Develop a production plan and calculate the annual cost for a firm whose demand
ID: 366649 • Letter: D
Question
Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $110 for each temp; layoff, $220 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.)
Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $110 for each temp; layoff, $220 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.)
Explanation / Answer
The aggregate plan is as follows:
Fall
Winter
Spring
Summer
A
Forecast
10000
8000
7000
12000
B
Beginning inventory
500
-2300
0
200
C = A - B
Production required
9500
10300
7000
11800
D = C/2
Production hours required
19000
20600
14000
23600
E = 30*60*8
Production hours available1
14400
14400
14400
14400
F
Overtime hours
0
6200
0
0
G
Temp workers2
0
0
0
20
H = G*8*60
Temp worker hours available
0
0
0
9600
I = E+F+H
Total hours available
14400
20600
14400
24000
J = I/2
Actual production
7200
10300
7200
12000
K = J -A
Ending inventory
-2300
0
200
200
L
Workers hired
0
0
0
20
M
Workers laid off
0
0
0
20
Rate
Fall
Winter
Spring
Summer
5
Straight time (5*(E+H))
$ 72,000
$ 72,000
$ 72,000
$ 120,000
8
Overtime (8*F)
$ -
$ 49,600
$ -
$ -
5
Inventory (5*K),
$ -
$ -
$ 1,000
$ 1,000
10
Backorder (10*K)
$ 23,000
$ -
$ -
$ -
110
Hiring (110*L)
$ -
$ -
$ -
$ 2,200
220
Layoff (220*M)
$ -
$ -
$ -
$ 4,400
Total
$ 95,000
$ 121,600
$ 73,000
$ 127,600
Annual cost
$ 417,200
Total cost pf plan = $417,200
Fall
Winter
Spring
Summer
A
Forecast
10000
8000
7000
12000
B
Beginning inventory
500
-2300
0
200
C = A - B
Production required
9500
10300
7000
11800
D = C/2
Production hours required
19000
20600
14000
23600
E = 30*60*8
Production hours available1
14400
14400
14400
14400
F
Overtime hours
0
6200
0
0
G
Temp workers2
0
0
0
20
H = G*8*60
Temp worker hours available
0
0
0
9600
I = E+F+H
Total hours available
14400
20600
14400
24000
J = I/2
Actual production
7200
10300
7200
12000
K = J -A
Ending inventory
-2300
0
200
200
L
Workers hired
0
0
0
20
M
Workers laid off
0
0
0
20
Rate
Fall
Winter
Spring
Summer
5
Straight time (5*(E+H))
$ 72,000
$ 72,000
$ 72,000
$ 120,000
8
Overtime (8*F)
$ -
$ 49,600
$ -
$ -
5
Inventory (5*K),
$ -
$ -
$ 1,000
$ 1,000
10
Backorder (10*K)
$ 23,000
$ -
$ -
$ -
110
Hiring (110*L)
$ -
$ -
$ -
$ 2,200
220
Layoff (220*M)
$ -
$ -
$ -
$ 4,400
Total
$ 95,000
$ 121,600
$ 73,000
$ 127,600
Annual cost
$ 417,200
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