Chapter 13, Problem 10P

a)

Summary Introduction

To evaluate: Plan C for the given information

Introduction: The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

Answer to Problem 10P

The Plan C has been evaluated. The total cost of Plan C is $104,000.

Explanation of Solution

Given information:

Production for all the months is 1,300 units. Ending inventory in June is 300 units. Overtime cost is $50 per unit. Demand requirement from July to December is given as follows:

Period	Demand	Production (units)
June
July	1,000	1,300
August	1,200	1,300
September	1,400	1,300
October	1,800	1,300
November	1,800	1,300
December	1,800	1,300

Evaluate the cost of the plan:

Plan C
Period	Demand	Production (units)	Subcontract (units)	Ending inventory	Extra cost
June				300
July	1,000	1,300		600	$15,000
August	1,200	1,300		700	$17,500
September	1,400	1,300		600	$15,000
October	1,800	1,300		100	$2,500
November	1,800	1,300	400	0	$24,000
December	1,800	1,300	500	0	$30,000
Total					$104,000

Note: Production is given as 1,300 units. Ending inventory for June is given as 300 units. If the production is more than or equal to the demand, then there would be inventory. If the demand is more, then there would be stock out.

Calculate ending inventory or subcontract for July:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for July is 600.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory of previous month}\right)-\text{Demand}\\ =\left(1,300+300\right)-1,000\\ =1,600-1,000\\ =600\end{array}$

Calculate ending inventory or subcontract for August:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for August is 700.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+600\right)-1,200\\ =1,900-1,200\\ =700\end{array}$

Calculate ending inventory or subcontract for September:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for September is 600.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+700\right)-1,400\\ =2,000-1,400\\ =600\end{array}$

Even though the demand is high, as there is enough ending inventory in previous month, there would be inventory rather than subcontract.

Calculate the ending inventory or subcontract for October:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for October is 100.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+600\right)-1,800\\ =1,900-1,800\\ =100\end{array}$

Even though the demand is high, as there is enough ending inventory in previous month, there would be inventory rather than subcontract.

Calculate ending inventory or subcontract for November:

As the demand is more than the production and there is no enough ending inventory, there would be subcontract.

It is calculated by adding production and ending inventory and the result should be subtracted with the demand. Hence, the subcontract units for November is 400 units.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+100\right)-1,800\\ =1,400-1,800\\ =-400\end{array}$

As the value is in negative, it would be subcontract.

Calculate ending inventory or subcontract for December:

As the demand is more than the production and there is no enough ending inventory, there would be subcontract.

It is calculated by adding production and ending inventory and the result should be subtracted with the demand. Hence, the subcontract units for December is 500 units.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+0\right)-1,800\\ =1,300-1,800\\ =-500\end{array}$

As the value is in negative, it would be subcontract.

Calculate extra cost for July:

It is calculated by multiplying ending inventory units and inventory holding cost. Inventory holding cost is given as $25 per unit. Hence, extra cost for July is $15,000

$\begin{array}{c}\text{Extra cost}=\text{Ending inventory}\times \text{Inventory holding cost per unit}\\ =600\times \$25\\ =\$15,000\end{array}$

Calculate extra cost for August:

It is calculated by multiplying ending inventory units and inventory holding cost. Inventory holding cost is given as $25 per unit. Hence, extra cost for August is $17,500

$\begin{array}{c}\text{Extra cost}=\text{Ending inventory}\times \text{Inventory holding cost per unit}\\ =700\times \$25\\ =\$17,500\end{array}$

Calculate extra cost for September:

It is calculated by multiplying ending inventory units and inventory holding cost. Inventory holding cost is given as $25 per unit. Hence, extra cost for September is $15,000

$\begin{array}{c}\text{Extra cost}=\text{Ending inventory}\times \text{Inventory holding cost per unit}\\ =600\times \$25\\ =\$15,000\end{array}$

Calculate extra cost for October:

It is calculated by multiplying ending inventory units and inventory holding cost. Inventory holding cost is given as $25 per unit. Hence, extra cost for October is $2,500

$\begin{array}{c}\text{Extra cost}=\text{Ending inventory}\times \text{Inventory holding cost per unit}\\ =100\times \$25\\ =\$2,500\end{array}$

Calculate extra cost for November:

It is calculated by multiplying ending inventory units and inventory holding cost. Inventory holding cost is given as $60 per unit. Hence, extra cost for November is $24,000

