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- Qn1. Find the optimal solution to the transportation problem using MODI method. Warehouses Supply WI W2 W3 W4 P1 19 30 50 12 Plants 5. 2. P2 70 30 40 60 P3 40 10 60 20 3. 15 Demand 4)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.3. Consider the transportation problem having the following parameter table: Source Demand Source 1 Source 2 650 Source 3 400 1 2 3 Destination 1 Destination 2 500 750 Demand 10 Vj Assume we have obtained an initial BF solution from northwest corner method, it is: X11 = 10, X12 = 2, X22 = 8, X23 = 9, So the initial transportation simplex tableau looks like below. (Boxed values are cost values, X33 = 1, X34 = 10 circled values are basic variable values.) V₁ = Destination 2 750 800 700 10 1 500 650 400 10 10 800 700 10 ܠ ܕܐ 2 3 300 400 500 10 8 400 500 Destination 3 Destination 4 300 450 10 4 450 600 550 10 9 1 600 Supply 12 550 10 V₁ = 17 11 (10 Supply 12 17 11 Ui U₁² 0 = U₂ = Uz = Do the optimality test (by finding out all u₁, v₁, and čij values, fill all these values in the above table) to determine if the current solution is optimal or not.
- 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 1,2004. 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?Q4. 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 5
- B. For each of the following, you are to set up a linear program and solve the problem using the Excel Solver. 5. Freshly Baked Hub has 3 warehouses and 3 branches store. The following table shows the shipping costs between each warehouses and store, the warehouse capabilities and store capacities. Branch Store To Capabilities From Y A P 350 P 400 P 280 7,000 B P 197 P 510 P 370 8,000 P 470 P 630 P 285 12,000 Сарacity 6,000 14,000 7,000 27,000 Linear Program: Solver Solution: х1 x2 х3 х4 х5 х6 х7 х8 х9 Decision: Constraints: Total Sign Capability 1 2 3 4 5 Minimize C: Warehouse9.2-6. Consider the transportation problem having the following parameter table: Plants respecti and 20 Th Destination 4 Supply mine the 1. 9. 20 30 30 20 to the re 8. 4 9. Source 7. minimiz (а) Fort 3. 6. 4(D) 0. 0. stru Demand (b) Use solu (c) Star tivel tima 25 25 10 20 After several iterations of the transportation simplex method, a BF solution is obtained that has the following basic variables, x= 20, 20. Continue the transportation simplex method for wo more iterations by hand. After two iterations, state whether the solution is optimal 25, 5, X2 =0, x – 0, 15 9.2-9. T systems The (1) electr ing. The and, if so, why. D1.9.2-7. Consider the transportation problem having the fol- 740O 20Qnl. Find the optimal solution to the transportation problem using MODI method. Warehouses Supply W1 W2 W3 W4 P1 19 40 50 20 Plants 17 P2 100 80 7 40 70 P3 40 40 1 60 12 15 Demand 20
- a. Goods have to be transported from sources S1, S2 and S3, to destinations D1, D2 and D3. The transportation cost per unit capacities of the sources and requirements of destinations are given in the following table: Destination Source S1 S2 S4 D1 8 15 3 150 D2 5 10 9 Demand 80 50 Determine the transportation schedule so that cost is minimized. D3 6 12 10 Supply 120 80 802. Distances between factory and its warehouses and demand at each warehouse given in the table. Transportation Table Factory/Warehouse W3 14 18 F1 16 F2 F3 DEMAND 150 SUPPLY 200 150 100 W1 16 18 8 175 W2 22 14 14 125 Solve the problem using least cost method, show total cost.A company has three existing warehouses to which it will ship furniture from a new factory whose location must be decided. The factory will receive raw materials from its wood supplier and fabric supplier. The annual number of shipments, shipment costs and the location of the suppliers and warehouses are shown below Existing facilities Annual L to or from fact cost Coordinate location Wood supplier 120 10 (100, 400) Fabric supplier 200 10 (800,700) Ware h 1 61 10 (300, 600) Ware h 2 40 10 (200, 100) Ware h 3 70 10 (600, 200) Using the median load answer the following questions –Where the factory should be located to minimize annual transportation cost –What will be the minimum annual transportation cost