Last home work of this crazy semester! Problem 13-1 Suppose you have been given
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Last home work of this crazy semester!Problem 13-1 Suppose you have been given responsibility for developing the six-month aggregate production plan at Soda Galore, a manufacturer of soft drinks. Your company makes three types of soft drinks: regular, diet, and super-caffeinated. Fortunately, all three types are made using the same production process, and the costs related to switching between the three types are so minimal that they can be ignored. Thus, you can treat your problem as an aggregate planning exercise where the planing unt is cases of soft drinks, regardiess of what types of drnis of drinks they are. The S&OP; team has developed a forecast of demand for the first six months of the year as shown in Table 13-3. The S&OP; team has also provided you with the cost data shown in Table 13-4 The material cost of a case of soda is the same regardless of whether it is produced in regular time or overtime. TABLE 13-3 Monthly Demand at Soda Galore January February March Apri May June Total Demand Average Monthly Demand 16,000 cases 32,000 cases 32,000 cases 36,000 cases 24,000 cases 112,000 cases 252,000 cases 42,000 cases TABLE 13-4 Soda Galore Planning Data 0 workers Current workforce Average monthly output per worker Inventory holding cost Reguiar wage rate Regular production Overtime wage rate Hiring cost 2,000 cases per month $ 0.70 per case per month $ 20 per hour 250 hours $ 30.00 per hour S 1,000 per worker $ 5.25 per case S 1,500 per worker cost Firinglayoff cost Beginning inventory 8,000 (all saflety stock) negotiate an increase in the regular production wage rate to $24 per hour and $36 per hour for overtime. Also assume that Soda Galore always plans to hold at Assume that
Explanation / Answer
1. In the first question, we need to solve using level production. So the outpout needs to be kept steady.
As given in the table, 13.1, the average monthly demand is 42,000. So this is our objective to keep the output steady.
The ending inventory is calculated as:
Ending inventory in the current period= Ending inventory in the previous period (Also the inventory at the start of this period period) + Production in the current period - demand satisfied in the current period
Given that the company intends to always have a safety stock of 8,000 cases, we should ensure that the ending inventory in any particular period cannot fall below 8,000.
The number of workers needed in any period = Production in that period / no.of cases per worker
The number of cases per worker is given as 2,000 per month.
Also, the current workforce is 10 workers. So, in order to produce the level output, if we will either hire or fire the workers.
Level Production Strategy
Month
Demand
Regular Production
Overtime or Subcontract Production
Ending inventory
Workers required (2000 cases/ worker)
Hire
Fire/ Layoff
Jan.
16,000
42,000
0
34,000
21
11
0
Feb.
32,000
42,000
0
44,000
21
0
0
Mar
32,000
42,000
0
54,000
21
0
0
Apr
36,000
42,000
0
60,000
21
0
0
May
24,000
42,000
0
78,000
21
0
0
Jun
112,000
42,000
0
8,000
21
0
0
Total
252,000
252,000
0
278,000
21
11
0
b. Let us now determine the cost of level production.
The total cost = cost of regular production + cost of overtime/subcontract + inventory holding cost + hiring/firing costs
Let us first calculate the cost of regular production.
It is given that the cost of regular time wage rates have increased.
So the revised regular time wage rate = $24 / hour
As given in data, the number of hours of regular time per worker per month = 250
The total number of workers = workers at the beginning of the month + workers hired at the beginning of the month - workers fired at the beginning of the month.
We see that we hired 11 workers at the beginning of the first month (Jan). and no firing in that month. After that we maintain a steady work force. Also, we have currently 10 workers.
So the total number of workers = 10 + 11 = 21.
Regular production cost in any month = wage per hour / worker x no. of workers x no. of hours in a month
= 24 x 21 x 250 = $126,000
So, for the 6 months, Total regular production cost = $ 126,000 x 6 = $756,000
Given the inventory holding cost = $ 0.70 per case per month
Please note that the cost given is per case per month, so in order to get the total inventory cost, we need to multiply this rate with the total ending inventory during each period.
From the table above we see that the total inventory for the first 6 months = 278,000.
So, the inventory holding cost = 0.7 x 278,000 = $194,600
We have not done any subcontracting or overtime, so that cost is zero.
Also, the hiring cost per worker = $1,000
Since we have hired 11 additional workers in the beginning, the total hiring cost = 11 x 1,000 = $11,000.
Please note that these workers we hire at the beginning of the production plan, will remain for all the six months, and hence the hiring cost is only incurred in the first month.
Thus, the cost of level production = 194,600 + 756,000 + 11,000 = 961,600
Thus the cost of level production = $961,600
c.
We do the demand planning using chase production. Here in the first case we match the production with demand, and thus we accordingly either hire or fire workforce to meet the demand. This is the first method where we adjust the workforce size.
