SPECIFIED FLOW IN A NON LINEAR CAPACITATED TRANSPORTATION PROBLEM (original) (raw)

ENHANCED FLOW IN A NON LINEAR CAPACITATED TRANSPORTATION PROBLEM MOAZZAM ARIF

The present paper presents an algorithm to find optimum time-cost trade off pairs in a fixed charge linear capacitated transportation problem with enhanced flow. Sometimes, situations arise where either reserve stocks have to be kept at supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. Moreover, sometimes a fixed charge (like set up cost for machines, landing fees at an airport, cost of renting a vehicle) is also associated with every origin that gives rise to fixed charge problem. In this paper a special class of transportation problem is studied, where the total transportation flow is enhanced to a specified level. A numerical example is given to illustrate the developed algorithm.

A Note on Feasibility and Optimality of Transportation Problem

Journal of the Institute of Engineering, 2014

Transportation problem is one of the predominant areas of operations research, widely used as a decision making tool in engineering, business management and many other fields. In this paper, we present a brief literature review of transportation problem with its mathematical models in balanced and unbalanced cases. We report the basic feasible solution and hence the methods to attain optimal solution of the balanced transportation problem. Finally, we describe the primal-dual case of the problem with counter examples.

An algorithm for solving a capacitated indefinite quadratic transportation problem with enhanced flow

Yugoslav Journal of Operations Research, 2014

The present paper discusses enhanced flow in a capacitated indefinite quadratic transportation problem. Sometimes, situations arise where either reserve stocks have to be kept at the supply points say, 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 the total transportation flow is enhanced to a known specified level. A related indefinite quadratic transportation problem is formulated, and it is shown that to each basic feasible solution called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this enhanced flow problem. The optimal solution to enhanced flow problem may be obtained from the optimal solution to the related transportation problem. An algorithm is presented to solve a capacitated indefinite quadratic transportation problem with enhanced flow. Numerical ill...

IJMIE A Monthly Double-Blind Peer Reviewed Refereed Open Access International e-Journal -Included in the International Serial Directories Restricted Flow In A Non Linear Capacitated Transportation Problem With Bounds on Rim Conditions KAVITA GUPTA

This paper discusses restricted flow in a fixed charge capacitated transportation problem with bounds on total source availabilities and total destination requirements. The objective function is the sum of two linear fractional functions consisting of variable costs and fixed charges respectively. Sometimes, situations arise when one wishes to keep reserve stocks at the sources for emergencies , thereby restricting the total transportation flow to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution 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 non linear capacitated transportation problem with restricted flow. Numerical illustration is included in support of theory.

Linear Plus Linear Fractional Capacitated Transportation Problem with Restricted Flow

American Journal of Operations Research, 2013

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.

A Brief Overview of the Classical Transportation Problem

JOURNAL OF XI'AN UNIVERSITY OF ARCHITECTURE & TECHNOLOGY, 2020

The classical transportation problem (TP) is a distribution problem where commodities are transferred from many sources to many destinations with a least total cost. Also, TP considered as one of the classification of a linear programming (LP) problem, and it has a great alliance to inaugurate the linear program and its solution procedure. The variations of classical TP generally depend on the supply and demand constraints. The effectiveness of the algorithm for solving TP is determined by the closeness to the least cost solution to the TP. In this paper, the existence of solution to the TP, the basic theorems of classical TP, are stated and proven in a new manner. Also, an analysis has been performed to indicate the limitations of the existing solution procedures. Finally, the necessary and sufficient conditions are carried out for the optimality to the TP.

Multi-location transshipment problem with capacitated transportation

European Journal of Operational Research, 2006

We consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, transfer of a product among locations at the same echelon level. We incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the locationÕs transshipment policy. We model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, we show the impact of transshipment capacity between stocking locations on system behavior. We observe that transportation capacity constraints not only increase total cost, they also modify the inventory distribution throughout the network.

On the Optimization of Transportation Problem

British Journal of Mathematics & Computer Science, 2016

The Transportation Problem which deals with the distribution of commodities from a variety of sources to a variety of destinations was considered in this research. In this work, existing theorems such as the duality theorems and complementary slackness theorem were used to analyse the transportation problem and their applicability was observed. Illustration was made with data gathered from a real-life production company (Owerri, Port-Harcourt and Enugu plants). The data collected was modeled as a Linear Programming Problem of the transportation type and solved with TORA optimization software (VAM-MODI Method) to generate an optimal and feasible solution. It was observed that the cost of transportation of finished Returnable Glass Bottle products of the company for a month was in general reduced by 11.58%.

An Effective Modification to Solve Transportation Problems: A Cost Minimization Approach

It is well-known that Linear Programming Problem (LPP) is one of the most potential mathematical tools for efficient allocation of operational resources. Many problems in real situation can be formulated as LPP. When a situation can be entirely modeled as a network, very efficient algorithms exist for the solution of the optimization problem which is many times more efficient than the solution methods of LPP. Transportation problems (TP), as is known, are a basic network problem which can be formulated as a LPP. The main objective of TP is to minimize the transportation cost of distributing a product from a number of sources (e.g. factories) to a number of destinations (e.g. ware houses). It is to be mentioned that Balanced TP and Unbalanced TP are the types of TP. If the sum of the supplies of all the sources is equal to the sum of the demands of all the destinations, the problem is termed as a balanced transportation problem. Again, if the sum of the supplies of all the sources is not equal to the sum of the demand of all the destinations, the problem is termed as unbalanced transportation problem. Here we have developed a new method of finding an Initial Basic Feasible Solution (IBFS) for both the Balanced TP and Unbalanced TP.

AN ALGORITHM TO FIND OPTIMUM TIME COST TRADE OFF PAIRS IN A FIXED CHARGE LINEAR CAPACITATED TRANSPORTATION PROBLEM WITH ENHANCED FLOW MOAZZAM ARIF

The present paper presents an algorithm to find optimum time-cost trade off pairs in a fixed charge linear capacitated transportation problem with enhanced flow. Sometimes, situations arise where either reserve stocks have to be kept at supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. Moreover, sometimes a fixed charge (like set up cost for machines, landing fees at an airport, cost of renting a vehicle) is also associated with every origin that gives rise to fixed charge problem. In this paper a special class of transportation problem is studied, where the total transportation flow is enhanced to a specified level. A numerical example is given to illustrate the developed algorithm.