Supplies and demands are shown along the margins of the matrix. Transportation network design 1 2 d 12 50 v 1 18, t 1 23 v 2 32, t 2 19 v 3 0, t 3. This is a method used to compute feasible solution of a transportation problem. This is something that the northwest corner rule did not do. On optimal solution of a transportation problem research india. Advanced approximation method for finding an optimal. Problem is unbalanced and therefore a dummy row has to be added to make it balanced. Introduction a transportation problem is one of the earliest and most important applications of linear programming problem. Pdf an optimal solution for transportation problem. 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. Transportation problem modi method u v method with. Evaluating the steps will result in the most optimal cost of transportation. The initial feasible solution can be obtained by any of the following three methods.
Optimization techniques for transportation problems of three. Description of a classical transportation problem can be given as follows. Obtain an initial bfs to the following transportation problem using. The problem of interest is to determine an optimal transportation scheme between the warehouses and the outlets, subject to the speci. But these two methods for finding optimal solution of a transportation problem do not reflect optimal solution proved by mohammed 10. Jul 16, 2016 an optimal solution is one where there is no other set of roots that will further reduce the total cost. Test for optimality modified distribution method modi modified distribution method modi it is a method for computing optimum solution of a transportation problem. We also learned we can use sensitivity analysis to tell us more about our solution than just the final optimal solution. Pdf a new method for finding an optimal solution for. Pdf an optimal solution for transportation problem using. A new method for the optimum solution of a transportation problem.
Transportation, assignment and transshipment problems. A feasible solution is optimal if its objective function value is equal to the smallest value zcan take over the feasible region. Now, we will discuss about the methods used for finding an optimal solution. This discourages the solution from using such cells. 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 concept of the optimal solution of the transportation problem with fuzzy cost coefficients. A heuristic for obtaining an initial solution for the transportation problem is presented. The modi and vam methods of solving transportation. The network model of the transportation problem is shown in fig. Transportation problem with trapezoidal fuzzy numbers. What is a degenerate optimal solution in linear programming by linear programming webmaster on december 17, 2015 in linear programming lp when applying the simplex method to calculate the minimum coefficient or feasibility condition, if there is a tie for the minimum ratio or minimum coefficient it can be broken arbitrarily. The optimum solution of degenerate transportation problem. An initial basic feasible solution is obtained by matrix minimum method and is shown in table 1. Among these, some methods directly attain the optimal solution namely zero suffix method 15, asmmethod 1 etc.
More precisely, if the data of the problem is in tegral, then the solution to the asso ciated lp will b e in tegral as w ell. Revising the solution until an optimal solution is obtained. The objective is to minimize the total transportation cost. Given needs at the demand locations, how should we take the limited supply at supply locations and move the goods. Optimal solution of a degenerate transportation problem. Solution of the transportation model b2 module b transportation and assignment solution methods. The main object is to determine the amounts shipped from each sources to each. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. General description of a transportation problem in general, a transportation problem.
Determine an initial basic feasible solution using any one of the following. Introduction transportation is a logistical problem for organizations especially for manufacturing and transport companies. All the optimal solution algorithms for solving transportation problems need an initial basic feasible solution to obtain the optimal solution 3,19. Ops 301 chapter c transportation models flashcards quizlet. 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 balanced transportation problem where all supplies and demands are equal to 1. Optimal solution of transportation problem using linear programming. Operations research or mba mca ca cs cwa cpa cfa cma bba bcom mcom caiib fiii transportation problem. 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. In this paper, the fuzzy transportation problems using. Nov 07, 2012 the stepping stone method is the second video in the series and is a good teaching tool to aid in the understanding of how to reach an optimal solution. This means that we have designated a route as being used although no goods are being sent along it. Pdf on optimal solution of a transportation problem. The transportation problem is the special class of linear programming problem.
Comparative study on mdma method with ofstf method in. On the other hand, vogel is believed to be an approximation. Pdf the new approach proposed in this paper namely dfsd difference form standard deviation method is applied for finding the optimal. Moreo v er, the problems are so sp ecial that when y ou solv e them as lps, the solutions y ou get automatically satisfy the in teger constrain t. In this publication, we discuss a special case of lp, the transportation problem. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. Optimal solution of transportation problem using linear. Since any transportation problem can be formulated as an lp, we can use the simplex method to find an optimal solution.
The lpsolve r package allows to solve lp transportation problems with just a few lines of code. It is possible that while finding an initial basic feasible solution both a supply and a demand constraint are satisfied simultaneously. The discrete network design problem transportation network design. Comparison of findings obtained by the new heuristic and vogels approximation method vam are. Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. The amount allocated is the most possible,subject tothe supply and demand constraints for that cell. Pricing of bottlenecks at optimal time in a transportation problem. The modi and vam methods of solving transportation problems. The set of feasible solutions is called the feasible space or feasible region. Check whether the problem is a balanced or unbalanced transportation problem. If the problem is not unbalanced then the concept of a dummy row or a dummy column to transform the unbalanced problem. 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.
Transportation problem is a special type of linear programming problem. Pdf transportation problem in operational research. Pdf an optimal solution for transportation problemdfsd 1. On each destination node a demand is a negative fixed external flow indicating that this amount must leave the network. Transportation problem is a specific case of linear programming problems and a. Jul, 2017 the proposed method is a unique, it gives always feasible may be optimal for some extant solution without disturbance of degeneracy condition. The modi method is considered as being a standardized technique when it comes to obtaining optimal solution. The steppingstone methodwill help us move from an initial feasible solution to an optimal solution. Thus, we have to evaluate each unoccupied cell in the. Transportation problem mathematical optimization linear. In this paper, transportation problem will be formulated as linear programming problems that will be solved using four methods1 atoum 2009.
