Nstepping stone method in transportation problem pdf merger

An efficient implementation of the transportation problem by alissa michele sustarsic chairperson of the thesis committee. Ggbl emerged out of a merger of guinness ghana limited ggl and ghana breweries. There are msources and destn inations, each represented by a node. Stepping stone number of basic allocated cells must be s. Transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2.

Using our new approach we get, optimal solution of. B2 module b transportation and assignment solution methods the cost of transporting one ton of wheat from each grain elevator source to each mill. In an s x d tableau, the number of basic allocated cells. The purpose is to offer an alternative to networkoriented or simplexbased methods such. Jan 12, 2018 stepping stone method this is a procedure to be followed to find improved solution and the optimal solution in turn of a transportation problem after getting its initial solution by applying.

The problem is unbalanced and cannot be solved by the transportation method. Rearrange individual pages or entire files in the desired order. Ops 301 chapter c transportation models flashcards quizlet. The stepping stone method of explaining linear programming calcu. The number of occupied squares in any solution initial or later must be equal to the number of rows. The problem will require a dummy demand with a capacity of 10 units. The two methods for solving a transportation model are the steppingstone method and the modified distribution method also known as modi.

As ap is a particular case of tp in this paper, i have proposed a new approach to solve an ubap, which overtakes the problem of degeneracy of transportation method. Procedure for finding optimal transportation tableau. Stepping stone method topic is not easier to learn without external help. These are methods of determining the optimal solutions for transportation problems following the determination of the initial basic feasible solution. In this video we learn how to optimize a transportation problem. Some well known and long use algorithms to solve transportation problems are vogels approximation method vam, north west corner nwc method, and matrix minima method. May 03, 20 transportation problem stepping stone method pamantasan ng lungsod ng maynilagraduate school of engineeringgem 805 optimization techniques 2.

The rest of the solution procedure for this transportation problem proceeds in the same manner as what was done earlier using the steppingstone method. An initial basic feasible solutionibfs for the transportation problem can be obtained by using the northwest corner. Maximization transportation problem can be converted into minimization transportation problem by subtracting each transportation cost from maximum transportation cost. Again, we will describe two methods for doing this. Live tutors are available for 24x7 hours helping students in their stepping stone method related problems. The stepping stone method involves testing each unused route to see if shipping one unit on that route would increase or decrease total transportation costs. Journal of internet banking and commerce, august 2015, vol. A new method for solving fuzzy transportation problems using. If you continue browsing the site, you agree to the use of cookies on this website. Transportation model step 4a stepping stone method youtube. The initial northwest corner solution is shown in table t4. Solve facility location and other application problems with transportation methods. Pandian abstract a new method namely, separation method based on zero point method 9 is. Stepping stone method this is a one of the methods used to determine optimality ofan initial basic feasible solution i.

Introduction there are two most popular methods used in literature for deriving the initial basic feasible solution ibf and hence the optimal solution. Stepping stone method examples, transportation problem. A new method for solving transportation problems considering. Northwest corner rule, leastcost or vogels approximation the. Northwest corner rule, least cost or vogels approximation the method is derived from the analogy of crossing a pond using stepping stones. One of these tools, which has already proved its worth in practical applications, is linear programming. The problem will require a dummy supply with a capacity of 10 units. To resolve degeneracy, we make use of an artificial quantityd.

A new technique for finding initial basic feasible solution to transportation problem. The total supply available at the origin and the total quantity demanded by the destinations are given in the statement of the problem. To achive optimum value, there are several methods, the stepping stone method, assignment method. A specialpurpose solution procedure 2 transportation, assignment, and transshipment problems a network model is one which can be represented by a set of nodes, a set of arcs, and functions e. Natarajan department of mathematics, school of advanced sciences, vit university, vellore14, tamil nadu, india corresponding author.

A greedy algorithm for solving ordinary transportation. Optimization techniques for transportation problems of three. Sep 07, 2016 optimal solution of transportation problem by stepping step method. The least cost method is another method used to obtain the initial feasible solution for the transportation problem. Charnes and cooper developed the stepping stone method which provides an alternative way of determining the simplex method information. The stepping stone method is the second video in the series and is a good teaching tool to aid in the. In this video, you will learn how to perform an optimality test on the basic initial feasible solution using the stepping stone method in order to find. Transportation problem is a logistical problem for organizations especially for manufacturing and transport companies. Stepping stone method the stepping stone method is an. This means that the entire transportation table is assumed to be a pond and the occupied cells are the stones needed to make certain movements within the pond. Rekha vivek joshi, lecturer, department of mathematics, sydenham college of commerce and economics, mumbai university, india abstract. Arts and science college, coimbatore, tamilnadu, india abstract solving transportation problem using the new technique, results in minimum transportation cost than the least cost method. Solving the arizona plumbing problem with modi let us try out these rules on the arizona plumbing problem. The two methods for solving a transportation model are the stepping stone methodand the modified distribution method.

