Answered: How many cases should be shipped from…

Business

Operations Management

How many cases should be shipped from each warehouse to minimize costs

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 53P

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Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
A beverage producer needs to minimize shipping costs from its two primary plants in Hamilton and Waterloo. All wholesale orders within the city are shipped from one of these plants. An outlet in Toronto orders 200 cases of soft drinks, on the same day an order for 240 cases comes from London. The plant in Hamilton has 300 cases ready to ship and the plant in Waterloo has 200 cases. The cost of shipping each case to Toronto is $0.50 from Hamilton, and $0.70 from Waterloo. The cost of shipping each case to London is $0.60 from Hamilton, and $0.65 from Waterloo. How many cases should be shipped from each warehouse to minimize costs?
Federated Oil has refineries in Los Angeles and Chicago. The Los Angeles refinery can refine up to two million barrels of oil per year, and the Chicago refinery up to three million. After the oil is refined, it is shippedto two distribution points, Houston and New York City. Federated Oil estimates that each distribution point can sell up to five million barrelsper year. Because of differences in shipping and refining costs, the profit earned (in dollars) per million barrels of oil shipped depends on where the oil was refined and on the point of distribution. This information is listed in the file P04_69.xlsx. The company is considering expanding the capacity of each refinery.Each million barrels of annual refining capacity that isadded will cost $120,000 for the Los Angeles refinery and $150,000 for the Chicago refinery. Determine how Federated Oil can maximize its profit (including expansion costs) over a 10-year period.
Fairway Inc. makes custom golf clubs. They are manufactured in 3 plants in Denver, Phoenix, and Dallas. They are then shipped to distribution centers in Sacramento, Salt Lake, Chicago, Albuquerque, and New York. Since shipping costs are a major expense, management requires an analysis to determine the optimal shipping routes and quantities shipped along those routes. Each plant has a maximum production capacity and each distribution center has a demand that must be satisfied. You must determine how many clubs to send along each route, staying within plant capacity, meeting demand, for the lowest total shipping cost. Shipping Costs per route Plants Sacramento Salt Lake Chicago Albeq New York Capacity Denver $10 $8 $6 $5 $4 310 Phoenix $6 $5 $4 $3 $6 260 Dallas $3 $4 $5 $5 $9 280 Demand 180 80 200 160 220 Number to ship from plant to warehouse: Plants Sacramento Salt Lake Chicago Albeq New York Total Shipped Denver Phoenix…
BC Petrol manufactures three chemicals at its chemical plant in Kentucky: BCP1, BCP2, and BCP3. These chemicals are produced in two production processes known as zone and man. Running the zoning process for an hour costs $48 and yields three units of BCP1, one unit of BCP2, and one unit of BCP3. Running the man process for one hour costs $24 and yields one unit of BCP1 and one unit of BCP2. To meet customer demands, at least 20 units of BCP1, 10 units of BCP2, and 6 units of BCP3 must be produced daily. Assuming a linear relationship, use Excel Solver to determine the optimal mix of processes zone and man to minimize costs and meet BC Petrol's daily demands.
Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below: Grand Rapids Blue Ridge Sunset Ohio Valley 50 40 100 Lakeview 60 50 75 Implement the LP model in Solver and obtain the optimal shipping plan. What is the optimized cost?
The town of Lexington purchases gasoline from three vendors to fuel its fleet of municipal vehicles. Each vendor delivers gasoline in 6,000 gallon quantities. Since vendors must deliver the fuel, a transportation fee (based on the distance the vendor must travel) is added to each delivery. The number of deliveries required by each location, the cost of supplying a truckload of gasoline to each location from each vendor, and the number of truckloads each vendor can deliver are provided below: PoliceStation FireStation BusDepot PublicWorksGarage Deliveries(truckloads)available Vendor A Vendor B Vendor C Deliveries(truckloads)required $500 $350 $400 12 $525 $425 $375 2 $550 $450 $625 18 $600 $575 $475 6 20 14 10 Assuming that the price per gallon of fuel is the same for each vendor, develop a linear programming model that minimizes the total transportation fee that Lexington must pay for supplying all of its facilities’ fuel needs.
Markus, Inc., has harvested 400 tons of lumber from a pine forest located outside of Manchester, 200 tons from a forest near Seattle, and 150 tons from a forest outside of Portland. Japan has placed an order for 300 tons at a price of $1200 per ton, Taiwan needs 300 tons and will pay $1000 per ton, and Singapore wants 250 tons at $1000 per ton. It costs Pine Trees, Inc. $500 to get each ton from the pine forest to the port in Manchester, $400 per ton to the port in Seattle, and $300 per ton to Portland. Assume that each pine forest only supplies its closest port. The following table provides the cost for shipping each ton by sea from these ports to the respective countries: ________________________________________________________________________ SHIPPING COST ($/TON) OF LUMBER BY SEA TO: FROM JAPAN TAIWAN SINGAPORE Manchester 250 250 200 Seattle 250 200 200 Portland…