Optimal solution of a degenerate transportation problem. Many solution procedures have been developed in the literature for solving balanced transportation problem 1,2,3. Optimization techniques for transportation problems of three variables mrs. Obtaining optimal solution by using very good nonbasic. This method finds an optimal solution without requiring an initial basic feasible solution. Natarajan department of mathematics, school of advanced sciences, vit university, vellore14, tamil nadu, india corresponding author. Transportation, assignment, and transshipment problems. The objective of this paper is to find an optimal solution for the unbalanced transportation problem using revised distribution method rdi. It took three iterations, or pivots, to find the optimal solution of. Aimms modeling guide formulating optimization models. Revising the solution until an optimal solution is obtained. A check of whether the found solution is optimal is performed.
How we measure reads a read is counted each time someone views a. Now, we will discuss about the methods used for finding an optimal solution. In general problems, such pairings are not known in advance, but must be determined by the solution of the full optimal transportation problem. Usually the objective is to minimize total shipping costs or distances. Transportation problem, mdma, ibfs, optimal solution. Depending on the objective we want to optimize, we obtain the typical assignment problems. The stepping stone method is for finding the optimal solution of a transportation problem.
An initial basic feasible solution ibfs for the transportation problem can be obtained by using the northwest corner nwc rule, row minima, column minima, matrix minima leastcost, or the vogels approximation method. Recently adlakha and kowalski 2009 suggested a systematic analysis for allocating loads to obtain an alternate optimal solution. Therefore, it is not necessary to add constraints to the model that restrict these variables to only have integer values. Multiple optimal solutions exist carol seems to have received the best allocation but overall the allocation seems relatively fair. Thus, the initial solution in the transportation method serves the same purpose as the initial solution in the simplex method. The modi and vam methods of solving transportation problems tutorial outline modi method. We will now discuss how to find solutions to a linear programming problem. However study on alternate optimal solution is limited in the literature of tp. Lecture notes on transportation and assignment problem bbe h qtm paper of delhi. Consider the transportation problem presented in the following table. From the above problem, we see this in fact occurs. Using the vam initial solution, find the optimal solution using the modified distribution method modi. A commonly occurring problem in distribution system design is the optimal location of. For the love of physics walter lewin may 16, 2011 duration.
Automating the computation of optimal solutions to. This is something that the northwest corner rule did not do. If the total sum of all the supply from sources o1, o2, and o3 is equal to the total sum of all the demands for destinations d1, d2, d3 and d4 then the transportation problem is a balanced transportation problem note. The total cost of the optimal solution to a transportation problem 1. Optimal solution of transportation problem using linear. How to solve a transportation problem using the modi modified distribution method and finding the optimal solution. In 1930, in the collection transportation planning volume i for. In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. A new approach for finding an optimal solution for. Application of revised distribution method for finding. If the problem is not unbalanced then the concept of a dummy row or a dummy column to transform the unbalanced problem to. In addition to the northwest corner and intuitive lowestcost methods of setting an initial solution to. In this paper a different approach namely zero suffix method is applied for finding an optimal solution for transportation problems directly.
During the past week, the total production of a special compressor unit out of each plant has been 35, 50, and 40 units respectively. Pdf an optimal solution for transportation problem. Keywords transportation problem, transportation cost, initial basic feasible solution, optimal solution 1. Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems.
For this reason the hungarian method is used for solving assignment problems. In this publication, we discuss a special case of lp, the transportation problem. Lecture notes on transportation and assignment problem bbe. Summary in the presence of degeneracy, the meaning of alternative optimal solutions may not necessarily imply the existence of alternative solution points. Transportation problem is a specific case of linear programming problems and a. Kore and thakur 4 have proposed another method, which discards the need of balancing the given problem. On optimal solution of a transportation problem 6205 after applying the least cost method, for initial basic feasible solution, the allocations are as follows. The variable x ij is represented by a line, or arc, joining the ith supply point plant i and the jth demand point city j. Transportation problem osu extension catalog oregon state.
