Find the initial basic feasible solution using northwest corner rule. Step 1. 2. Dec 21, 2023 · Transportation Problem | Set 4 (Vogel’s Approximation Method) The North-West Corner method and the Least Cost Cell method has been discussed in the previous articles. North-West Corner Method (NWC Rule) t is a simple and efficient method to obtain an initial basic feasible solution. Initial basic feasible solution. 1 F F W→ F ↓ W W 2 W 3 W 4 Factory Capacity 1 19 30 50 10 7 F 2 70 30 40 60 9 3 40 8 70 20 18 Warehouse Requirement 5 8 7 14 34 1 Sep 1, 2019 · An initial basic feasible solution for the transportation problem can be obtained by using the North West corner Rule, Least-cost or the Vogel’s Approximation method. The AEDs are sold through three wholesalers. North West Corner Rule (5 Pts) b. Step1: Find the initial basic feasible solution by using any of three methods discussed above. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Hence a feasible solution c omputed by the north-west corner rule can have at most m + n - 1 posi tive xij if the t ransportation problem has m origins and n destination s. Types An introduction to Transportation problem has been discussed in the previous Section, in this, finding the initial basic feasible solution using the NorthWest Corner Cell Method will be discussed. Mar 20, 2009 · The Northwest Corner method (NWC) is one of the methods that obtains a basic feasible solution to various transportation problems [2]. Determine an initial basic feasible solution using any one of the following: North West Corner Rule. 1-Find the initial basic feasible solution by using North-West Corner Rule 1. b) Minimum cost method. They are: (1). Find an initial basic feasible solution using the North-West Corner Rule method. The methods for finding an initial basic feasible solution are well documented. Initial basic feasible solution by Method : 1. Various steps of the. In the present problem m = 3, n = 5. Solution. 9] S 1001 80, and d 140. May 22, 2024 · One disadvantage of using the North-West corner rule to find initial solutions to the transportation problem is that it does not take into account cost of transportation. Northwest Corner Rule, Least Cost or Vogel’s Approximation, and proposed “Mount order method”). a dummy row or a dummy column. LCM (Least Cost method) 3. 20 X 1 + 10 X 2 + 30 X 3 + 20 X 2 + 10 X 5 + 10 X 9 = 310. Exhaust the supply (source) Table 1. Jul 24, 2019 · Problem: [17] Use Vogel’s method to find an initial basic feasible solutions and then find the minimum transportation cost for the following transportation pro blem by Modi method. They are summarized below. Using the tabular values find an initial basic feasible solution (BFS) and the total transportation cost by one of the following method depending on the number of students in your group*: (a) Northwest Corner Method (1-member group) (b) Least Cost Method. Solution: For each row find the least value and then the second least value and take the absolute Find an optimal solution of the transportation problem given in example 1. The cell AE (20) is empty so allocate one unit to it. Use the northwest-corner method to find an initial feasible solution. May 1, 2022 · The initial basic feasible solution (IBFS) is a significant step to achieve the minimal total cost (optimal solution) of the transportation problem. Step 2. Operations Management questions and answers. Vogel’sApproximation Method Remarks: a. For finding the initial basic feasible solution total supply must be equal to total demand. 3. 5. The procedure for constructing an initial basic feasible Aug 26, 2020 · Determine an initial basic feasible solution to the following transportation problem by using (i) NorthWest Corner rule asked Aug 27, 2020 in Operations Research by Vijay01 ( 48. - Hint: The table must be balanced before you can proceed. We will consider only the North West corner rule of developing an initial solution. 2 Check Optimality . In the first phase, the initial basic feasible solution has to be found and the second phase involves optimization of the initial basic feasible solution that was obtained in the first phase. For the following assignment problem where the objective is to minimize the total cost, find an initial basic feasible solution by using - Narthurant Cnmann D1 mast s ) Northwest Corner Rolution (15pts) Z=x=x=x= - Minimum'Cost Rule (3 pts) Minimum Cost Rule Solution ( 15pts) Z= x=x=x= May 12, 2016 · Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the a) Use the Northwest Corner Rule (NCR) to construct a complete initial Basic Feasible Solution. Warehouses W1 W2 W3 W4 Capacity. neither previously selected to be basic nor eliminated from consideration by eliminat-ing their row or column) associated with that row or column to be basic with the only feasible allocation. A feasible solution must satisfy all the equality constraints of the balanced transportation problem. It is a linear programming problem. arriving at an Initial Basic Feasible solution (IBF) with an adequate number of entries needed to initiate the transportation simplex algorithm [1], which is then used to get an optimal solution. Determine a starting basic feasible solution, and go