8.3-1. Consider the assignment problem having the following cost table. Assignee A B C D 1 8676 2 6587 7 Task 3 5 3 5345 5 4 7 4 496 (a) Draw the network representation of this assignment problem. (b) Formulate this problem as a transportation problem by con- structing the appropriate parameter table. (c) Display this formulation on an Excel spreadsheet. c (d) Use the Excel Solver to obtain an optimal solution.
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- 9-7 The management of the Executive Furniture Corporation decided to expand the production capacity at its Des Moines factory and to cut back the production capacities at its other two factories. It also recognizes a shifting market for its desks and revises the requirements at its three warehouses. The table on this page provides the requirement at each of the warehouses, the capacity at each of the factories, and the shipping cost per unit to ship from each factory to each warehouse. Find the least-cost way to meet the requirements given the capacity at each factory.b) Table 2 shows the transportation costs, demands and supplies of a transportation problem. Table 2: Transportation problem To From A B C Supply 1 7 4 150 8 11 50 3 250 10 11 12 Demand 100 200 150 i) Find the initial solution using the Minimum Cost method and identify the special case if any. ii) Suppose the initial solution to the above problem takes the basic variables x11 = 100, x12 = 50, X23 = 50, x32 = 150 and x33 = 100. Find the optimal solution using Modified Distribution method. iii) Present the optimal solution obtained in ii) graphically.4. Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. Set up the solution in Excel and solve with Solver. What are total costs?
- Explain how to determine the number of variables and constraints that would be in a transportation problem simplyby knowing the number of sources and the number of destinations.For the transportation problem having the following parameter table: Warehouse 2 Plant 1 1 40 2 35 3 100 80 65 69 40 50 85 42 80 68 70 demand 65 85 (a) Formulate the network representation of this problem as a minimum cost flow problem. Use the northwest corner rule to obtain an initial BF solution. (b) Apply one iteration of the network simplex method to find the next BF solution. 3 70 4 supply 75 125 100Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Supply 200 Source Destination Demand 50 A 125 125 в 100 Y 150 Shipping costs are: Source 3 9 Destination Y 2 A в 10 6. (Source B cannot ship to destination Z) A. According to the Northwest Corner method, the initial solution would have a total transportation cost of B. According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of C. According to the minimum cell cost method, the initial solution would have a total transportation cost of D. According to the Northwest Corner method, the initial solution would give to cell CIII a loading of E. According to the Vogel's Approximation Method, the initial solution would give to cell Cll a loading of F. According to the minimum cell cost method, the initial solution would give to cell BI a loading of
- 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 25Problem1 Acme Manufacturing Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next 4 months is shown in the following table along with the expected production costs and the expected Month Demand Production Cost Production Capacity 1 420 $49.00 500 a) Formulate an LP model for this problem. b) Create a spreadsheet model for this problem and solve it using Solver. 2 580 $45.00 520 3 310 $46.00 450 4 540 $47.00 550 capacity for producing these items. Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. The company also wants to maintain a safety stock of at least 50 units per month. Acme wants to determine how…A product is produced at three plants and shipped to three warehouses. Plant capacity, warehouse demands and transportation costs per unit are shown in the table. Plant Warehouse A B C Plant Capacity 1 20 16 26 500 2 10 14 8 500 3 12 18 6 400 Warehouse Demands 200 600 600 a) Find an initial feasible solution and calculate the cost for this solution. b) If improvement can be made, make one step improvement to the solution in part a, and calculate the cost for the improved solution.
- TRANSPORTATION . Given the following transport. tion matrix where the numbers in the cells represent cost of transporting 1 unit from a specific source to a specific destination, determine the initial solution using the 3 methods and determine the optimum solution by using the initial solution with the lowest value of Z. 3 4 40 35| M M 20 30 From/To 5 6 Dummy | Supply 1 M 100 60 45 M 200 3 12 M 300 4 15 10 300 5 M M 15 300 Demand 300 300 300 | 150 150 1,200Q4. Solve the following transportation problem using the following table. Obtain an Initial BFS to the following Transportation problem using NORTH WEST CORNER RULE method? D1 D2 D3 D4 SUPPLY 01 1 7 4 300 02 2 400 03 8 3 3 2 500 DEMAND 250 350 400 200 1200 5Consider the assignment problem having the following cost table. Task Assignee A B C D 1 8696 7 2 6589 7 3 5345 4 7 4 6 6 a. Formulate this problem as a transportation problem by constructing the appropriate parameter table. b. Display this formulation on an Excel spreadsheet, and use the Excel Solver to obtain an optimal solution. c. Manually apply the Hungarian algorithm to solve this problem.