Based on demand for each month, and the production rate of 2,000 cases/month/worker, we compute the number of workers we would need for each period.
And we have 10 workers at the beginning of the planning period. So, if the required number of workers in any period is lower than available at the beginning of the period, we fire the additional workers and if it is otherwise, we hire them.
To illustrate, the demand for Jan is 16,000 and to meet this demand we would need, 16000/2000 = 8 workers.
However, since we have 10 workers at the beginning of Jan, we fire 2 workers. So our workforce reduces to 8.
Now, in the month of Feb, the demand is 32,000 and we would need, 32000/2000 = 16 workers. Since we already have 8 by end of Jan, we will hire 8 more at the beginning of Feb to meet the required production demand.
We will do this exercise for the subsequent months as well.
Please note that in this planning method, the inventory level will remain constant across periods, which is the beginning inventory (safety stock) because we match the capacity/regular production with demand.
Chase Production Strategy - Adjusting Workforce size
Month
Demand
Regular Production
Overtime or Subcontract Production
Ending inventory
Workers required (2000 cases/ worker)
Hire
Fire/ Layoff
Jan.
16,000
16,000
0
8,000
8
0
2
Feb.
32,000
32,000
0
8,000
16
8
0
Mar
32,000
32,000
0
8,000
16
0
0
Apr
36,000
36,000
0
8,000
18
2
0
May
24,000
24,000
0
8,000
12
0
6
Jun
112,000
112,000
0
8,000
56
44
0
Total
252,000
252,000
0
48,000
126
52
8
We do the demand planning using chase production. Here in the second case we should have a constant workforce and the balance production will need to be subcontracted or overtime, and thus the total production matches demand.
As given in the question, the constant workforce to be used is the one corresponding to lowest demand month. The lowest demand month is Jan, with a demand of 16,000.
To meet this demand, we need 16000/2000 = 8 workers. So we fire the remaining extra 2 workers (10-8) at the beginning of the month and maintain a constant workforce of 8 workers for the planning period. So the production with regular workforce size = 16,000 per month across all the months.
The difference for a particular month, i.e. demand in a month - production with regular workforce size needs to be subcontracted.
To illustrate, the demand in Feb is 32,000 and the production by regular workforce is 16,000. So the balance 16,000 needs to be subcontracted.
In this case as well, the ending inventory level will remain constant across periods, which is the beginning inventory (safety stock) because we match the demand with regular production and subcontracting.
Month
Demand
Regular Production
Overtime or Subcontract Production
Ending inventory
Workers required (2000 cases/ worker)
Hire
Fire/ Layoff
Jan.
16,000
16000
0
8,000
8
0
2
Feb.
32,000
16000
16,000
8,000
8
0
0
Mar
32,000
16000
16,000
8,000
8
0
0
Apr
36,000
16000
20,000
8,000
8
0
0
May
24,000
16000
8,000
8,000
8
0
0
Jun
112,000
16000
96,000
8,000
8
0
0
Total
252,000
96,000
156,000
48,000
48
0
2
d. Let us compute the cost for each of these chase strategies.
Where the workforce size is adjusted:
The Total Production cost cost can also be computed as
Total Production cost = No.of workers required during the entire planning period x Cost per worker / month
Cost per worker/month = cost per worker/hour x no. of working hours
So total production cost = 126 x 24 x 250 = $756,000
Also, the inventory holding cost = total inventory during the period x cost per case per month
= 48,000 * 0.7 = 33,600
We have hired 54 workers and fired 8 workes in worksize adjustment,
Giving the hiring cost per worker = 1000 and firing cost = 1500 per worker
Total worksize adjustment cost = 54 X 1000 + 8 x 1500 = $66,000
Thus the total cost of production = 756,000+ 33,600 + 66,000 = 855,600
However, in case of subcontracting, the total cost of production can be similarly calculated as:
Subcontracting cost = subcontracting cost per case X no.of cases
= 5.25 x 156,000 = 819,000
Total cost = inventory cost + subcontracting cost + regular production cost + hiring/firing costs
= 48,00 *0.7 + 819,000 + 48 x 24 x 250 + 2 x1500 = 1,143,600
Month
Demand
Regular Production
Overtime or Subcontract Production
Ending inventory
Workers required (2000 cases/ worker)
Hire
Fire/ Layoff
Jan.
16,000
42,000
0
34,000
21
11
0
Feb.
32,000
42,000
0
44,000
21
0
0
Mar
32,000
42,000
0
54,000
21
0
0
Apr
36,000
42,000
0
60,000
21
0
0
May
24,000
42,000
0
78,000
21
0
0
Jun
112,000
42,000
0
8,000
21
0
0
Total
252,000
252,000
0
278,000
21
11
0
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