Download portable pdf merge tool merge pdf files with this program. We convert the above problem into a dual problem and construct a greedy algorithm to solve it. A new technique for finding initial basic feasible solution. Transportation models are solved manually within the context of a tableau, as in the simplex method. The quantity d is assigned to that unoccupied cell, which has the minimum transportation cost. Northwest corner, least cost method or vogels approximation method. To get an optimal solution for the transportation problem, we use the modi method modified distribution method. Mar 15, 2016 a read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Adel boules department of mathematics and statistics the transportation problem is a special type oflinear program in which the objective is to. Because of its special structure the usual simplex method is not suitable for solving transportation problems. Destinations c and d must each receive 5 units less than they require. Unbalanced transportation problemnorthwestleast costvam. The solution of transportation problems by the methods described in refs. This method is designed on the analogy of crossing the pond using the stepping stone.

Transportation problem using stepping stone method and. Note that the only change in the transportation table is the border labeling the r i. Again, we will use the previous example to illustrate the method. Optimal solution of transportation problem by stepping step. Solving a balanced minimization transportation problem. Online tutorial the modi and vam methods of solving. One of them is the northwest corner rule for a given transportation problem. Stepbystep guide on how to solve a balanced minimization transportation problem. During the past week, the total production of a special compressor unit out of each plant has been 35, 50, and 40 units respectively. The transportation problem deals with a special class of linear programming problems in which the objective is to transport a homogeneous product manufactured at several plants origins to a number of different destinations at a minimum total cost. In this video, you will learn how to perform an optimality test on the basic initial feasible solution using the stepping stone method in order to find out if the solution is optimal or not.

Z z o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o. Optimization techniques for transportation problems of three variables mrs. Stepping stone method calculator transportation problem. Thus, the stepping stone method is a procedure for finding the potential of any nonbasic variables empty cells in terms of the objective function. The lower cost cells are chosen over the highercost cell with the objective to have the least cost of transportation. The stepping stone and the modified distribution method modi stepping stone. Transportation problem in linear programming stepping stone method stepping stone method after computing the initial solution by using any of the three methods explained above, the solution needs to be tested to see whether the solution is optimum or not, by using the stepping stone method. Hitung nilai pinalti selisih 2 ongkos terkecil pada semua baris dann kolom. The transportation problem is a special type of lpp where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations. Structure special lp problems using the transportation and assignment models. Transportation problem stepping stone method stepping stone method this is a one of the methods used to determine optimality of an initial basic feasible solution i.

Kore 2008 made an attempt to solve unbalanced transportation problem without balancing it. The network representation for a transportation problem with two sources. The linear programming model for this problem is formulated in the equations that follow. Since number of basic variables is less than 6, therefore, it is a degenerate transportation problem. For clarity of exposition, consider the following transportation problem example 1. Here is the video about unbalanced transportation problem by using northwest corner cell method, least cost cell method and vogels approximation method. Nov 14, 20 stepping stone method to find the optimum solution in a transportation problem slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. It is worth noting that sometimes problems that are solved using the transportation method have nothing to do with an actual movement. Through stepping stone method, we determine that what effect on the transportation cost would be in case one unit is assigned to the empty cell.

Lecture notes on transportation and assignment problem bbe. The transportation tableau associated with the basic feasible. In industry, people are concerned with efficiency and. In the previous section, we used the stepping stone method to find the optimal solution of a transportation problem.

The transportation tableau associated with the basic feasible solution produced by the leastcost. Solving transportation problems using the best candidates method. With the help of this method, we come to know whether the solution is optimal or not. Transportation problems transportation problems pearson. Stepping stone method, assignment help, transportation.

