like this fill the boxes A fruit juice manufacturer has recently begun negotiations with brokers in the areas where it intends to distribute itsproducts. Before finalizing the agreements, however, the manager wants to determine shipping routes and costs.The firm has three plants with the capacities as shown below: Estimate demands in each of the warehouse localities are:PLANT CAPACITY (BOXES PER WEEK)WAREHOUSE DEMAND (BOXES PER WEEK)12325,00045,00030,000The estimated ship cost per box for the various routes are:TOFROMABCDI12452233234121Row/Column Opportunity CostDemandABCDRow/ColumnOpportunity Cost10,00020,00040,00020,000SupplyCellCost of the aboveallocationTest of unallocated Cells AmountTotal Cost

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Answered: A fruit juice manufacturer has recently…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.5: Set-covering And Location-assignment Models

Problem 34P

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Consider a supply chain network with three potential sites for warehouses and eight retailer regions. The fixed costs of locating warehouses at the three sites are given as follows: Site 1: $100,000 Site 2: $80,000 Site 3: $110,000 The capacities of the three sites are 100,000, 80,000, and 125,000 respectively. The retailer demands are 20,000 for the first four retailers and 25,000 for the remaining. The unit transportation costs ($) are given in Table below: a. Formulate a mixed integer linear program to determine the optimal location and distribution plan that will minimize the total cost. You must define your variables clearly, write out the constraints, explaining briefly the significance of each and write the objective function. Assume that the retailers can receive supply from multiple sites. Solve using any optimization software. Write down the optimal solution. b. Reformulate the optimization problem as a linear integer program, assuming dedicated warehouses, that is, each…
Noble Amazon sells books online. Management is trying to determine the best sites for the company's warehouses. The five potential sites under consideration are listed in the first column of the following table. Most of the sales come from customers in the United States. The average weekly demand from each region of the country, the average shipping cost from each warehouse site to each region of the country, the fixed cost per week of each warehouse if it is operated, and the maximum capacity of each warehouse (if it is operated) are shown in the following table. (a) Formulate the above case algebraically and on a spreadsheet as a mixed BIP model (b) Solve the spreadsheet model to determine which warehouse sites Noble Amazon should operate and how books should be distributed from each warehouse to each region of the country to minimize total cost. (c) Comment on the final results using your own words.
The Acme Company operates four factories that ship products to five warehouses. The shipping costs, requirements capacities, and optimal allocations are shown below. Factory Shipping Cost per Case to Warehouses Capacity W1 W2 W3 W4 W5 F1 $1.50 $4.50 $6.00 $7.50 $9.00 40,000 30,000 10,000 F2 $3.00 $3.00 $1.50 $6.00 $7.50 30,000 25,000 5,000 F3 $1.50 $7.50 $1.50 $4.50 $1.50 30,000 10,000 20,000 F4 $7.50 $3.00 $6.00 $7.50 $6.00 25,000 25,000 Demand 30,000 35,000 25,000 15,000 20,000 125,000 What is the total cost of the optimal solution? Total cost = $nothing. (Enter your response to the nearest dollar.)
Paul Bergey is in charge of loading cargo ships for International Cargo Company (ICC) at the port in Newport News, Virginia. Paul is preparing a loading plan for an ICC freighter destined for Ghana. An agricultural commodities dealer wants to transport the following products aboard this ship. Commodity A B C D Amount Available (tons)4,8002,5001,2001,700 Volume per Ton (cubic feet) 40256055 Profit per Ton ($)70506080 Paul can elect to load any and/or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions. Cargo Hold Forward Center Read Weight Capacity (tons) 3,000 6,000 4,000 Volume Capacity (cubic feet) 145,000 180,000 155,000 More than one type of commodity can be placed in the same cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 10% of the weight in the rear cargo hold, and the center cargo hold must be between 40% and 60% of the total…
The Palestinian ministry of sports has four basketball games on a particular night. The ministry wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The supply is always one team of officials and the demand is for only one team of officials at each game. The distances in km for each team of officials to each game location are shown in the following table officials 1 2 3 a 100 150 120 b 130 210 90 c 120 170 90 A) Formulate this problem as Assignment Model (the objective function and constraint equations for the demand and supply) . b) Use QM to solve the Model.