Optimal solution lec14 transportation problem optimal solutions lecture series on fundamentals of operations research by prof. Direct methods for finding optimal solution of a transportation. Keywords transportation problem, optimal solution and asmmethod. The optimal solution is obtained either by using stepping stone method or by modi method in the second phase. Formulate the given problem and set up in a matrix form.
The transportation costs in dollar from one country i to the other country j are given in the table below. A fuzzy transportation problem ftp includes cost, supply and demand of transportation problems. Usually the objective is to minimize total shipping costs or distances. Two types of transportation problem balanced transportation problem where the total supply equals total demand unbalanced transportation problem where the total supply is not equal to the total demand.
A comparative study of optimization methods for fuzzy. Conclusion this paper presents an algorithm, which is developed and implemented based on a mathematical model to find an optimal solution for. The objective of this paper is to find an optimal solution for the unbalanced transportation problem using revised distribution method rdi. The modi and vam methods of solving transportation problems tutorial outline modi method. Vogels approximation method tackles the problem of finding a good initial solution by taking into account the costs associated with each route alternative.
Direct methods, sources, destinations, optimal solution, transportation problem, reliable. Keywords unbalanced transportation problem, linear programming problem, redi method, modi method abstract unbalanced transportation problem is a special type of linear programming problem. Optimal solution of transportation problem based on revised. 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. A new method for the optimum solution of a transportation. All the supplies and demands for the machineco problem and for any assignment problem are integers, so all variables in machinecosoptimal solution must be integers. Srinivasan, department of management studies, iit madras. In the paper optimal solution of a transportation problem, a method was developed in 6 to get the initial basic feasible solution or near to the optimal solution of transportation problem.
Ofstf with non linear to linear equation method an optimal. Transportation problem 8 optimal solution part 1 of 3 youtube. 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. Special cases of linear programming problems part 3.
This method takes least iterations to reach optimality. Usually, the initial basic feasible solution of any transportation problem is obtained by using well known methods such as northwest corner method nwcm or. In this article, a new approach is proposed to find an initial basic feasible solution for the transportation problems. Details about balanced and unbalanced transportation problem you find in attached pdf notes at end of this article. Pdf a concept of the optimal solution of the transportation. A numerical example is solved to check the validity of the proposed method and degeneracy problem is also discussed. Transportation problem set 6 modi method uv method. 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, assignment, and transshipment problems. Pdf in this paper, we develop a new method to find the initial basic feasible solution as well as the optimal solution or near to the optimal. Phases of solution of transportation problem phase i obtains the initial basic feasible solution phase iiobtains the optimal. Optimization techniques for transportation problems of.
Variations of the classical transportation problem are easily handled by modifications of the network model. Module b transportation and assignment solution methods. 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. This method is a useful tool in decisionmaking process which. Determine the optimal solution of the above problem. In a transportation problem degeneracy can occur in two ways. Thus, the initial solution achieved by using the minimum cell cost method is usually better in that, because it has a lower cost, it is closer to the optimal solution.
Multiple optimal solutions exist carol seems to have received the best allocation but overall the allocation seems relatively fair. Procedure for finding an optimum solution for transportation problem. Lec14 transportation problemoptimal solutions youtube. Transportation problem, degeneracy, difference cost,optimum solution.
What is a degenerate optimal solution in linear programming. Transportation problem an overview sciencedirect topics. Due to difference in raw material cost and transportation cost, the profit for unit in rupees differs which is given in the table below. It arises when the situation in which a commodity is shipped from sources to destinations. Application of revised distribution method for finding. Zohreh khooban, in logistics operations and management, 2011. Use of linear programming to solve transportation problem in quantitative techniques for management use of linear programming to solve transportation problem in quantitative techniques for management courses with reference manuals and examples pdf. Transportation problem, basic feasible solution, optimal solution, linear programming 1. The transportation problem represents a particular type of linear programming problem used for allocating resources in an optimal way. It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. Here we proposed the modi method with modifications to solve the degenerate transportation problem. Thus, the initial solution in the transportation method serves the same purpose as the initial solution in the simplex method.
Lecture series on fundamentals of operations research by prof. For this reason the hungarian method is used for solving assignment problems. Consider the transportation problem presented in the following table. Steps involved in solving transportation problem is a special type of linear programming problems that involves the following steps. Nov 17, 2015 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. The method used to compute the optimal solution of a transportation problem is actually a direct adaptation of the simplex method. Optimal solution a feasible solution is said to be optimal solution if it minimize total transportation cost. There are various heuristic methods available to get an initial basic feasible solution, such. When applying it, we test each unused cell, or square, in the transportation. Solve the following transportation problem for maximizing the profit. Pdf transportation problem in operational research download. In addition to the northwest corner and intuitive lowestcost methods of setting an initial solution to. The conventional transportation problem deals with minimizing the cost of transporting a homogeneous product from various supply points to a number of destinations without caring for the time of transportation.
The transportation problem one of the most important and successful applications of quantitative analysis to solving business problems has been in the. As in the example, the classic transportation problem has total supply equal to total demand. A transportation problem has an optimal solution when. 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. The stepping stone method is for finding the optimal solution of a transportation problem. Graphically, a transportation problem is often visualized as a network with m source nodes, n sink nodes, and a set of m. Transportation, basic feasible solution, arithmetic mean, optimal solution. Optimization techniques for transportation problems of three variables mrs. Method using a simple logic with solved problem, hope. 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. Because of the special structure of a transportation lp, the iterations of the simple method have a very special form. The linear programming model for this problem is formulated in the equations that follow.