Dear reader how i can calculate the overtime production units in each month for
ID: 406242 • Letter: D
Question
Dear reader how i can calculate the overtime production units in each month for the following question (thanks in advance)
Skycell, a major European cell phone manufacturer, is making production plans for the coming year. Skycell has worked with its customers (the service providers) to come up with forecasts of monthly requirements (in thousands of phones) as shown in table below: Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates for 22 days a month, eight hours each day. One person can assemble a phone every 12 minutes. Workers are paid 25 euros per hour and a 60 percent premium for overtime. The plant currently employs 1,450 workers. Component cost for each cell phone totals 30 euros. Given the rapid decline in component and finished-product prices, carrying inventory from one month to the next incurs a cost of 3 euros per phone per month. Skycell currently has a no-layoff policy in place. Overtime is limited to a maximum of 25 hours per month per employee. Assume that Skycell has a starting inventory of 45,000 units and wants to end the year with the same level of inventory.Explanation / Answer
Answer:
Inventory constraints:
Overtime constraints:
Production constraints:
Full-Time Workforce constraints:
Temporary Workforce constraints:
(a)
Total cost =
$ 358,210,000
Ht
Lt
Tt
Wt
Pt
Period
# Hired
# Laid off
# Temp
# Workforce
Production
0
0
0
0
1,250
0
1
0
-
-
1,250
950
2
0
-
-
1,250
1184
3
-
-
0
1,250
1200
4
50
-
50
1,250
1404
5
0
-
50
1,250
1404
6
-
-
50
1,250
1404
7
-
0
50
1,250
1404
8
-
50
-
1,250
900
9
-
-
-
1,250
1100
10
(0)
-
-
1,250
1200
11
50
-
50
1,250
1346
12
0
-
50
1,250
1404
(b)
Total cost =
$ 356,658,667
Ht
Lt
Tt
Wt
Pt
Period
# Hired
# Laid off
# Temp
# Workforce
Production
0
0
0
0
1,250
0
1
0
-
-
1,250
950
2
(0)
-
-
1,250
1100
3
0
-
-
1,250
1200
4
100
-
100
1,250
1326
5
-
-
100
1,250
1458
6
0
-
100
1,250
1458
7
-
0
100
1,250
1458
8
-
100
-
1,250
900
9
(0)
-
-
1,250
1100
10
(0)
-
-
1,250
1200
11
96
-
96
1,250
1292
12
4
-
100
1,250
1458
(c) If Skycell only carries 1100 permanent employees but has 200 seasonal employees, the total cost will be reduced to $356,984,667, a 0.34% cost saving compared to (a)
(d) Since there is no difference between regular employees and temporary employees in terms of productivity and cost of hiring and layoffs, this problem is equivalent to using at most 1300 employees and allowing hiring and layoffs. So, the formulation can be revised as follows.
Minimize
Subject to:
Inventory constraints:
Overtime constraints:
Production constraints:
Full-Time Workforce constraints:
Temporary Workforce constraints: (not needed)
Total cost =
$ 356,926,500
Ht
Lt
Wt
Pt
Period
# Hired
# Laid off
# Temp
# Permanent
# workforce
Production
0
0
0
50
1,250
1,300
0
1
-
310
0
990
990
950
2
156
-
0
1,146
1,146
1100
3
154
-
50
1,250
1,300
1284
4
-
-
50
1,250
1,300
1404
5
-
-
50
1,250
1,300
1404
6
-
-
50
1,250
1,300
1404
7
-
-
50
1,250
1,300
1404
8
-
363
0
938
938
900
9
208
-
0
1,146
1,146
1100
10
44
-
0
1,190
1,190
1142
11
110
-
50
1,250
1,300
1404
12
0
-
50
1,250
1,300
1404
So, if the no layoff no hiring policy for the permanent employees can be relaxed, Skycell will be able to further reduce the total cost. However, the reduction from case (c) is marginal.
Total cost =
$ 358,210,000
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