Develop a production schedule to produce the exact production requirements by va
ID: 455261 • Letter: D
Question
Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem. The monthly forecasts for Product X for January, February, and March are 960, 1,510, and 1,210, respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are 22 working days in January, 19 in February, and 21 in March. Beginning inventory is 510 units. Storage cost is $5 per unit per month based on ending inventory level, standard pay rate is $7 per hour, hiring and training cost is $300 per worker, layoff cost is $400 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 48 workers and that they work 8 hours per day. (Leave no cells blank - be certain to enter "0" wherever required. Input all values as positive values. Round Workers Required up to next higher whole number. Round all other variables to nearest whole number.)
Explanation / Answer
January
February
March
Forecast
960
1,510
1,210
Safety stock
480
755
605
Beginning inventory
510
483
767
Net production required
930
1,782
1,048
Workers required
53
118
63
Hired
5
65
0
Laid off
0
0
55
Actual production
933
1794
1058
Ending inventory
483
767
615
Explanation:
For January Month
Safety Stock is half of the forecast for that month. Hence Safety Stock = 960/2 = 480.
Beginning Inventory = 510 units
Net production units = Month’s forecast + safety stock – Beginning Inventory
= 960+480-510 = 930 units.
Workers hired = Production quantity/((productivity/hour)*8 hours*no.of days )
= 930/(0.1*8*22) = 53.
Available workers = 48.
Workers to be hired = 53-48 = 5 workers.
Actual production = workers*productivity*8 hours*no.of days = 53*0.1*8*22 = 933.
Ending inventory = Actual production + Beginning Inventory – Forecast
= 930+510-960 = 483 units.
The ending inventory of January is the beginning inventory of February. Same calculation is followed for the next month.
January
February
March
Labor cost
$ 65,296
$ 1,25,552
$ 74,088
Inventory cost
$ 2,415
$ 3,835
$ 3,075
Hiring cost
$ 1,500
$ 19,500
$ -
Layoff cost
$ -
$ -
$ 22,000
Total cost
$ 69,211
$ 1,48,887
$ 99,163
Total
$ 3,17,261
Labour Cost = No.of workers*No.of days*Hour rate* 8 hours
= 53*22*8*7 = $65,296
Inventory cost = Ending inventory * Monthly storage cost
= 483*5 = $ 2,415
Hiring Cost = No.of workers hired*300 = 5*300 = $1500
Layoff cost for January is $ 0.
January
February
March
Forecast
960
1,510
1,210
Safety stock
480
755
605
Beginning inventory
510
483
767
Net production required
930
1,782
1,048
Workers required
53
118
63
Hired
5
65
0
Laid off
0
0
55
Actual production
933
1794
1058
Ending inventory
483
767
615
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