Find an initial solution to the following transpor. In addition to the northwest corner and intuitive lowestcost methods of setting an initial solution to. During the past week, the total production of a special compressor unit out of each plant has been 35, 50, and 40 units respectively. Rekha vivek joshi, lecturer, department of mathematics, sydenham college of commerce and economics, mumbai university, india abstract. In 1930, in the collection transportation planning volume i for. The problem in nphard and most resembles a categorized bottleneck. Transportation problem transport various quantities of a single homogeneous commodity to different destinations in such a way that total transportation cost is minimum. The transportation problem represents a particular type of linear programming problem used for allocating resources in an optimal way. 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. In this article we present a new method for the optimal transportation problem for general convex target sets.
Determine the optimal solution of the above problem. Using the vam initial solution, find the optimal solution using the modified distribution method modi. Automating the computation of optimal solutions to. 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. Multiple optimal solutions exist carol seems to have received the best allocation but overall the allocation seems relatively fair. Transportation problem which gives also an optimal solution. Kore and thakur 4 have proposed another method, which discards the need of balancing the given problem. Feb 19, 2012 phases of solution of transportation problem phase i obtains the initial basic feasible solution phase iiobtains the optimal basic solution 9. A2 module a the simplex solution method t he simplex method,is a general mathematical solution technique for solving linear programming problems.
Comparison of findings obtained by the new heuristic and vogels approximation method vam are. 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. To solve this small lp by hand would have required computations for at least three simplex. Transportation problem optimal solution with modi and zq total. Usually the objective is to minimize total shipping costs or distances.
The planners decision problem can be formulated in terms of a mathematical. Here we proposed the modi method with modifications to solve the degenerate transportation problem. Optimal solution of a degenerate transportation problem. Consider the following transportation tableau and solution. The stepping stone method is for finding the optimal solution of a transportation problem. Variations of the classical transportation problem are easily handled by modifications of the network model.
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. The optimal solution is obtained either by using stepping stone method or by modi method in the second phase. 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. Keywords unbalanced transportation problem, linear programming problem, redi method, modi method abstract unbalanced transportation problem is a special type of linear programming problem. The total cost of the optimal solution to a transportation problem 1. Application of revised distribution method for finding. Math models that find the best solution with respect to some evaluation. The best solution attainable is when the profit line is shifted as far to the right.
It arises when the situation in which a commodity is shipped from sources to destinations. Test for optimality modified distribution method modi modified distribution method modi it is a method for computing optimum solution of a transportation problem. For this reason the hungarian method is used for solving assignment problems. A the simplex solution method university of babylon. We will now discuss how to find solutions to a linear programming problem. Consider the transportation problem presented in the following table.
Ops 301 chapter c transportation models flashcards quizlet. Is this a balanced or an unbalanced transportation problem. A check of whether the found solution is optimal is performed. The lpsolve r package allows to solve lp transportation problems with just a few lines of code. Many solution procedures have been developed in the literature for solving balanced transportation problem 1,2,3. Aimms modeling guide formulating optimization models. 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. A commonly occurring problem in distribution system design is the optimal location of. Pdf an optimal solution for transportation problem. Introduction transportation problem is famous in operation research for its wide application in real life. Details about balanced and unbalanced transportation problem you find in attached pdf notes at end of this article. If it is possible to reduce the transportation costs for any of the. Obtaining optimal solution by using very good nonbasic feasible solution of the transportation and linear programming problem r. Optimal solution of transportation problem using linear.
If it is degenerate, show how it would be put into proper form. 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. A polynomial algorithm for linear optimization which is strongly. A new approach for finding an optimal solution for. Obtaining optimal solution by using very good nonbasic. Module b transportation and assignment solution methods. In general problems, such pairings are not known in advance, but must be determined by the solution of the full optimal transportation problem. In this paper a different approach namely zero suffix method is applied for finding an optimal solution for transportation problems directly. This is something that the northwest corner rule did not do. This method finds an optimal solution without requiring an initial basic feasible solution. Transportation problem modi method u v method with. Revised distribution method of finding optimal solution for. The robust software to be developed will make the computation of optimal solutions to transportation problems easier, faster and more accurate.
A new method for the optimum solution of a transportation problem. Numerical solution of the optimal transportation problem. In 2003, saad and abbas 12 discussed an algorithm to solve a transportation problem in fuzzy environment. It took three iterations, or pivots, to find the optimal solution of. Transportation, assignment, and transshipment problems. The assignment problems is a special case of transportation problem.
An optimal solution to a linear program is the feasible solution with the largest objective function value for a maximization problem. The method is also illustrated with numerical examples. Next, it is assumed that p xy has a finite optimal solution x for every y. Lecture notes on transportation and assignment problem bbe h qtm paper of delhi. On optimal solution of a transportation problem 6205 after applying the least cost method, for initial basic feasible solution, the allocations are as follows. Transportation problem, mdma, ibfs, optimal solution. Therefore, it is not necessary to add constraints to the model that restrict these variables to only have integer values. Transportation problem, degeneracy, difference cost,optimum solution. A fuzzy transportation problem ftp includes cost, supply and demand of transportation problems. Thus, the initial solution in the transportation method serves the same purpose as the initial solution in the simplex method. 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. Test for optimal solution to a transportation problem learning objective.
Transportation problem solution lets solve this problem using the transportation problem method, actually a simplified version of the simplex technique. The transportation problem is the special class of linear programming problem. The starting solution using northwestcorner method is. A new method for finding an optimal solution of fully. It is a method for computing optimum solution of a transportation problem. Phases of solution of transportation problem phase i obtains the initial basic feasible solution phase iiobtains the optimal basic solution 9. 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. Pdf an alternate approach to find an optimal solution.