To solve this small lp by hand would have required computations for at least three simplex. A new simple method of finding an optimal solution for the. Here is the video about transportation problem in modi methodu v method using north west corner method, optimum solution in operation research, with sample problem in simple manner. A fuzzy transportation problem ftp includes cost, supply and demand of transportation problems. Pdf on optimal solution of a transportation problem. Transportation problem transport various quantities of a single homogeneous commodity to different destinations in such a way that total transportation cost is minimum. An efficient implementation of the transportation problem. A comparative analysis of assignment problem 1shweta singh, 2g. Pdf alternate solutions analysis for transportation problems. The assignment problems is a special case of transportation problem. Operations research or mba mca ca cs cwa cpa cfa cma bba bcom mcom caiib fiii transportation problem. Sharma department of industrial and management engineering, indian institute of technology, kanpur, india abstract for the transportation problem, sharma and sharma have given a very 1. Transportation problem, degeneracy, difference cost,optimum solution. Related works this is work is alternative for existing modi modified distribution method method 3 in which the number of iteration is minimized.
The modified distribution method is useful for finding the optimal solution for the transportation problem. It arises when the situation in which a commodity is shipped from sources to destinations. Supply 911 20 3 4 6 9 8 1022 2 8 1 5 30 7 11 20 9 40 6 3 15 7 2 6 1 9 14 16 demand 40 6 8 18 6 total78. A2 module a the simplex solution method t he simplex method,is a general mathematical solution technique for solving linear programming problems. Transportation problem set 6 modi method uv method. Procedure to solve transportation problem in quantitative techniques for management procedure to solve transportation problem in quantitative techniques for management courses with reference manuals and examples pdf. One of the most commonly adopted methods of combatting road congestion in medium and small towns or in districts of larger centres is the construction of bypasses to divert throughtraffic. Test for optimal solution to a transportation problem learning objective. A the simplex solution method university of babylon.
In this article, a new approach is proposed to find an initial basic feasible solution for the transportation problems. Math models that find the best solution with respect to some evaluation. Here we proposed the modi method with modifications to solve the degenerate transportation problem. Phases of solution of transportation problem phase i obtains the initial basic feasible solution phase iiobtains the optimal basic solution 9. We also learned we can use sensitivity analysis to tell us more about our solution than just the final optimal solution. Test for optimality stepping stone method before learning the methods to find the optimal solution try and practice few more. General description of a transportation problem in general, a transportation problem is speci. If it is possible to reduce the transportation costs for any of the. In 2006, gani and razak 7 discussed a two stage cost minimizing fuzzy transportation in which the demand and supply quantities are trapezoidal. On each destination node a demand is a negative fixed external flow indicating that this amount must leave the network. Adel boules department of mathematics and statistics the transportation problem is a special type oflinear program in which the objective is to. The transportation problem a simple example a compressor company has plants in three locations. The optimal solution is coincide with the modi method.
An efficient implementation of the transportation problem by alissa michele sustarsic chairperson of the thesis committee. The modi and vam methods of solving transportation problems. The robust software to be developed will make the computation of optimal solutions to transportation problems easier, faster and more accurate. Introduction transportation problem is famous in operation research for its wide application in real life.
B4 module b transportation and assignment solution methods the northwest corner method with the northwest corner method, an initial allocation is made to the cell in the upper lefthand corner of the tableau i. The optimum solution of degenerate transportation problem. A polynomial algorithm for linear optimization which is strongly. Variations of the classical transportation problem are easily handled by modifications of the network model. Transportation problem optimal solution with modi and zq total. In a minimization problem, a negative improvement index in a cell indicates that the. Transportation problem solution lets solve this problem using the transportation problem method, actually a simplified version of the simplex technique. They solve an unbalanced transportation problem, after balancing it by creating dummy origin andor destination as required. The lpsolve r package allows to solve lp transportation problems with just a few lines of code. The problem of interest is to determine an optimal transportation scheme between the warehouses and the outlets, subject to the speci.
An initial basic feasible solution is obtained by matrix minimum method and is shown in table 1. The transportation problem is the special class of linear programming problem. Transportation problems the transportation or shipping problem involves determining the amount of goods or items to be transported from a number of sources to a number of destinations. In this article we present a new method for the optimal transportation problem for general convex target sets. The objective of this paper is to find an optimal solution for the transportation problem which having objective function is to be maximized using new approach revised distribution method, and vogels approximation method. A decade of combinatorial optimization 1 introduction. The best solution attainable is when the profit line is shifted as far to the right. Given a transportation problem with the following costs, supply, and demand, find the initial solution using the minimum cell cost method and vogels approximation model. Optimization techniques for transportation problems of three. The following common steps may be helpful in solving the problems of urban transport. Linear programming 507 given sum by the dealer in purchasing chairs and tables is an example of an optimisation problem as well as of a linear programming problem.
