A manager is attempting to put together an aggregate plan for the coming nine mo
ID: 2594397 • Letter: A
Question
A manager is attempting to put together an aggregate plan for the coming nine months. She has obtained a forecast of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in periods 3 and 4 and again in period 8, as can be seen from the following forecasts:
The department now has 20 full-time employees, each of whom can produce 10 units of output per period at a cost of $7 per unit. Inventory carrying cost is $4 per unit per period, and backlog cost is $17 per unit per period.
Suppose another option is to use part-time workers to assist during seasonal peaks. The cost per unit, including hiring and training, is $14. The output rate is 10 units per worker per period for all workers. A maximum of 10 part-time workers can be used, and the same number of part-time workers must be used in all periods that have part-time workers. The ending inventory in period 9 should be 10 units. The limit on backlogs is 20 units per period. Try to make up backlogs as soon as possible. Compute the total cost for this plan. Assume 20 full-time workers. (Omit the "$" sign in your response.)
A manager is attempting to put together an aggregate plan for the coming nine months. She has obtained a forecast of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in periods 3 and 4 and again in period 8, as can be seen from the following forecasts:
Explanation / Answer
Period
Forecast
Units Produced
Employees Used
Carried Forward Stock
Backlog Stock
Cost of Stock
Overtime Cost
Carried Forward cost
Backlog Cost
Total Cost
1
190
200
20
10
-
1400
-
40
-
1440
2
230
250
25
30
-
1400
700
120
-
2220
3
260
250
25
20
-
1400
700
80
-
2180
4
280
250
25
-
10
1400
700
-
170
2270
5
210
200
20
-
20
1400
-
-
340
1740
6
170
200
20
10
-
1400
-
40
-
1440
7
160
200
20
50
-
1400
-
200
-
1600
8
260
200
20
-
10
1400
-
-
170
1570
9
180
200
20
10
-
1400
-
40
-
1440
TOTAL
15900
The number of part time employees used are 5 over and above the 20 full time employees and have been consistent throughout period 2, 3, 4. Carried forward stocks are the opening stocks minus the forecast demand. Backlog stock are the stocks required for the demand for a period but have not been able to meet the demand for the period.
Carried forward cost = Carried forward stock*4
Backlog Cost = Backlog stock*17
Overtime Cost = stocks produced above 200*14
Cost of regular stock = 1400 for all periods as 200 units will be produced by full time employees in all periods.
Total cost = Sum of all the above costs
Total cost after meeting all these conditions comes out to be 15900
Period
Forecast
Units Produced
Employees Used
Carried Forward Stock
Backlog Stock
Cost of Stock
Overtime Cost
Carried Forward cost
Backlog Cost
Total Cost
1
190
200
20
10
-
1400
-
40
-
1440
2
230
250
25
30
-
1400
700
120
-
2220
3
260
250
25
20
-
1400
700
80
-
2180
4
280
250
25
-
10
1400
700
-
170
2270
5
210
200
20
-
20
1400
-
-
340
1740
6
170
200
20
10
-
1400
-
40
-
1440
7
160
200
20
50
-
1400
-
200
-
1600
8
260
200
20
-
10
1400
-
-
170
1570
9
180
200
20
10
-
1400
-
40
-
1440
TOTAL
15900
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