An XYZ company has a W, H, O plant with a monthly production capacity of 60 tons, 50 tons, and 42 tons, respectively; and has 3 sales warehouses in cities A, B, C, D Where each warehouse has a monthly requirement of 30 tons, 34 tons, 44 tons and 25 tons. With shipping cost W to ABCD = IDR 12,000,-, IDR. 8.000,-, Rp. 12.000,-, Rp. 14,000,-; H to A B C D = Rp. 8.000,-, Rp. 18.000,-, Rp. 10,000,-, Rp. 6.000,-; and O to ABCD = Rp. 16.000,-, Rp. 16.000,-, Rp. 2,000, Rp. 10,000,-. Please calculate using Vogel's Approximation Method or VAM Question a. What is the best transportation model in your opinion to solve the above problems? b. What is the minimum transportation cost to solve the shipping transportation problem! c. Based on these calculations, give suggestions regarding the transportation model and the amount of costs incurred by the company!

An XYZ company has a W, H, O plant with a monthly production capacity of 60 tons, 50 tons, and 42 tons, respectively; and has 3 sales warehouses in cities A, B, C, D Where each warehouse has a monthly requirement of 30 tons, 34 tons, 44 tons and 25 tons. With shipping cost W to ABCD = IDR 12,000,-, IDR. 8.000,-, Rp. 12.000,-, Rp. 14,000,-; H to A B C D = Rp. 8.000,-, Rp. 18.000,-, Rp. 10,000,-, Rp. 6.000,-; and O to ABCD = Rp. 16.000,-, Rp. 16.000,-, Rp. 2,000, Rp. 10,000,-. Please calculate using Vogel's Approximation Method or VAM Question a. What is the best transportation model in your opinion to solve the above problems? b. What is the minimum transportation cost to solve the shipping transportation problem! c. Based on these calculations, give suggestions regarding the transportation model and the amount of costs incurred by the company!

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 15P

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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?
PRICING SUITS AT SULLIVANS Sullivans is a retailer of upscale mens clothing. Suits cost Sullivans 320. The current price of suits to customers is 350. which leads to annual sales of 300 suits. The elasticity of the demand for mens suits is estimated to be 2.5 and assumed to be constant over the relevant price range. Each purchase of a suit leads to an average of 2.0 shirts and 1.5 ties being sold. Each shirt contributes 25 to profit, and each tie contributes 15 to profit. Determine a profit-maximizing price for suits. In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must determine the prices of shirts and ties, as well the price of suits. Assume that the unit costs of shirts and ties are, respectively, 20 and 15. Continue to assume that, on average, 2.0 shirts and 1.5 ties are sold along with every suit (regardless of the prices of shirts and ties), but that shirts and ties have their own separate demand functions. These demands are for shirts and ties purchased separately from suit purchases. Assume constant elasticity demand functions for shirts and ties with parameters 288,500 and 1.7 (shirts), and 75,460 and 1.6 (ties). Assume the same unit cost and demand function for suits as in Example 7.3. a. How much should the company charge for suits, shirts, and ties to maximize the profit from all three products? b. The assumption that customers will always buy, on average, the same number of shirts and ties per suit purchase, regardless of the prices of shirts and ties, is not very realistic. How might you change this assumption, and change your model from part a accordingly, to make it more realistic?