A new method for finding an optimal solution of fully interval integer transportation problems p. The method is also illustrated with numerical examples. Express the solution of the original problem in terms of optimal solutions for smaller problems. Module b transportation and assignment solution methods. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Numerical solution of the optimal transportation problem. An optimal solution to a linear program is the feasible solution with the largest objective function value for a maximization problem. Revised distribution method of finding optimal solution for. Keywords unbalanced transportation problem, linear programming problem, redi method, modi method abstract unbalanced transportation problem is a special type of linear programming problem. Steps step 1 determine an initial basic feasible solution using any one of the three methods. Although kantorovichs innovation and subsequent development of linear programming provided a basic apparatus for the solution of such problems, it is only within the last 20 years or so that the optimal transportation.
The main object is to determine the amounts shipped from each sources to each. Application of assignment problem with side constraints. The linear programming model for this problem is formulated in the equations that. The problem in nphard and most resembles a categorized bottleneck. A heuristic for obtaining an initial solution for the transportation problem is presented. The starting solution using northwestcorner method is. A new method for the optimum solution of a transportation problem.
The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. Numerical examples for the new simple method is explained and compared with the results of modi method. It is a method for computing optimum solution of a transportation problem. Optimal solution of transportation problem using linear programming. Rekha vivek joshi, lecturer, department of mathematics, sydenham college of commerce and economics, mumbai university, india abstract. The intent of this work is to present various rules governing load distribution for alternate optimal solutions in transportation problems, a subject that has not attracted much attention in the. Feb 19, 2012 phases of solution of transportation problem phase i obtains the initial basic feasible solution phase iiobtains the optimal basic solution 9.
The total cost of the optimal solution to a transportation. Tolstoi was one of the first to study the transportation problem mathematically. Types of transportation problem in operational research. Vogels approximation method tackles the problem of finding a good initial solution by taking into account the costs associated with each route alternative. Consider the following transportation tableau and solution. The main open question here is if there exist randomized algorithms that solve linear optimization problems in strongly. If it is degenerate, show how it would be put into proper form. A new method for solving fuzzy transportation problems using.
Transportation problem is considered a vitally important aspect that has been studied in a wide range. Find the initial basic feasible solution of the following transportation problem by northwest corner method and then optimize the solution using uv method modi destination source d1 d2 d3 d4 supply s1 3 1 7 4 250 s2 2 6 5 9 350 s3 8 3 3 2 400 demand 200 300 350 150 25. Transportation problem is a special type of linear programming problem. Initial basic feasible solution north west corner rule nwcr row minima method column minima method least cost method vogle approximation method vam 10. Determine an initial basic feasible solution using any one of the following. Next, it is assumed that p xy has a finite optimal solution x for every y. The transportation problem represents a particular type of linear programming problem used for allocating resources in an optimal way. The modi and vam methods of solving transportation. Transportation, assignment and transshipment problems. Procedure for finding an optimum solution for transportation problem. Pdf transportation problem in operational research.
For this type of problem, all units available must be supplied. Test for optimality modified distribution method modi modified distribution method modi it is a method for computing optimum solution of a transportation problem. In the simplex method, the model is put into the form of a table, and then a number of mathematical steps are performed on the table. Transportation problem which gives also an optimal solution. The problem was formalized by the french mathematician gaspard monge in 1781 in the 1920s a. In 2003, saad and abbas 12 discussed an algorithm to solve a transportation problem in fuzzy environment. Transportation problem modi method u v method with. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. A new method for finding an optimal solution of fully. Thus, we have to evaluate each unoccupied cell in the. Pdf an alternate approach to find an optimal solution.
When the linearprogramming problem contains many constraints, this approach for recovering an optimal solution is very effective. The optimal solution is obtained either by using stepping stone method or by modi method in the second phase. Details about balanced and unbalanced transportation problem you find in attached pdf notes at end of this article. Dec 28, 2011 transportation problem in operational research 1. Is this a balanced or an unbalanced transportation problem. Transportation problem 8 optimal solution part 1 of 3 youtube. Test for optimality stepping stone method before learning the methods to find the optimal solution try and practice few more questions to find the initial solution of the transportation problem. Before finding the initial solution, a dummy should be introduced. The purpose of tp is to transport the goods from sources to destinations. The optimum solution for the example is shown in fig. Optimal solution a feasible solution non necessarily basic is said to be. Based on the given demand and supply, the given transportation problem is. The planners decision problem can be formulated in terms of a mathematical.
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