to step 2. The requirements of dealers A, B, C and D are 6, 10, 15 and 4 units per month respectively. Given the initial basic feasible solution, the next step is to check if the current solution is optimal. Apr 18, 2017 · The algorithm for North-West Corner Rule is: 1. North-West corner method (NWCM) The North West corner rule is a method for computing a basic feasible solution of a transportation problem where the basic variables are selected from the North – West corner (i. The shipping cost per unit distributed. There are m + n functional constraints, but 1 of them is redundant. Harold Kuhn (1955) developed and publishes the Hungarian method which is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which Jul 1, 2019 · There are two steps in obtaining the optimal solution of TP. The North-West Corner Rule is a method adopted to compute the initial feasible solution of the transportation problem. Question: Find an initial solution to the following transportation problem. Solve the following transportation problem to find its optimal solution using stepping-stone method. 20 appears in cell (P 1, W 1). Steps in Stepping Stone Method: Transportation Problem. The name North-west corner is given to this method because the basic variables are selected from the extreme left corner. - Report the optimal solution (BVs and their values) and the objective function Solution: Step 1: To find initial basic feasible solution using least cost method: Here the lowest cost (Rs. c) Row Minimum Method. Source: author. Here we shall discuss only three of them. The minimum transportation cost is given by=1x20+1x10+3x20+2x20+1x10+2x20=180. Aug 7, 2018 · Two new divergent approaches to find initial basic feasible solution for transportation problem (TP) are presented in this paper. methods such a s North-West corner method (NWCM) or L east-Cost Method (LCM) or. Step 2: Allocate as much as possible to Start from the new north-west corner of the transportation table and repeat steps 1 and 2 until all the requirements are satisfied. Find a starting solution (i. We discuss here only the following three. Q3. The first step is finding an Initial Basic Feasible Solution (IBFS) and the second one is finding an optimal solution from IBFS [10]. May 24, 2018 · The North-West Corner Rule is a method adopted to compute the initial feasible solution of the transportation problem. 3. Otherwise, return to step 1. The transportation cost per unit is given in the following table. But now we must compute a value for each row (call the values R 1, R 2, R 3 if there are three rows) and for each column (K 1, K 2, K 3) in the transportation table. Find the initial basic feasible solution for the following transportation problem using a. Heuristic method-1 8. Computational source code written in Notepad++ and generated in GNU Octave for finding the basic feasible solution using Northwest Corner Method is given in Appendix A. and B). d) Column Minimum Method. Find the initial feasible solution for the transportation problem using least . Three new methods to find initial basic feasible solution 1807. Now draw a closed path from AD. Minimum Cost Method (5 Pts) SUPPLY 20 30 15 13 TO 10 FROM7 20 40 16 18 DEMAND 40 Step 2: Obtain an initial basic feasible solution. Apr 28, 2021 · This study presents an extensive experimental study of heuristic methods or initial basic feasible solution (IBFS) methods, which is one of the main steps to achieve an optimal or accepted (near-optimal) solution, for a transportation problem (TP). , basic feasible solution) using North-West (Top-Left) Corner Rule and answer questions 1, 2, and 3. VAM (Vogel's approximation method) Sources Supply si S2 S3 Demand Destinations DI 25 8 28 50 D2 21 43 52 100 D3 29 38 33 50 D4 67 30 55 40 90 80 70 d. But there isn’t any superiority among these methods. 1 for a short description. Figure 3. In this study, we proposed 23 new IBFS methods (18 new IBFS methods, and 5 variants of existing IBFS methods) for a TP. Initial basic feasible solution: Least Cost Cell Method will be used here to find the initial basic feasible solution. method are Step 1. , top left corner Example: MODI Method (Modified Distribution Method) Consider the transportation problem presented in the following table. 0. Vogel’s Approximation Method (VAM) is one of the methods used to calculate the initial basic feasible solution to a transportation problem. The concept of North-West Corner can be well understood through a transportation problem given below: A, B, C and D. Proceeding in this way, we observe that F 1 W 2 = 10, F 2 W 2 = 30, F 2 W 3 = 20, F 3 W 3 = 10, F 3 W 4 = 10. NWCM (North-West Corner method) 2. (Adjust supply and demand accordingly). 