Problem 4-23 (Algorithmic)
EZ-Windows, Inc., manufactures replacement windows for the homeremodeling business. In January, the company produced 15,000windows and ended the month with 9,500 windows in inventory.EZ-Windows’ management team would like to develop a productionschedule for the next three months. A smooth production schedule isobviously desirable because it maintains the current workforce andprovides a similar month-to-month operation. However, given thesales forecasts, the production capacities, and the storagecapabilities as shown, the management team does not think a smoothproduction schedule with the same production quantity each month ispossible.
| February | March | April |
| Sales forecast | 15,000 | 17,000 | 20,000 |
| Production capacity | 14,000 | 15,500 | 17,000 |
| Storage capacity | 6,000 | 6,000 | 6,000 |
The company’s cost accounting department estimates thatincreasing production by one window from one month to the next willincrease total costs by $1.00 for each unit increase in theproduction level. In addition, decreasing production by one unitfrom one month to the next will increase total costs by $0.65 foreach unit decrease in the production level. Ignoring production andinventory carrying costs, formulate and solve a linear programmingmodel that will minimize the cost of changing production levelswhile still satisfying the monthly sales forecasts. If required,round your answers to two decimal places. If an amount is zero,enter "0".
Let:
F = number of windows manufactured in February
M = number of windows manufactured in March
A = number of windows manufactured in April
Im = increase in production level necessaryduring month m
Dm = decrease in production level necessaryduring month m
sm = ending inventory in monthm
| Min | I1 + I2 +I3 + D1 +D2 + D3 | |
| s.t. | | |
| (1) | F - s1 = | February Demand |
| (2) | s1 + M - s2= | March Demand |
| (3) | s2 + A - s3= | April Demand |
| (4) | F - I1 + D1= | Change in February Production |
| (5) | M - F - I2 +D2 = | Change in March Production |
| (6) | A - M - I3 +D3 = | Change in April Production |
| (7) | F ? | February Production Capacity |
| (8) | M ? | March Production Capacity |
| (9) | A ? | April Production Capacity |
| (10) | s1 ? | February Storage Capacity |
| (11) | s2 ? | March Storage Capacity |
| (12) | s3 ? | April Storage Capacity |
If required, round your answers to the nearest dollar.
Cost: $
