are shipped
from various sources to the destinations and the fractional function gives the
ratio of sales tax to the total public expenditure. Our objective is to
determine the transportation schedule which minimizes the sum of total
transportation cost and ratio of total sales tax paid to the total public
expenditure. Sometimes, situations
arise where either reserve stocks have to be kept at the supply points, for
emergencies or there may be extra demand in the markets. In such situations,
the total flow needs to be controlled or enhanced. In this paper, a special
class of transportation problems is studied where in the total transportation
flow is restricted to a known specified level. A related transportation
problem is formulated and it is shown that to each basic feasible solution
which is called corner feasible solution to related transportation problem,
there is a corresponding feasible solution to this restricted flow problem. The
optimal solution to restricted flow problem may be obtained from the optimal
solution to related transportation problem. An algorithm is presented to solve
a capacitated linear plus linear fractional transportation problem with
restricted flow. The algorithm is supported by a real life example of a
manufacturing company.