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 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

A Literature Survey for Hazardous Materials Transportation

2016 ◽  
pp. 371-393 ◽  
Author(s):  
Serpil Erol ◽  
Zafer Yilmaz
Keyword(s):  
Special Kind ◽  
Hazardous Materials ◽  
Literature Survey ◽  
Optimal Solutions ◽  
Transport Costs ◽  
Hazardous Materials Transportation ◽  
Transportation Problems ◽  
Hazmat Transportation ◽  
The Cost ◽  
Cost Of Transportation

Transportation has the greatest importance in logistics. The main focus for the carriers is the cost of transportation. Transportation of hazardous materials (hazmat) is a special kind of transportation due to freight transported. Causalities due to the accidents caused by vehicles that are carrying hazardous materials will be intolerable. For hazmat transportation, in addition to transport costs, risk of transporting hazmat also has to be considered. Many researchers studied on hazmat transportation problems in order to propose optimal solutions with respect to cost, risk, emergency response, facility location etc. In this study, a literature survey of articles about hazmat transportation was prepared. The articles published in refereed journal from 1973 to 2014 were taken into consideration. The articles were also classified according to their main focuses and hazmat type carried.

A METHOD FOR GENERATING ALL THE EFFICIENT SOLUTIONS OF A 0-1 MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM

2004 ◽  
Vol 21 (01) ◽  
pp. 127-139 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
F. HOSSEINZADEH LOTFI ◽  
N. SHOJA ◽  
G. TOHIDI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Solution ◽  
Efficient Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective ◽  
Feasible Solutions ◽  
Single Objective

In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

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