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.
The High-Price Oil Company owns a pipeline network that is used to convey oil from its source to several storage locations. A portion of the network is as follows: Due to the varying pipe sizes, the flow capacities vary. By selectively opening and closing sections of the pipeline network, the firm can supply any of the storage locations. a. If the firm wants to fully utilize the system capacity to supply storage location 7, how long will it take to satisfy a location 7 demand of 100,000 gallons? What is the maximal flow for this pipeline system? b. If a break occurs on line 2–3 and that line is closed down, what is the maximal flow for the system? How long will it take to transmit 100,000 gallons to location 7?
The following table presents cost, capacity, and demand data for a transportation problem in Stephanie Robbin’s furniture company. Set up the appropriate transportation table and find the optimal solution using Excel's solver. From/To 1 2 3 Supply A 30 10 5 20 B 10 10 10 30 C 20 10 25 75 Demand 40 60 55 a. Is the problem balanced? [ Select ] ["Yes", "it is balanced", "No", "cannot determine"] , If not, where? [ Select ] ["Neither", "Supply", "Demand"] , and by how much? [ Select ] ["0", "40", "30", "25"] b. What is the optimal cost? $ [ Select ] ["2,500", "1,100", "1,275", "1,300"] c. Were you able to meet all demand requirement? [ Select ] ["no", "cannot determine based on the information given", "yes"] If not, which destination (s) was/were not met? [ Select ] ["none, all destinations were met based on supply and demand being equal", "destination 3 by 30 units", "destination 2 by 30 units", "destination 1 by 25 units…
Tommy Hilfiger is currently considering to source certain textile goods, Tommy Jeans, from Mexico. The estimated shipping time from Mexico to the U.S. for each shipment of Tommy Jeans is 4 days and the estimated freight cost of each shipment is $800. On the other hand, the current average shipping time from Vietnam to the U.S. for each shipment of Tommy Jeans is 23 days and the average freight cost is $2300. Even though the shipping time and freight cost seem to be much lower in case of Mexico, Tommy Hilfiger management is concerned about the production cost of each Jeans shipment. The management anticipates that the production cost of each Jeans shipment will be higher in Mexico compared to Vietnam. However, Tommy Hilfiger management has decided that even if the total cost (sum of production cost, freight cost, and holding cost) remain similar to Vietnam, Tommy Hilfiger will still source Jeans from Mexico because of the reduced shipping time, which, in turn, will result in better…
The Gulf Coast Foundry is developing a long-range strategic plan for buying scrap metal for its foundry operations. The foundry can buy scrap metal in unlimited quantities from two sources, Atlanta (A) and Birmingham (B), and it receives the scrap daily in railroad cars. The scrap is melted down, and lead and copper are extracted for use in the foundry processes. Each railroad car of scrap from source A yields 1 ton of copper and 1 ton of lead and costs $10,000. Each railroad car of scrap from source B yields 1 ton of copper and 2 tons of lead and costs $15,000. If the foundry needs at least 21/2 tons of copper and at least 4 tons of lead per day for the foreseeable future, how many railroad cars of scrap should be purchased per day from Source A and Source B to minimize the long-range scrap metal cost?
A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 30x1 + 30x2 + 25x3+ 20x4s.t. 5x1 + 10x2 + 8x3 + 12x4 ≤ 22 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5} xj = {1, if location j is selected0, otherwise xj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected? What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)? (Round your answer to the nearest whole number.)
A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 35x1 + 25x2 + 15x3+ 30x4s.t. 7x1 + 8x2 + 7x3 + 13x4 ≤ 18 {Constraint 1}x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}x1 + x2 ≤ 1 {Constraint 3}x1 + x3 ≥ 1 {Constraint 4}x2 = x4 {Constraint 5} xj = {1, if location j is selected0, otherwisexj = 1, if location j is selected0, otherwise Solve this problem to optimality and answer the following questions:

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