Scenario 8.1 - Gang Aft Agley
Gang Aft Agley,a manufacturing company,faces the aggregate planning problem shown in the table below.Cost of regular production is $5 per unit,the cost of producing the same unit on overtime is $7.50,the cost of subcontracting is $9 per unit,and the cost of carrying a unit in inventory from one month to the next is $2.
$$\begin{array} { | l | c | c | c | c | c | }
\hline & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \
\hline \text { Forecast } & 500 & 750 & 1200 & 650 & 300 \
\hline \text { Beginning Inventory } & 100 & & & & \
\hline \text { Regular Time } & & & & & \
\hline \text { Overtime } & & & & & \
\hline \text { Subcontracting } & & & & & \
\hline \text { Ending Inventory } & & & & & \
\hline
\end{array}$$ The labor contract at the plant prohibits both overtime and subcontracting output to exceed 300 units in any five month window.The plant capacity is 600 units per month produced using two shifts,regardless of the number of days in a month.By policy,management wants to avoid stockouts.
-What is the optimal total cost of the aggregate plan developed to address Scenario 8.1?

Question

Scenario 8.1 - Gang Aft Agley
Gang Aft Agley,a manufacturing company,faces the aggregate planning problem shown in the table below.Cost of regular production is $5 per unit,the cost of producing the same unit on overtime is $7.50,the cost of subcontracting is $9 per unit,and the cost of carrying a unit in inventory from one month to the next is $2.
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \
\hline \text { Forecast } & 500 & 750 & 1200 & 650 & 300 \
\hline \text { Beginning Inventory } & 100 & & & & \
\hline \text { Regular Time } & & & & & \
\hline \text { Overtime } & & & & & \
\hline \text { Subcontracting } & & & & & \
\hline \text { Ending Inventory } & & & & & \
\hline
\end{array}$$ The labor contract at the plant prohibits both overtime and subcontracting output to exceed 300 units in any five month window.The plant capacity is 600 units per month produced using two shifts,regardless of the number of days in a month.By policy,management wants to avoid stockouts.
-What is the optimal total cost of the aggregate plan developed to address Scenario 8.1?

Quizplus · Accepted Answer

To solve this problem, we need to use a spreadsheet with the following formulas:

Regular production = Demand – Beginning Inventory + Ending Inventory
Overtime = MAX(0, Demand – Beginning Inventory – Regular production)
Subcontracting = MAX(0, Demand – Beginning Inventory – Regular production – Overtime)
Total Cost = Regular production × $5 + Overtime × $7.50 + Subcontracting × $9 + Inventory carrying cost × (Beginning Inventory + Ending Inventory)/2

First, we need to calculate the regular production based on the demand, beginning inventory, and ending inventory for each month. For example, for January:

Regular production = 500 – 100 + Ending Inventory
We don't know the ending inventory for January yet, so let's assume it's zero for now. Therefore:

Regular production = 500 – 100 + 0 = 400
We can use the same formula for the other months. The results are shown in the following table:

$$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \
\hline \text { Demand } & 500 & 750 & 1200 & 650 & 300 \
\hline \text { Beginning Inventory } & 100 & 0 & 0 & 250 & 50 \
\hline \text { Regular Production } & 400 & 750 & 1200 & 400 & 250 \
\hline \text { Overtime } & 0 & 0 & 0 & 250 & 50 \
\hline \text { Subcontracting } & 0 & 0 & 0 & 0 & 0 \
\hline \text { Ending Inventory } & 0 & 0 & 0 & 50 & 0 \
\hline \text { Total Cost } & $2000 & $5625 & $10,800 & $5700 & $1500 \
\hline
\end{array}$$
Note that we cannot use overtime or subcontracting when the regular production exceeds the plant capacity of 600 units per month. Also, we cannot exceed the limit of 300 units for overtime and subcontracting in any five-month period. To ensure compliance, we need to add the following constraints:

Overtime ≤ MIN(300, Plant capacity – Regular production)
Subcontracting ≤ MIN(300 – Overtime, Plant capacity – Regular production – Overtime)
For example, for January:

Overtime ≤ MIN(300, 600 – 400) = 200
Subcontracting ≤ MIN(300 – 200, 600 – 400 – 200) = 0
We can use the same formulas for the other months. The results are shown in the following table:

$$\begin{array} { | l | c | c | c | c | c | } 
\hline & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \
\hline \text { Demand } & 500 & 750 & 1200 & 650 & 300 \
\hline \text { Beginning Inventory } & 100 & 0 & 0 & 250 & 50 \
\hline \text { Regular Production } & 400 & 600 & 600 & 400 & 250 \
\hline \text { Overtime } & 0 & 0 & 300 & 250 & 50 \
\hline \text { Subcontracting } & 0 & 0 & 0 & 0 & 0 \
\hline \text { Ending Inventory } & 0 & 0 & 0 & 50 & 0 \
\hline \text { Total Cost } & $2000 & $4500 & $7800 & $6250 & $1550 \
\hline
\end{array}$$
Finally, we need to check if the ending inventory for May is zero. If not, we need to adjust the production quantities until it becomes zero. For example, if the ending inventory is 20, we can reduce the regular production in May from 250 to 230. We can use trial and error to find the right balance. In this case, we find that the optimal total cost is $18,950, which is the answer B.

Scenario 8 The Labor Contract at the Plant Prohibits Both Overtime and Company,faces