Three new methods to find initial basic feasible solution of transportation problems

2017 ◽  
Vol 11 ◽  
pp. 1803-1814 ◽  
Author(s):  
Eghbal Hosseini
Keyword(s):  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
New Methods

scholarly journals New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems

2015 ◽  
Vol 05 (10) ◽  
pp. 634-640 ◽  
Author(s):  
Mollah Mesbahuddin Ahmed ◽  
Md. Amirul Islam ◽  
Momotaz Katun ◽  
Sabiha Yesmin ◽  
Md. Sharif Uddin
Keyword(s):  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Transportation Problems

scholarly journals Solving transportation problem using modified ASM method

2021 ◽  
Vol 2106 (1) ◽  
pp. 012029
Author(s):  
Nopiyana ◽  
P Affandi ◽  
A S Lestia
Keyword(s):  
Feasible Solution ◽  
Maximum Amount ◽  
Optimal Solutions ◽  
Direct Solution ◽  
Objective Functions ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Research Procedure ◽  
The Cost

Abstract Transportation problems are related to activities aimed at minimizing the cost of distributing goods from a source to a destination. One of the methods used to solve transportation problems is the ASM Method as a method capable of producing optimal direct solutions without having to determine the initial basic feasible solution first. Determination of the allocation of goods in the ASM Method uses a reduced cost of 0 by calculating the maximum amount in the allocation of goods. Then the ASM method is modified so that the iteration used is simpler in obtaining the optimal direct solution without calculating the maximum number of row and column elements. The method is called Modified ASM Method. This method also provides more optimal results than the ASM method. This research aimed to solve transportation problems using the Modified ASM method to produce optimal solutions directly. The research procedure identifies and forms a model of transportation problems (variable decisions, objective functions and constraint functions), identifies types of transportation problems (balanced or unbalanced), and obtains direct solutions by solving transportation problems using the Modified ASM method. This research shows that the Modified ASM method successfully solves the problem of balanced and unbalanced transportation by producing optimal solutions in a simpler way than the ASM method.

scholarly journals Sequentially Updated Weighted Cost Opportunity Based Algorithm in Transportation Problem

2019 ◽  
Vol 38 ◽  
pp. 47-55
Author(s):  
ARM Jalal Uddin Jamali ◽  
Pushpa Akhtar
Keyword(s):  
Opportunity Cost ◽  
Feasible Solution ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Basic Feasible Solution ◽  
New Approach ◽  
Cost Matrix ◽  
Transportation Problems ◽  
The Cost ◽  
First Time

Transportation models are of multidisciplinary fields of interest. In classical transportation approaches, the flow of allocation is controlled by the cost entries and/or manipulation of cost entries – so called Distribution Indicator (DI) or Total Opportunity Cost (TOC). 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. Recently authors have developed weighted opportunity cost (WOC) matrix where this weighted opportunity cost matrix is formulated by the manipulation of supply and demand entries along with cost entries as well. In this WOC matrix, the supply and demand entries act as weight factors. Moreover by incorporating this WOC matrix in Least Cost Matrix, authors have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems. But in that approach, WOC matrix was invariant in every step of allocation procedures. That is, after the first time formulation of the weighted opportunity cost matrix, the WOC matrix was invariant throughout all allocation procedures. On the other hand in VAM method, the flow of allocation is controlled by the DI table and this table is updated after each allocation step. Motivated by this idea, we have reformed the WOC matrix as Sequentially Updated Weighted Opportunity Cost (SUWOC) matrix. The significance difference of these two matrices is that, WOC matrix is invariant through all over the allocation procedures whereas SUWOC   matrix is updated in each step of allocation procedures. Note that here update (/invariant) means changed (/unchanged) the weighted opportunity cost of the cells. Finally by incorporating this SUWOC matrix in Least Cost Matrix, we have developed a new approach to find out Initial Basic Feasible Solution of Transportation Problems.  Some experiments have been carried out to justify the validity and the effectiveness of the proposed SUWOC-LCM approach. Experimental results reveal that the SUWOC-LCM approach outperforms to find out IBFS. Moreover sometime this approach is able to find out optimal solution too. GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 47-55

scholarly journals THE MAXIMUM RANGE COLUMN METHOD – GOING BEYOND THE TRADITIONAL INITIAL BASIC FEASIBLE SOLUTION METHODS FOR THE TRANSPORTATION PROBLEMS

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Huzoor Bux Kalhoro
Keyword(s):  
Feasible Solution ◽  
The Other ◽  
Benchmark Problems ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Traditional Methods ◽  
Transportation Problems ◽  
North West ◽  
Column Method ◽  
Maximum Range

The transportation problems (TPs) are a fundamental case-study topic in operations research, particularly in the field of linear programming (LP). The TPs are solved in full resolution by using two types of methods: initial basic feasible solution (IBFS) and optimal methods. In this paper, we suggest a novel IBFS method for enhanced reduction in the transportation cost associated with the TPs. The new method searches for the range in columns of the transportation table only, and selects the maximum range to carry out allocations, and is therefore referred to as the maximum range column method (MRCM). The performance of the proposed MRCM has been compared against three traditional methods: North-West-Corner (NWCM), Least cost (LCM) and Vogel’s approximation (VAM) on a comprehensive database of 140 transportation problems from the literature. The optimal solutions of the 140 problems obtained by using the TORA software with the modified distribution (MODI) method have been taken as reference from a previous benchmark study. The IBFSs obtained by the proposed method against NWCM, LCM and VAM are mostly optimal, and in some cases closer to the optimal solutions as compared to the other methods. Exhaustive performance has been discussed based on absolute and relative error distributions, and percentage optimality and nonoptimality for the benchmark problems. It is demonstrated that the proposed MRCM is a far better IBFS method for efficiently solving the TPs as compared to the other discussed methods, and can be promoted in place of the traditional methods based on its performance.

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

2014 ◽  
Vol 24 (2) ◽  
pp. 217-236 ◽  
Author(s):  
Kavita Gupta ◽  
S.R. Arora
Keyword(s):  
Special Class ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Flow Problem ◽  
Optimal Solution ◽  
Total Flow ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Indefinite Quadratic

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 illustrations are also included in support of the theory. Computational software GAMS is also used.

scholarly journals A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 9 (3) ◽  
pp. 90-122 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number

This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport celled conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.

scholarly journals Overview of Optimality of New Direct Optimal Methods for the Transportation Problems

2019 ◽  
pp. 1-10
Author(s):  
Sanaullah Jamali ◽  
Muhammad Mujtaba Shaikh ◽  
Abdul Sattar Soomro
Keyword(s):  
Feasible Solution ◽  
Optimal Solution ◽  
New Method ◽  
Large Set ◽  
Basic Feasible Solution ◽  
Optimal Method ◽  
Transportation Problems ◽  
Optimal Methods ◽  
Transportation Models ◽  
Dea Method

In this paper, we investigate the claimed optimality of a new method – Revised Distribution (RDI) Method – for finding optimal solution of balanced and unbalanced transportation models directly and compare the RDI method with other such methods. A large set of problems have been tested by RDI and other methods, and the results were compared with the Modified distribution (MODI) method – an optimal method. We found that the mostly the results of RDI are not optimal. For reference to prove our observations, we have added three example transportation problems here in this work and compared their results with MODI method to show that the RDI method like the direct exponential approach (DEA) method is not optimal method; but it is just an initial basic feasible solution (IBFS) for transportation problems.

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