Optimal solution a feasible solution non necessarily basic is said to be. In a minimization problem, a negative improvement index in a cell indicates that the. Application of assignment problem with side constraints. Transportation, assignment and transshipment problems.
General description of a transportation problem in general, a transportation problem is speci. The optimum solution of degenerate transportation problem. The main open question here is if there exist randomized algorithms that solve linear optimization problems in strongly. Procedure for finding an optimum solution for transportation. Types of transportation problem in operational research. Transportation problem is a specific case of linear programming problems and a. The problem was formalized by the french mathematician gaspard monge in 1781 in the 1920s a. For this type of problem, all units available must be supplied. An efficient implementation of the transportation problem. Transportation problem set 6 modi method uv method. A new simple method of finding an optimal solution for the. From the above problem, we see this in fact occurs. A decade of combinatorial optimization 1 introduction.
When the linearprogramming problem contains many constraints, this approach for recovering an optimal solution is very effective. The modi and vam methods of solving transportation problems. Tolstoi was one of the first to study the transportation problem mathematically. They solve an unbalanced transportation problem, after balancing it by creating dummy origin andor destination as required. Transportation problem 8 optimal solution part 1 of 3 youtube. Pdf on optimal solution of a transportation problem. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The total cost of the optimal solution to a transportation. Recently adlakha and kowalski 2009 suggested a systematic analysis for allocating loads to obtain an alternate optimal solution. Optimal solution of transportation problem using linear programming.
The optimal solution is coincide with the modi method. Depending on the objective we want to optimize, we obtain the typical assignment problems. Test for optimality stepping stone method before learning the methods to find the optimal solution try and practice few more. Operations research or mba mca ca cs cwa cpa cfa cma bba bcom mcom caiib fiii transportation problem. Express the solution of the original problem in terms of optimal solutions for smaller problems. The transportation problem a simple example a compressor company has plants in three locations. Determine an initial basic feasible solution using any one of the following. The main object is to determine the amounts shipped from each sources to each. Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. Vogels approximation method tackles the problem of finding a good initial solution by taking into account the costs associated with each route alternative. The problem was formalized by the french mathematician gaspard monge in 1781.
Pdf transportation problem in operational research. 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. How to solve a transportation problem using the modi modified distribution method and finding the optimal solution. In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The modified distribution method is useful for finding the optimal solution for the transportation problem. Dec 28, 2011 transportation problem in operational research 1. Transportation problem osu extension catalog oregon state. A new method for finding an optimal solution of fully interval integer transportation problems p. Now, we will discuss about the methods used for finding an optimal solution. Initial basic feasible solution north west corner rule nwcr row minima method column minima method least cost method vogle approximation method vam 10. Transportation problem is a special type of linear programming problem. A comparative analysis of assignment problem 1shweta singh, 2g.
The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. Optimization techniques for transportation problems of three variables mrs. Natarajan department of mathematics, school of advanced sciences, vit university, vellore14, tamil nadu, india corresponding author. However study on alternate optimal solution is limited in the literature of tp. How we measure reads a read is counted each time someone views a. The optimum solution for the example is shown in fig. Pdf alternate solutions analysis for transportation problems. 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. The linear programming model for this problem is formulated in the equations that. Thus, we have to evaluate each unoccupied cell in the.
Transportation problem is considered a vitally important aspect that has been studied in a wide range. Lecture notes on transportation and assignment problem bbe. Keywords transportation problem, transportation cost, initial basic feasible solution, optimal solution 1. The objective of this paper is to find an optimal solution for the unbalanced transportation problem using revised distribution method rdi. Numerical examples for the new simple method is explained and compared with the results of modi method.
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. A heuristic for obtaining an initial solution for the transportation problem is presented. The purpose of tp is to transport the goods from sources to destinations. A new method for solving fuzzy transportation problems using. 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. Procedure for finding an optimum solution for transportation problem.
An efficient implementation of the transportation problem by alissa michele sustarsic chairperson of the thesis committee. Optimization techniques for transportation problems of three. 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. For the love of physics walter lewin may 16, 2011 duration. 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. Steps step 1 determine an initial basic feasible solution using any one of the three methods.
An initial basic feasible solution is obtained by matrix minimum method and is shown in table 1. In 2006, gani and razak 7 discussed a two stage cost minimizing fuzzy transportation in which the demand and supply quantities are trapezoidal. We also learned we can use sensitivity analysis to tell us more about our solution than just the final optimal solution. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. Summary in the presence of degeneracy, the meaning of alternative optimal solutions may not necessarily imply the existence of alternative solution points.
In this article, a new approach is proposed to find an initial basic feasible solution for the transportation problems. The modi and vam methods of solving transportation. If the problem is not unbalanced then the concept of a dummy row or a dummy column to transform the unbalanced problem to. Before finding the initial solution, a dummy should be introduced. The modi and vam methods of solving transportation problems tutorial outline modi method.
Adel boules department of mathematics and statistics the transportation problem is a special type oflinear program in which the objective is to. Revising the solution until an optimal solution is obtained. 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. The following common steps may be helpful in solving the problems of urban transport. 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. The problem of interest is to determine an optimal transportation scheme between the warehouses and the outlets, subject to the speci. Related works this is work is alternative for existing modi modified distribution method method 3 in which the number of iteration is minimized. 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.
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