Plan production for a four-month period: February through May. For February and
ID: 378925 • 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 90 workers on January 31. You are given the following demand forecast: February, 80,960; March, 66,240; April, 100,080; May, 40,080. Productivity is four units per worker hour, eight hours per day, 23 days per month. Assume zero inventory on February 1. Costs are hiring, $55 per new worker; layoff, $75 per worker laid off; inventory holding, $11 per unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 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.)
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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 90 workers on January 31. You are given the following demand forecast: February, 80,960; March, 66,240; April, 100,080; May, 40,080. Productivity is four units per worker hour, eight hours per day, 23 days per month. Assume zero inventory on February 1. Costs are hiring, $55 per new worker; layoff, $75 per worker laid off; inventory holding, $11 per unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 per unit.
Explanation / Answer
Productivity = 4 units per worker hour
Hours available per worker = 8 x 23 = 184 hours
February
March
April
May
a
Forecast
80960
66240
100080
40080
b
Beginning inventory
0
0
0
-13840
c = a-b
Production required
80960
66240
100080
53920
d = c/4
Production hours required
20240
16560
25020
13480
e = d/(8*23)
Regular workforce
110.0
90.0
90*
90*
f = e*4*8*23
Regular production
80960
66240
66240
66240
g
Overtime hours
0
0
5000
0
h= g*4
Overtime production
0
0
20000
0
I = f + h
Total production
80960
66240
86240
66240
j = l - c
Ending inventory
0
0
0
12320
k = c - l
Ending backorders
0
0
13840
0
l
Workers hired
20
0
0
0
m
Workers laid off
0
20.0
0
0
= 10*e*8*23
Straight Time
202400
165600
165600
165600
= 15*g
Overtime
0
0
75000
0
= 11*j
Inventory
0
0
0
135520
= 20*k
Backorder
0
0
276800
0
= 55*l
hiring
1100
0
0
0
= 75*m
Layoff
0
1500
0
0
Total
203500
167100
517400
301120
Total Cost
$1,189,120
*For April and May, no. of workers required = workers available in March.
February
March
April
May
a
Forecast
80960
66240
100080
40080
b
Beginning inventory
0
0
0
-13840
c = a-b
Production required
80960
66240
100080
53920
d = c/4
Production hours required
20240
16560
25020
13480
e = d/(8*23)
Regular workforce
110.0
90.0
90*
90*
f = e*4*8*23
Regular production
80960
66240
66240
66240
g
Overtime hours
0
0
5000
0
h= g*4
Overtime production
0
0
20000
0
I = f + h
Total production
80960
66240
86240
66240
j = l - c
Ending inventory
0
0
0
12320
k = c - l
Ending backorders
0
0
13840
0
l
Workers hired
20
0
0
0
m
Workers laid off
0
20.0
0
0
= 10*e*8*23
Straight Time
202400
165600
165600
165600
= 15*g
Overtime
0
0
75000
0
= 11*j
Inventory
0
0
0
135520
= 20*k
Backorder
0
0
276800
0
= 55*l
hiring
1100
0
0
0
= 75*m
Layoff
0
1500
0
0
Total
203500
167100
517400
301120
Total Cost
$1,189,120