
Concept explainers
a)
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.
a)

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.
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.
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.
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.
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.
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.
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
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
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
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
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
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
Calculate total cost of Plan C:
It is calculated by adding the extra costs of all the periods.
Hence, the total cost for Plan C is $104,000.
b)
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.
b)

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Calculate total cost of Plan D:
It is calculated by adding the extra costs of all the periods.
Hence, the total cost for Plan D is $93,800.
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.
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Chapter 13 Solutions
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
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