Plan production for a four-month period: February through May. For February and
ID: 463868 • Letter: P
Question
Plan production for a four-month period: February through May. For February and March, you should produce to exact demand forecast. For April and May, you should use overtime and inventory with a stable workforce; stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May (zero overtime in February and March). If demand exceeds supply, then backorders occur. There are 100 workers on January 31. You are given the following demand forecast: February, 81,984; March, 67,200; April, 100,320; May, 40,320. Productivity is four units per worker hour, eight hours per day, 21 days per month. Assume zero inventory on February 1. Costs are hiring, $50 per new worker; layoff, $70 per worker laid off; inventory holding, $11 per unit-month; straight-time labor, $12 per hour; overtime, $18 per hour; backorder, $22 per unit. Develop a production plan and calculate the total cost of this plan. Note: Assume any layoffs occur at beginning of next month. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.) February March April May Forecast 81,984 67,200 100,320 40,320 Beginning inventory Production required Production hours required Regular workforce Regular production Overtime hours Overtime production Total production Ending inventory Ending backorders Workers hired Workers laid off
Explanation / Answer
Productivity
4
units/worker/hr
Days available per month
21
Productivity per unit
0.25
hours per unit
Hours available per day
8
Beginging Workforce
100
Regular Hours available per month
168
Beg. Inv.
0
Chase
Chase
Stable Wrk
Stable wrk
Formulas
Forecast
81984
67200
100320
40320
Beginning inventory
0
0
0
-13120
Forecast - Beg. Inv.
Production required
81984
67200
100320
53440
Prod. Req. x productivity
Production hours required
20496
16800
25080
13360
Prod. Hrs. req - Prod. Hrs. Available
Regular workforce
122
100
100
100
Regular workforces x 168
Regular production hrs.
20496
16800
16800
16800
OT = min(5000, Prod. Hrs req. - reg. prd. Hrs)
Overtime hours
0
0
5000
0
OT hrs./productivity
Overtime production
0
0
20000
0
Rrg. Prod. Hrs/productivity + OT prod.
Total production
81984
67200
87200
67200
Total prod. - prod. Req.
Ending inventory
0
0
0
13760
Total prod. - prod. Req.
Ending backorders
0
0
-13120
0
Workers hired
22
0
0
0
Workers laid off
0
22
0
0
February
March
April
May
$12.00
Straight time
$245,952
$201,600
$300,960
$160,320
$18.00
Overtime
$0
$0
$360,000
$0
$11.00
Inventory
$0
$0
$0
$151,360
$22.00
Backorder
$0
$0
$288,640
$0
$50.00
Hiring
$1,100
$0
$0
$0
$70.00
Layoff
$0
$1,540
$0
$0
Total
$247,052
$203,140
$949,600
$311,680
Total cost
$1,711,472
Productivity
4
units/worker/hr
Days available per month
21
Productivity per unit
0.25
hours per unit
Hours available per day
8
Beginging Workforce
100
Regular Hours available per month
168
Beg. Inv.
0
Chase
Chase
Stable Wrk
Stable wrk
Formulas
Forecast
81984
67200
100320
40320
Beginning inventory
0
0
0
-13120
Forecast - Beg. Inv.
Production required
81984
67200
100320
53440
Prod. Req. x productivity
Production hours required
20496
16800
25080
13360
Prod. Hrs. req - Prod. Hrs. Available
Regular workforce
122
100
100
100
Regular workforces x 168
Regular production hrs.
20496
16800
16800
16800
OT = min(5000, Prod. Hrs req. - reg. prd. Hrs)
Overtime hours
0
0
5000
0
OT hrs./productivity
Overtime production
0
0
20000
0
Rrg. Prod. Hrs/productivity + OT prod.
Total production
81984
67200
87200
67200
Total prod. - prod. Req.
Ending inventory
0
0
0
13760
Total prod. - prod. Req.
Ending backorders
0
0
-13120
0
Workers hired
22
0
0
0
Workers laid off
0
22
0
0
February
March
April
May
$12.00
Straight time
$245,952
$201,600
$300,960
$160,320
$18.00
Overtime
$0
$0
$360,000
$0
$11.00
Inventory
$0
$0
$0
$151,360
$22.00
Backorder
$0
$0
$288,640
$0
$50.00
Hiring
$1,100
$0
$0
$0
$70.00
Layoff
$0
$1,540
$0
$0
Total
$247,052
$203,140
$949,600
$311,680
Total cost
$1,711,472