a.Find the starting solution of this transportation model by Least Cost Method. (Unit transportation costs are given in the table) Then find the optimal solution of this transportation model by Stepping Stone Method.
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- a.Find the starting solution of this transportation model by Least Cost Method. (Unit transportation costs are given in the table)
- Then find the optimal solution of this transportation model by Stepping Stone Method.
|
D1 |
D2 |
D3 |
D4 |
Supply |
M1 |
16 |
24 |
14 |
11 |
25 |
M2 |
21 |
18 |
17 |
9 |
30 |
M3 |
15 |
13 |
21 |
14 |
40 |
Demand |
25 |
25 |
20 |
25 |
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- A. An Electrical Company has three workshops in Koforidua, Accra and Kumasi. These workshops produce the following quantities of electric fan. Workshops Monthly production (units) Koforidua 130 Аccra 70 Kumasi 100 The monthly demand for these fans in three towns: Sunyani, Cape Coast and Ho is given below: Destination Weekly Demand (units) Sunyani 80 Саре Сoast 110 Но 60 The unit transportation costs per unit (in GH¢000) from the sources to the destinations are as shown: To From Sunyani Саре Сoast Но Koforidua 9. 14 12 Accra 11 10 6. Kumasi 12 15 00Explain how to determine the number of variables and constraints in a transportation problem when only the number of sources and the number of destinations are known. Be sure to provide examples to illustrate your understanding of these concepts.1. Central Construction Company moves materials between three plants and three projects. Project A requires 72 truckloads each week, project B requires 102, and project C requires 41. Plant W can supply 56 loads, plant X can supply 82, and plant Y can supply 77. Using the cost information given in the following table, compute the optimum transportation cost using the stepping stone method. COST INFORMATION From To Project A To Project B To Project C Plant w P 4.00 8.00 8.00 Plant X 16.00 24.00 16.00 Plant Y 8.00 16.00 24.00
- Using the the 3 methods: Vogel's Approximation Method, Northwest Corner Method and Minimum Cost Method what is the total transportation cost per method?a) Define the Transportation model. b) A Power company has three plants that supply the need of three cities. Each plant can supply the following numbers of kWh of electricity. Plants 1, 2 and 3 can supply 30, 40 and 50 million kWh respectively. The demand at City 1, City 2 and City 3 are 20, 40 and 40, respectively. Table 1 shows the cost of sending electricity from each plant to each city depends on the distance the electricity must travel. Table 1: Transportation costs From City 1 City 2 City 3 To Plant 1 10 11 16 Plant 2 8 14 11 Plant 3 7 10 13 Formulate the above problem as a balanced Transportation problem.Given the following cost information, solve for the optimal transportation cost: Use MODI Method How much is the cost of the initial solution? How much is the cost of the second solution? At the initial solution, what is the value of R4? At the initial solution, what is the value of K4?
- Obtain the initial basic feasible solution to the following transportation problem using north- west corner rule D1 D2 D3 D4 SUPPLY O1 6 4 1 5 14 O2 8 9 2 7 16 O3 4 3 6 2 5 DEMAND 6 10 15 4 Where O1, O2, O3, O4 are the origins and D1, D2, D3, D4 are requirements respectively. Obtain the minimum cost and comment upon the concept of transportation problem and its significance in detail.(b)Consider a transportation model with m sources and n destinations. Describe briefly how you can resolve the following situations while solving the problem: (i) Total supply is greater than total demand,Travelling Salesman Problem (TSP); Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance? Distances W 1 2 3 4 in miles 18 57 27 50 18 0 65 29 61 57 65 0 36 99 3 27 29 36 0 76 4 50 61 99 76 Route=W-1-3-2-4, Distance=182 miles Route=W-3-1-2-4-W, Distance=270 miles Route = W-3-1-2-4, Distance=220 miles Route=W-1-3-2-4-W, Distance=232 miles Route=W-1-3-4-2, Distance=272 miles 1, 2.
- 2. Unbalanced. Provide the transportation model for the calculation of cost given the following data: Use the Stepping Stone Method to solve the following. Use degeneracy method or dummy method if necessary.eBook Problem 10-31 A long-distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over that branch of the network. To keep up with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a oty located at node 7. 3 Maximum number of messages -1. Central Construction Company moves materials between three plants and three projects. Project A requires 140 truckloads each week, project B requires 200, and project C requires 80. Plant W can supply 120 loads, plant X can supply 160 , and plant Y can supply 140. Using the cost information given in the following table, compute the optimal transportation cost using the stepping-stone method. Cost Information From To project A To project B To project C Plant W $10 $4 $9 Plant X 6. 5 Plant Y 7 4