What is the optimal total cost of the aggregate plan developed to address Scenario 8.1?

A) $16,700
B) $18,950
C) $18,450
D) $16,250

Question

What is the optimal total cost of the aggregate plan developed to address Scenario 8.1?A) $16,700B) $18,950C) $18,450D) $16,250

Mario Sanchez · Accepted Answer

Final Answer : B, Explanation :   To solve this problem, we need to use a spreadsheet with the following formulas:Regular production = Demand – Beginning Inventory + Ending InventoryOvertime = 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)/2First, 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 InventoryWe don't know the ending inventory for January yet, so let's assume it's zero for now. Therefore:Regular production = 500 – 100 + 0 = 400We 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  &  	ext { January }  &  	ext { February }  &  	ext { March }  &  	ext { April }  &  	ext { May } \\hline 	ext { Demand }  &  500  &  750  &  1200  &  650  &  300 \\hline 	ext { Beginning Inventory }  &  100  &  0  &  0  &  250  &  50 \\hline 	ext { Regular Production }  &  400  &  750  &  1200  &  400  &  250 \\hline 	ext { Overtime }  &  0  &  0  &  0  &  250  &  50 \\hline 	ext { Subcontracting }  &  0  &  0  &  0  &  0  &  0 \\hline 	ext { Ending Inventory }  &  0  &  0  &  0  &  50  &  0 \\hline 	ext { 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) = 200Subcontracting ≤ MIN(300 – 200, 600 – 400 – 200) = 0We 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  &  	ext { January }  &  	ext { February }  &  	ext { March }  &  	ext { April }  &  	ext { May } \\hline 	ext { Demand }  &  500  &  750  &  1200  &  650  &  300 \\hline 	ext { Beginning Inventory }  &  100  &  0  &  0  &  250  &  50 \\hline 	ext { Regular Production }  &  400  &  600  &  600  &  400  &  250 \\hline 	ext { Overtime }  &  0  &  0  &  300  &  250  &  50 \\hline 	ext { Subcontracting }  &  0  &  0  &  0  &  0  &  0 \\hline 	ext { Ending Inventory }  &  0  &  0  &  0  &  50  &  0 \\hline 	ext { 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.

What is the optimal total cost of the aggregate plan developed to address Scenario 8.1?

A) $16,700
B) $18,950
C) $18,450
D) $16,250

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