Multiple –Objective Fractional Costs Transportation Problem with Bottleneck Time and Impurities

Abstract

In various real life applications of nonlinear programming a function is to be maximized or minimized which is characterized by one or several ratios of given functions. Such optimization problems are commonly called Fractional Programming Problems or Fractional Programs. These problems take into account minimizing or maximizing of ratios of physical and/or economic functions, for example profit/capital, total tax/total public expenditure, subject to certain constraints. These optimization problems describe an efficiency measure for a transportation system. In between the two extremes of minimization of cost and time, there exist a number of situations where the decision maker would like a partial trade-off on cost to attain a certain degree of time advantage. This paper presents multiple objective fractional cost-bottleneck time transportation problem with impurity constraints. An algorithm is developed to determine all efficient basic solutions for the problem by lexicographic approach. By means of the primal algorithm, the vector of partial flow is minimized in a lexicographic sense on the feasible set. The Algorithm is based on some duality results of the fractional transportation problem and special structure due to impurity constraints and is supported by a numerical example to determine all efficient transportation schedules.

Keywords:

• Fractional programming
• transportation problem
• multiple objective
• impurity constraints
• efficient transportation schedules