Time Minimizing Solution Procedures for the Transportation Problem with Mixed Constraints

Abstract

The present thesis focuses on the development of methodologies to find an optimal solution of Time Minimizing Transportation Problem with Mixed Constraints (TMTP-MC). To obtain an optimum transportation time of TMTP-MC, four methods are developed along with their algorithms. newlineIn the first method, greatest time cells are avoided for allotment, one by one, in decreasing order of time till the feasibility sustains in the absence of avoided cells. Then, assignment of cells along with objective value, is the optimal solution. newlineSecond method starts with a basic infeasible solution and moving towards a basic feasible solution by updating the basis iteratively. This basic feasible solution is an optimal solution of TMTP-MC. newlineThird approach initiates with a basic feasible solution. A method for finding it, is exclusively developed. To improve that basic feasible solution, allotment of a basic cell with highest time, is shifted to a cell with lesser time than that. In this way, that cell is vacated to reduce the time of transportation. Shifting is made through an open loop initiated with that basic cell and terminated at the cell having lower time. After termination of shifting process, the solution in the transportation table is the optimal solution with corresponding shipment time. newlineIn fourth method, some parameters are introduced to equality constraints of TMTP-MC to analyze the More-for-Less (MFL) paradoxical situation in it. Treating these parameters also as basic variables, a basic infeasible solution is obtained. By updating the basis of the solution iteratively, a basic solution is improved to obtain a basic feasible solution. This solution is the MFL solution, if at least one of the parameters remain in the basis at positive level. Otherwise, the MFL situation does not exist in the problem and the solution obtained is an optimal solution. Through MFL solution, an optimal solution of the problem can also be obtained. newline