$\begin{array}{c}\text{Extra cost}=\text{Subcontract}\times \text{Subcontract cost per unit}\\ =400\times \$60\\ =\$24,000\end{array}$

Calculate extra cost for December:

It is calculated by multiplying ending inventory units and inventory holding cost. Inventory holding cost is given as $60 per unit. Hence, extra cost for December is $30,000

$\begin{array}{c}\text{Extra cost}=\text{Subcontract}\times \text{Subcontract cost per unit}\\ =500\times \$60\\ =\$30,000\end{array}$

Calculate total cost of Plan C:

It is calculated by adding the extra costs of all the periods.

$\begin{array}{c}\text{Total cost}=\text{Extra costs of all periods}\\ =\$15,000+\$17,500+\$15,000+\$2,500+\$24,000+\$30,000\\ =\$104,000\end{array}$

Hence, the total cost for Plan C is $104,000.

b)

Summary Introduction

To determine: Evaluate plan D for the given information

Introduction: The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

Answer to Problem 10P

The Plan D has been evaluated. The total cost of Plan D is $93,800.

Explanation of Solution

Given information:

Production for all the months is 1,300 units. Ending inventory in June is 300 units. Overtime cost is $50 per unit. Demand requirement from July to December is given as follows:

Period	Demand	Production (units)
June
July	1,000	1,300
August	1,200	1,300
September	1,400	1,300
October	1,800	1,300
November	1,800	1,300
December	1,800	1,300

Evaluate the cost of the plan:

Plan D
Period	Demand	Regular production (units)	Overtime production (units)	Ending inventory	Sub-contract (units)	Idle time (units)	Extra cost
June
July	1,000	1,300		180		120	$11,700
August	1,200	1,300		180		100	$10,500
September	1,400	1,300		80			$2,000
October	1,800	1,300	260	0	160		$20,000
November	1,800	1,300	260	0	240		$24,800
December	1,800	1,300	260	0	240		$24,800
Total							$93,800

Note: Production is given as 1,300 units. If the production is more than or equal to the demand, then there would be inventory. If the demand is more, then there would be stock out. Maximum overtime units allowed is 260 units (20% of production)

Calculate ending inventory or subcontract for July:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for July is 180.

$\begin{array}{c}\text{Ending inventory}=\text{Production}-\text{Demand}\\ =1,300-1,000\\ =300\end{array}$

It is given that the ending inventory should not exceed 180 units. Hence, the ending inventory would be 180 units and remaining units of 300 (120 units) would be in idle time.

Calculate ending inventory or subcontract for August:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for August is 180.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+180\right)-1,200\\ =1,480-1,200\\ =280\end{array}$

It is given that the ending inventory should not exceed 180 units. Hence, the ending inventory would be 180 units and remaining units of 280 (100 units) would be in idle time.

Calculate ending inventory or subcontract for September:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Ending inventory for September is 80.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+180\right)-1,400\\ =1,480-1,400\\ =80\end{array}$

Calculate the ending inventory or subcontract for October:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Subcontract for October is 160.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+80\right)-1,800\\ =1,380-1,800\\ =-420\end{array}$

As the value is in negative, it would be subcontract. Overtime production should not exceed 260 units. Hence, 260 units would be production in overtime production and 160 units (remaining from 420) would be produced in subcontract.

Calculate the ending inventory or subcontract for November:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Subcontract for November is 240.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+0\right)-1,800\\ =1,300-1,800\\ =-500\end{array}$

As the value is in negative, it would be subcontract. Overtime production should not exceed 260 units. Hence, 260 units would be production in overtime production and 240 units (remaining from 500) would be produced in subcontract.

Calculate the ending inventory or subcontract for December:

It is calculated by adding the production and ending inventory of previous month and subtract the result from the demand. Subcontract for December is 240.

$\begin{array}{c}\text{Ending inventory}=\left(\text{Production}+\text{Ending inventory}\right)-\text{Demand}\\ =\left(1,300+0\right)-1,800\\ =1,300-1,800\\ =-500\end{array}$

As the value is in negative, it would be subcontract. Overtime production should not exceed 260 units. Hence, 260 units would be production in overtime production and 240 units (remaining from 500) would be produced in subcontract.