The stepping stone method of explaining linear programming. This paper extends the standard stepping stone method to the case of capacitated transportation problems. To start with let us assess the potential for improvement of the non basic variable 1,1. Charnes and cooper 1 developed the stepping stone method, which provides. A new method for finding an optimal solution of fully. It is not the purpose of this article to explore the full ramifications of these research developments or even to explore the general field of linear programming. Index termsrussell method, transportation simplex method i. Transportation and assignment models chapter 10 transportation and assignment models. Dantzig and thapa used the simplex method to the transportation problem as the primal simplex transportation method. The northwest corner rule is a method adopted to compute the initial feasible solution of the transportation problem. The name northwest corner is given to this method because the basic variables are selected from the extreme left corner. We need to work on step by step procedure to solve the transportation problem. Module b transportation and assignment solution methods.

The transportation problem a simple example a compressor company has plants in three locations. This method typically gets you closer to a solution than the northwest corner method. Development of a new optimal method for solution of. Consider the ordinary transportation problem with the objective to minimize the cost of transporting a single commodity from m warehouses to n demand locations. Least cost method step i write the transportation problem in a tabular form. The tableau for our wheat transportation model is shown in table b1.

Two federal transportation laws, the intermodal surface transportation efficiency act istea of 1992 and the transportation equity act for the 21st century tea21 of 1998 have been important to advancing smart growth principles. Stepping stone method to apply the stepping stone method to a transportation problem, we must observe a rule about the number of shipping routes being used. Continue the above example containing the initial basic feasible solution obtained by least cost rule. An efficient implementation of the transportation problem. Find an initial basic feasible solution using any one of the three methods nwcm, lcm or vam. Dimana, sebelum metode ini dapat digunakan, harus dicari terlebih dahulu solusi awalnya atau initial solution baik dengan metode nwcr north west corner rule, vam vogel approximation method, ataupun lc least cost. Request pdf on oct 31, 2012, abdallah a hlayel and others published.

Metode transportasi stepping stone adalah salah satu metode dalam transportasi untuk mencari solusi akhir terminal solution. Afterwards many researchers provide many methods and algorithms to solve transportation problems. Lecture notes on transportation and assignment problem bbe h qtm paper of delhi. The stepping stone method the stepping stone methodwill help us move from an initial feasible solution to an optimal solution. Given the s 3 supply and d 3 demands tableau below, first create feasible tableau by using the northwest, vam, minimum cell, or russell method. Transportation and assignment models learning objectives students will be able to. It is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution. Only transportation type problems and models will be discussed in any detail. The method is derived from the analogy of crossing a pond using stepping stones. Jika matriks solusi awal menggunakan metode vam dan penyelesaian optimalnya menggunakan stepping stone, dapat dilakukan sebagai berikut. Transportation model step 4a stepping stone method.

Stepping stone method is one of the method used to find the optimal solution for the transportation problem. Pdf transportation and assignment models chapter 10. Transportation problem is considered a vitally important aspect that has been studied in a wide range. Vam and matrix minima method always provide ibfs of a transportation problem. Stepping stone method the stepping stone method is an iterative technique for moving from an initial feasible solution to an optimal feasible solution. The stepping stone method again, we will use the previous example to illustrate the method. This method is a useful tool in decisionmaking and process of allocating. The stepping stone method is used to check the optimality of the initial feasible solution determined by using any of the method viz.

Both istea and tea21 helped strengthen the connections. When applying it, we test each unused cell, or square, in the transportation. Stepping stone method transportation problem d49oqokvp049. Here, the allocation begins with the cell which has the minimum cost. The illustrate example to be presented in this paper will be employed to explain the stepping stone method for solving these kind of problems. Network representation and mathematical model of transportation problem generally the transportation model is represented by the network in figure 1. In this section, we provide another example to boost your understanding. During this time, the method of solving transportation problem was conducted by northwestcorner nwc, leastcost lc, and vogel approximation vam. Modi will be used to compute an improvement index for each unused square.

The balanced model will be used to demonstrate the solution of a transportation problem. An initial basic feasible solution ibfs for the transportation problem can be obtained by. Solution of the transportation model b2 module b transportation and assignment solution methods. We could set up a transportation problem and solve it using the simplex method as with any lp problem see using the simplex method to solve linear programming maximization problems, em 8720, or another of the sources listed on page 35 for information about the simplex method. The modi and vam methods of solving transportation problems.

Charnes and cooper 1 also developed a method for finding an optimal solution from ibfs named as stepping stone method. Stepping stone method to find the optimum solution in a transportation problem slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. However, tolsto 1930 was a pioneer in operations research and hence wrote a book on. A company has three factories a, b, and c with production capacity 700, 400, and 600 units per week respectively. Transportation 23 stepping stone method part 2 of 3.