Consider the following cost matrix to solve a warehouse location problem to minimize the total setup and cransportation costs. Warehouse sites Cust. Loc. A B 1 100 1000 200 2 1000 100 200 3 500 500 500 Fixed Cost 300 300 X What is the largest integer value for X (fixed cost of cite C) for which the greedy algorithm we have seen in the class gives a solution that is not optimal, regardless of how one break the ties?
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- 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.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 costQn1. 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)
- 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.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: Warehouse4. 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?
- Consider the transportation table below. (a) Use the Northwest-Corner Method, the Least-Cost Method and the VAM to get the starting feasible solution. (b) Find the optimal solution by considering the smallest value of the objective function computed in (a). Cost to ship one unit from factory 1 to warehouse A A D Supply Factory 1 can supply 100 units per period 100 Factory 2 200 3 150 Total supply capacity per period Demand 4 12 8 B 7 3 10 80 90 Warehouse B can use 90 units per period 120 8 16 160 1 8 5 (450 450 Total demand per periodsolve for y in part b9.2-6. 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 20
- A retail store in Des Moines, Iowa, receives shipments of a particular product from KansasCity and Minneapolis. Let x 5 number of units of the product received from Kansas City y 5 number of units of the product received from Minneapolisa. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost$0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model…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.1. To find the optimal solution to a linear programming problem using the graphical method a. find the feasible point that is the farthest away from the origin. b. find the feasible point that is at the highest location. c. find the feasible point that is closest to the origin. d. None of the alternatives is correct. Let xij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units, which of the following constraints are correct? P13 - P14 < 100; P14 - P13 < 100 (a) P13 - P14 < 100; P13 - P14 > 100 (b) P13 - P14 < 100; P14 - P13 > 100 (c) P13 - P14 > 100; P14 - P13 > 100 (d) 3. Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in a. standard form. b. bounded form. c. feasible form. d. alternative form.