12. Refer to Problem 11. Suppose that shipments between the two warehouses are permitted at $2 per unit and that direct shipments can be made from Plant 3 to Customer 4 at a cost of $7 per unit. a. Develop a network representation of this problem. b. Formulate a linear programming model of this problem. C. Solve the linear program to determine the optimal shipping plan.
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- 1. Cars are shipped from three distribution centre's to five dealers. The following table summarizes the mileage between the distribution center's and the dealers together with the monthly supply. Dealer 1 3 4 Supply 1 38 Center 2 3 4 19 3 4 4 16 4 4 9. 4 6. 23 Demand 25 29 21 | 21 a) Find the Initial basic feasible solution using any of the three methods. b) Check the Optimum solution using UV method.summanzed below: WAREHOUSE FACTORY F1 9 12 7 18 6 8 13 9 21 20 7 10 11 12 7 F3 14 15 22 Factory output and warehouse supplies that must be maintained are as follows: Eachory Mnits produced/day Warehouse Daily Supply #1 35 1 15 #2 25 2. 12 #3 40 3. 22 24 32 4. 30 5. 20 Determine; a. The best possible factory-to-warehouse shipping program using Vogel's Approximation Method. b. What is the cost of this shipping program?2) A company is considering a plan to produce or buy/outsource a certain item used in the production of new type of cars. Making the item would involve annual lease costs of $150,000. Cost and volume estimates are as follows: Make Buy Annual fixed cost $150,000 None Variable cost/unit $60 $80 Annual volume 12,000 12,000 (units) a. Given these numbers, should the firm buy or make this item? b. There is a possibility that volume could change in the future. At what volume would the company be indifferent between making and buying?
- Consider the following distribution system: Single product. Two plants, referred to as plant p1 and plant p2. Plant p2 has an annual capacity of 40,000 units. The two plants have the same production costs. • • Two existing warehouses, referred to as warehouse w1 and warehouse w2, have identical warehouse handling costs. • Three markets areas, c1, c2, and c3, with demands of 50,000, 100,000 and 50, 000, respectively, Table 1 provides distribution cost per unit. For instance, distributing one unit from plant p1 to warehouse w2 costs $5. Convert the following diagram into the table. No need for any calculation. Facility warehouse w1 W2 p1 2 3 p2 2 0 c1 3 5 c2 3 2 C3 4 3(1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). B C 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route B 1 2 3 4 A 10 11 9 14 Step 1b: Column subtraction. Truck / Route 1 2 3 4 A 10-6=4 = = = = = B = с = C Step 2: Testing for optimal solution (show your lines covering the zero entries). What is the minimum number of lines required to cover all zeros? D 8 14 10 13 D = = D =Required information The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec- tively. Each distribution center heeds to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Plant 1 2 3 1 1450 1750 1250 Distribution Center 3 1050 1250 1450 Obtain an optimal solution, and determine the total cost. Total Cost = $ 2 1950 2050 1850 The freight cost for each shipment is $100 plus 50 cents per mile. 4 1350 1650 1550
- Q2) (a) A Missouri job shop has four departments--machining (M), dipping in a chemical bath (D), finishing (F), and plating (P)-assigned to four work areas. The operations manager, Mary Marrs, has gathered the following data for this job shop as it is currently laid out. It costs $0.50 to move 1 workpiece 1 foot in the job shop. Determine cost of material handling in the current layout. Further, suggest a revised layout that has the lowest material handling cost. 100s of Workpieces Moved Between Work Areas Distances Between Work Areas in Feet M D F P M D F P M 18 2 20 12 8 4 2 6. 10 F 18 4The method for determining facility location which involves determining x and y co-ordinates of the proposed new location O a. Factor Rating Method O b. Locational Break-even Analysis O C. Transportation Method Od. Centroid MethodQ.) Given the following network, with the indicated flow capacities along each branch, determine the maximum flow from source rode 1 to destination node 6 and the flow along each branch: 15 12 20 0 14 11
- Destination Destination Destination Supply Source 1 75 8 320 Source 2 6 160 13120 4. Source 3 6.5 Demand 160 200 240 Based on the transportation table shown, total transportation cost using North- West Corner Method will be: a. 3040 Ob. 4100 O c. 2640 O d. 1920A company with a network of 10 pipelines transports mango juice according to the details shown in Table 1. Determine the maximum flow per hour. 1. Table/Jadual 1 Сарacity Node Node (m3/h) 140 100 120 100 120 80 110 100 100 100 Reverse Capacity |(m³/h) 60 20 40 40 40 20 30 40 60 60 Start End Pipeline 1 2 3 4 1 1 1 2 3 4 6 6 7 3 7 7 8 8 10Q3)) A firm has established a distribution network for the supply of a raw material critical to its manufacturing Currently there are three origins for this raw material, which must be shipped to three manufacturing plants. The current network has the following characteristics: Origin 1 Origin 2 Origin 3 DEMAND Plant 1 $7 $10 Plant 2 $5 $7 $8 45 Plant 3 $2 $3 SUPPLY 30 40 50 120/120 $3 $9 35 40 (a) Calculate a solution using the northwest-corner rule. Calculate the cost of this solution. (b) Calculate the solution using intuitive lowest cost method. Calculate the cost of this solution. (c) Using the solution in (c), calculate improvement indices, iterate once. Can you achieve a better solution? If yes, what is the cost of this solution?