Calculate extra cost for July:

It is calculated by adding the multiple of ending inventory units and inventory holding cost and the multiple of idle time and idle time cost. Inventory holding cost is given as $25 per unit and idle time per unit is $60. Hence, extra cost for July is $11,700.

$\begin{array}{c}\text{Extra cost}=\left(\begin{array}{l}\text{Ending inventory}\times \\ \text{Inventory holding cost per unit}\end{array}\right)+\left(\begin{array}{l}\text{Idle time}\times \\ \text{Idle time cost}\end{array}\right)\\ =\left(180\times \$25\right)+\left(120\times \$60\right)\\ =\$11,700\end{array}$

Calculate extra cost for August:

It is calculated by adding the multiple of ending inventory units and inventory holding cost and the multiple of idle time and idle time cost. Inventory holding cost is given as $25 per unit and idle time per unit is $60. Hence, extra cost for August is $10,500.

$\begin{array}{c}\text{Extra cost}=\left(\begin{array}{l}\text{Ending inventory}\times \\ \text{Inventory holding cost per unit}\end{array}\right)+\left(\begin{array}{l}\text{Idle time}\times \\ \text{Idle time cost}\end{array}\right)\\ =\left(180\times \$25\right)+\left(100\times \$60\right)\\ =\$10,500\end{array}$

Calculate extra cost for September:

It is calculated by adding the multiple of ending inventory units and inventory holding cost and the multiple of idle time and idle time cost. Inventory holding cost is given as $25 per unit and idle time per unit is $60. Hence, extra cost for September is $2,000.

$\begin{array}{c}\text{Extra cost}=\left(\begin{array}{l}\text{Ending inventory}\times \\ \text{Inventory holding cost per unit}\end{array}\right)+\left(\begin{array}{l}\text{Idle time}\times \\ \text{Idle time cost}\end{array}\right)\\ =\left(80\times \$25\right)+\left(0\right)\\ =\$2,000\end{array}$

Calculate extra cost for October:

It is calculated by adding the multiple of overtime units and overtime cost per unit and subcontract units and subcontract cost per unit. Overtime cost per unit is $40 per unit and subcontract cost is $60 per unit. Hence, extra cost for October is $20,000.

$\begin{array}{c}\text{Extra cost}=\left(\begin{array}{l}\text{Overtime units}\times \\ \text{Overtime cost per unit}\end{array}\right)+\left(\begin{array}{l}\text{Subcontract units}\times \\ \text{Subcontract cost per unit}\end{array}\right)\\ =\left(260\times \$40\right)+\left(160\times \$60\right)\\ =\$20,000\end{array}$

Calculate extra cost for November:

It is calculated by adding the multiple of overtime units and overtime cost per unit and subcontract units and subcontract cost per unit. Overtime cost per unit is $40 per unit and subcontract cost is $60 per unit. Hence, extra cost for November is $24,800.

$\begin{array}{c}\text{Extra cost}=\left(\begin{array}{l}\text{Overtime units}\times \\ \text{Overtime cost per unit}\end{array}\right)+\left(\begin{array}{l}\text{Subcontract units}\times \\ \text{Subcontract cost per unit}\end{array}\right)\\ =\left(260\times \$40\right)+\left(240\times \$60\right)\\ =\$24,800\end{array}$

Calculate extra cost for December:

It is calculated by adding the multiple of overtime units and overtime cost per unit and subcontract units and subcontract cost per unit. Overtime cost per unit is $40 per unit and subcontract cost is $60 per unit. Hence, extra cost for December is $24,800.

$\begin{array}{c}\text{Extra cost}=\left(\begin{array}{l}\text{Overtime units}\times \\ \text{Overtime cost per unit}\end{array}\right)+\left(\begin{array}{l}\text{Subcontract units}\times \\ \text{Subcontract cost per unit}\end{array}\right)\\ =\left(260\times \$40\right)+\left(240\times \$60\right)\\ =\$24,800\end{array}$

Calculate total cost of Plan D:

It is calculated by adding the extra costs of all the periods.

$\begin{array}{c}\text{Total cost}=\text{Extra costs of all periods}\\ =\$11,700+\$10,500+\$2,000+\$20,000+\$24,800+\$24,800\\ =\$93,800\end{array}$

Hence, the total cost for Plan D is $93,800.

Conclusion

Total cost for Plan D is preferable when compare with Plan C. However, Plan D with the total cost of $93,800 is preferable than other plans.