3 Initial solution - Northwest Corner Rule The initial basic feasible solution can be obtained by using one of several methods. For each row of the 4. Question: Problem 1: Consider the transportation problem given in table 1. It defines the method, outlines the steps which include allocating supply to the north-west corner cell and crossing out satisfied rows and columns. A Company has three factories F1, F2 and F3 which supply to four warehouses W1, W2, W3 and W4. Aug 27, 2020 · Determine an initial basic feasible solution to the following transportation problem by using (i) NorthWest Corner rule (ii) least-cost method. Advanced Math questions and answers. Problem 2 ( 2 7 points) Heart Start produces automated external defibrillators ( AEDs) in each of two different plants ( A. The procedure for constructing an initial basic feasible arriving at an Initial Basic Feasible solution (IBF) with an adequate number of entries needed to initiate the transportation simplex algorithm [1], which is then used to get an optimal solution. A new heuristic method of finding the initial basic feasible solution to solve Northwest Corner Method, Least Cost Method are the well-known adding a rule if there is the same value of Question: Question 1: Initial basic feasible solution by North West Corner Rule, Minimum cost method, and Vogel's Approximation Method Question 2: The below table is the initial solution for transportation model using Least cost method. In steps Obtain the initial basic feasible solution to the following transportation problem using northwest corner rule Where O1, O2, O3, O4 are the origins and D1, D2, D3, D4 are requirements respectively. Consider the below transportation problem. The company's goal is to minimize the cost of meeting customers' demands. (a) Formulate this problem as a transportation problem by constructing the appropriate The steps of the transportation algorithm are exact parallels of the simplex algorithm. Vogel Nov 15, 2021 · The document describes the North-West Corner Rule method for finding an initial feasible solution to a transportation problem. They are discussed below. The article [13] proposed a novel Karagul Step 2. Because production at company P 1 and warehouse requirement of W 1 are 50 and 100 units respectively. We conducted a series of Question: Two plants supply three customers with medical supplies. In this article, the Vogel’s Approximation method will be discussed. Advanced Math. In general, we let The MODI method then requires five Aug 9, 2018 · The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the Operations Management questions and answers. magnitude excluding the costs in the last row. It is necessary to start with IBFS to solve transportation problem [1], [3], [4], [10]. In this article, you will learn how to find the initial basic feasible solution Find the basic feasible solution (bfs) using northwest corner rule. Fortunately, the unit coefficients of the unknown variables in the constraints guarantee an optimal solution with only integer values. There Question: Solve Transportation Problems Problem 1: Consider the transportation problem having the following parameter table: Destination 2 3 4 Supply Source WN- みんw WA Demand 2 2 (1) Find the initial basic feasible solution using (a) North west corner rule (b) Least cost method (c) Vogel's approximation method (ii) Find the optimal solution Jan 1, 2017 · 1. 1. Thus the solution is a basic feasible solution. One can also use NorthWest Corner Method or Vogel’s Approximation Method to find the initial basic feasible solution. Solution: This problem is balanced transportation problem as total supply is equal to total demand. Dec 1, 2022 · Transportation problem is an important branch of operational research. e) Vogel s Approximation Method Question: Consider the following transportation table: - Find an initial feasible solution using the northwest corner rule. Determine the optimal solution of the above problem. Finding an initial basic feasible solution using northwest corner rule. We already understand the North West Corner Method for transportation problem, to obtain feasible solution. However, the existing methods of IBFS do not always provide a good feasible solution which can reduce the number of iterations to find the optimal solution. Jan 1, 2014 · The first step in the approach toward solving a transportation problem is to find the initial basic feasible solution (IBFS) and further optimize the IBFS to obtain an optimal solution. The production capacity of these factories is 14, 16 and 5 units per month respectively. It is also sometimes called as Hitchcock problem. 1 Methods to Solve a Transportation Problem Solution: First, find out an initial basic feasible solution by Vogel’s approximation Method Factory D E F Capacity A 16 140 20 12 60 200 B 14 40 8 120 18 160 C 26 24 16 90 90 Requirement 180 120 150 450 Here, m + n - 1 = 5 So the solution is not degenerate. Determine the values of dual variables, u i and v j, using u i + v j = c ij. An initial basic feasible solution is obtained by Matrix Minimum Method and is shown in table 1. Column minima method 6. Alternative Criteria for Step 1 1. Lines from 1 to 112 are common to each method. The unit costs of shipping from the plants tothe customers, along with the supplies and demands, are given in the following table. Vogel’s Approximation Method [VAM] (or Penalty Method) Let’s dive into each method. Nov 11, 2021 · New Approach of North West Corner Rule Method. Use the optimality condition of the simplex method to determine the entering variable from among all the nonbasic variables. Apr 20, 2010 · The difference among these three methods is the quality of the initial basic feasible