Mondo Motorcycles is determining its production schedule for the next 4 quarters. Demands for motorcycles are forecasted to be 400 in quarter 1; 700 in quarter 2; 500 in quarter 3; 200 in quarter 4. It costs Mondo $800 to manufacture each motorcycle. At the end of each quarter, a holding cost of $100 per motorcycle left in inventory is incurred. When production is increased from one quarter to the next, a cost is incurred, primarily for training employees, at a cost of $700 per motorcycle. When production is decreased from one quarter to the next, a cost is incurred, primarily for severance pay and decreased morale, at a cost of $600 per motorcycle. All demands must be met on time, and a quarter's production can be used to meet demand for the current quarter (as well as future quarters). During the quarter immediately preceding quarter 1,500 motorcycles were produced. Assume that at the beginning of quarter 1, no motorcycles are in inventory. Formulate an IP to minimize the total costs. Which OR problem is this? Decision variables? Objective and objective function? Constraints?

Mondo Motorcycles is determining its production schedule for the next 4 quarters. Demands for motorcycles are forecasted to be 400 in quarter 1; 700 in quarter 2; 500 in quarter 3; 200 in quarter 4. It costs Mondo $800 to manufacture each motorcycle. At the end of each quarter, a holding cost of $100 per motorcycle left in inventory is incurred. When production is increased from one quarter to the next, a cost is incurred, primarily for training employees, at a cost of $700 per motorcycle. When production is decreased from one quarter to the next, a cost is incurred, primarily for severance pay and decreased morale, at a cost of $600 per motorcycle. All demands must be met on time, and a quarter's production can be used to meet demand for the current quarter (as well as future quarters). During the quarter immediately preceding quarter 1,500 motorcycles were produced. Assume that at the beginning of quarter 1, no motorcycles are in inventory. Formulate an IP to minimize the total costs. Which OR problem is this? Decision variables? Objective and objective function? Constraints?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section: Chapter Questions

Problem 41P

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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.)
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