solution they produce, in the sense that a better that a better initial solution yields a smaller objective value. However, VAM is an iterative procedure such that in each step, we should find the penalties for each available row and column by taking the least cost and second least cost. The requirements of each warehouse, the capacities for each factory and per unit transport cost in US Dollars are given in the table below. This process very easily allocates the amounts when few May 22, 2024 · One disadvantage of using the North-West corner rule to find initial solutions to the transportation problem is that it does not take into account cost of transportation. If the optimality condition is satisfied, stop. An example is provided and the solution found using the North-West The Transportation problem Assignment First Formulate, then find the Initial Basic Feasible Solution (IBFS) for the following Transportation Models using: North-West Corner method - Least Cost Cell method - Vogel's Approximation method After, apply the U-V method to obtain the optimal solution using the best starting solution obtained initially 1. This process very easily allocates the amounts when few Steps in Modified Distribution Method (MODI) 1. Find the basic feasible solution (bfs) using northwest corner rule. Row minima method 5. Determine an initial basic feasible solution using any one of the three methods given below: North West Corner Rule. Final Table. b. [2] See Answer. Before any method is applied the problem is reduced to a rectangular array of m by n unit costs c ij, a right margin column of supplies a i and a bottom margin row of demands b j. Jul 7, 2021 · These methods used to determine optimality of a basic feasible solution (i. Basically it depends on the problem. We assign x 11 = 50 . B) Improve the solution (do only one iteration). What must you do before beginning the solution steps? There are several methods of finding initial basis feasible solution. Number of basic variables = m + n – 1 = 3 + 4 – 1 = 6. LEARN IN EASY STEPS TO FIND INITIAL FEASIBLE SOLUTION OF A TRANSPORTATION PROBLEM BY NORTH WEST CORNER RULE (NWC) IN QUANTITATIVE TECHNIQUES / OPERATIONS RES Question: Problem 1: Consider the transportation problem having the following parameter table: Destination 1 2 2 3 4 Supply Source 1 2 3 3 2 4 7 4 3 6 3 8 4 2 5 5 2 3 Demand 3 3 2 2 (i) Find the initial basic feasible solution using (a) North west corner rule (b) Least cost method (c) Vogel's approximation method (ii) Find the optimal solution Mar 20, 2009 · The Northwest Corner method (NWC) is one of the methods that obtains a basic feasible solution to various transportation problems [2]. Jul 24, 2019 · North-West Corner Rule all cell evaluations are positive, initial basic feasible solution is optimal. Other methods can be found in standard texts on linear programming. Determine an initial basic feasible solution to the following transportation problem using the North-West corner rule: Jul 7, 2021 · These methods used to determine optimality of a basic feasible solution (i. Find the initial feasible solution of the following transportation problem using 1. The name north-west corner is given to this method because the basic variable is selected from entrance left corner. Solution: An initial basic feasible solution of the transportation problem as given by VAM is : The north-west corner rule is a method adopted to compute the initial feasible solution of the transportation problem. Nov 9, 2023 · There are two phases to solve the transportation problem. North-west is an easy way to find a solution and works efficiently most of the time. Find initial basic feasible solution for given problem by using (a) North-West corner method (b) Least cost method (c) Vogel's approximation method (d) obtain an optimal solution by MODI method if the object is to minimize the total transportation cost. Northwest corner rule: Begin by selecting x 11 (that is, start in the northwest corner Solve transportation problem using vogel's approximation method. Least cost method 3. e. Step 1: Arrange the costs in each row in ascending order of. [2] Question: 1. In Exercises 2-4 find an initial basic feasible solution using (a) the minimum cost rule, (b) Vogel's method, and (c) Larson's method if a hand calculator is available. From X Y Z Demand A $10 $17 $20 80 TO B $19 $13 $18 120 C $12 $9 $14 60 Supply 150 100 50 Based on the given demand and supply the given transportation problem is Before finding the initial solution, a dummy should be introduced The starting solution using The total. 4. See Answer See Answer See Answer done loading Question: Q) Determine the initial basic feasible solution to the following transportation problem using i) Northwest corner rule ii) Least cost method iii) Vogel's approximation method: And find the Find step-by-step Management solutions and your answer to the following textbook question: Refer to the table that follows. Question: 3) Determine the initial basic feasible solution to the following transportation problem using Northwest corner rule And find the optimal solution by u-v method. Select the north-west (upper left hand) comer cell of the transportation table and allocate. North-West corner method 2. The algorithm is as follows: 1. Northwest Corner Method b. Synthesis: Read the following questions and solve. An initial basic feasible solution is exhibited below. The first method supply–demand reparation method (SDRM) uses the supply and demand entities for a problem as the key to find the allocations, rather than the generic transportation cost matrix. Vogel Approximation Method. Find an initial basic feasible solution using one of the following methods. There are five methods or approaches to solve a transportation problem. (2-member group) (c) Vogel Approximation Method (3-member group) Q7. along with the monthly demand from each wholesaler ( warehouse) and monthly production from. Using the North-West Corner Rule method, an amount x Jul 3, 2020 · BASIC FEASIBLE SOLUTION(BFS) There are different methods available to obtain the initial basic feasible solution. Least Cost Method c. This initial basic feasible solution can be obtained by using any of the following five methods: a) North West Corner Rule . Consider the following problem: From/to Customer 1 Customer 2 Customer 3 Customer 4 Supply Plant A 6 8 10 7 38 Plant B 13 9 8 12 63 Plant C 12 7 16 47 Demand 47 23 34 38 11 A) Find an initial basic feasible solution using the North West corner rule. Least Cost Method (or The Matrix Minimum Method) (3). basic feasible solution of any transportation problem is obtained by using well known. Start allocation from upper left hand corner of the table. Two methods are being used extensively for getting the IBF. There are three methods for finding an initial basic feasible solution, NorthWest Corner MethodLeast Nov 1, 2023 · There are three methods for finding an initial basic feasible solution, NorthWest Corner Method; Least Cost Cell Method; Vogel’s Approximation Method; This article will discuss how to optimize the initial basic feasible solution through an explained example. There are various kind of algorithms for finding basic feasible solution of transportation problem, such as the Northwest Corner Method (NWCM), the Least Cost Entry Method (LCEM) and the Vogel Approximation Method (VAM). a. It is a standard method for computing a basic feasible solution (which will be denoted BFS NW in the following), and it does so by fixing the values of the basic variables one by one and starting from the Northwest corner of matrix C; see Fig. North-West(N-W) Corner Rule (2). b) Use the Least Cost Method (LCM) to construct a complete initial Basic Feasible Solution. Mar 19, 2019 · A new modification to the Vogel's Approximation Method was introduced in [12] to find an initial feasible basic solution to the transportation problem. Jul 31, 2017 · Usually, the initial. - Solve this problem using the transportation simplex method outlined in class. c) Use Vogel's Approximation Method (VAM)to select first basic feasible solution. One of them is the Northwest Corner Rule Method and the other one is the Russell Method. Russell's approximation method 7. Vogel's approximation method 4. 1k points) operations research Find initial basic feasible solution for given problem by using (a) North-West corner method (b) Least cost method (c) Vogel's approximation method (d) obtain an optimal solution by MODI method if the object is to minimize the total transportation cost. This allocation meets the requirements of warehouse W 1 and still have a Demand of Oct 23, 2020 · Unlike many LP problems, the transportation problem is feasible to solve by hand using a series of tables and well-documented strategies such as the Northwest-Corner Method to find an initial basic feasible solution and then using techniques like the Least-Cost Method or the Stepping Stone Method. There are several methods available to obtain an initial basic feasible solution of a transportation problem. Oct 26, 2021 · The calculations resulted in a degenerated solution for which the total cost of transport was €165,109. Matrix Minimum Method. Find an initial basic feasible solution of the following problem using north west corner rule. Hence using the north west corner rule we have derived a basic feasible solution In applying the MODI method, we begin with an initial solution obtained by using the northwest cor-ner rule or any other rule. If the total supply and demand aren’t equal, make them equal by adding. Generally the Vogel Approximation Method produces the best initial basic feasible solution, and the North West Corner Method produces the worst, but the North West Corner Method involves least Least cost Method is one of the method to obtain feasible solution of Transportation Problem. 1 The Transportation Problem 325 C- 15 2 (1 2 7 3 3 7 6 6 4. Obtain the minimum cost and comment upon the concept of a transportation problem and its significance in detail. Jul 28, 2011 · The so-called Northwest corner rule appears in virtually every text-book chapter on the transportation problem. Table 1. Jan 18, 2024 · Transportation problem is a special kind of Linear Programming Problem (LPP) in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the sources and destination respectively such that the total cost of transportation is minimized. kz bm ot hm pq ab by sx wa ph