Sample Answer
Aggregate Planning
Problem 2
Listing out the known data:
Cost data | |
Regular-time labor cost per hour | $ 10.00 |
Overtime labor cost per hour | $ 15.00 |
Subcontracting cost per unit (labor only) | $ 84.00 |
Holding cost per unit per period | $ 20.00 |
Back-order cost per unit per period | $ 10.00 |
Hiring cost per employee | $ 600.00 |
Firing cost per employee | $ 450.00 |
Capacity data | |
Beginning workforce | 210 |
Beginning Inventory | 400 |
Labor standard per unit | 6 |
Regular time available per period | 160 |
Overtime available per period | 32 |
Subcontracting maximum per period | 1000 |
Subcontracting minimum per period | 500 |
Demand data | |
Period 1 | 6000 |
Period 2 | 4800 |
Period 3 | 7840 |
Period 4 | 5200 |
Period 5 | 6560 |
Period 6 | 3600 |
Total Number of periods | 6 |
To develop the aggregate plan:
Choose the kind of aggregate plan. We will use a level plan.
Calculate the aggregate production rate. Since back-orders are not allowed, the period with the highest production rate will determine the aggregate production rate to be used in this plan.
Calculate the workforce size given the aggregate production rate.
The plan is shown below.
Level Aggregate Plan, using inventories but no back orders | |||||||
Detailed plan computations | Period | ||||||
1 | 2 | 3 | 4 | 5 | 6 | Total | |
Demand (units) | 5600 | 4800 | 7840 | 5200 | 6560 | 3600 | |
Cumulative demand (units) | 5600 | 10400 | 18240 | 23440 | 30000 | 33600 | |
Cumulative demand/periods | 5600 | 5200 | 6080 | 5860 | 6000 | 5600 | |
Period production (units) | 6080 | 6080 | 6080 | 6080 | 6080 | 6080 | 36480 |
Cumulative production (units) | 6080 | 12160 | 18240 | 24320 | 30400 | 36480 | |
Cum.Dem. Minus Cum.Prod. | -480 | -1760 | 0 | -880 | -400 | -2880 | |
Ending Inventory (units) | 480 | 1760 | 0 | 880 | 400 | 2880 | 6400 |
Back-orders (units) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Compute Level Production Rate and Workforce Needed | |||||||
Production Rate (units) | 6080 | ||||||
Units per Employee per Period | 26.67 | ||||||
Employees Needed | 228 | ||||||
Number to Hire | 18 | ||||||
Number to Fire | 0 | ||||||
Cost Calculations for Plan B | |||||||
Regular-time labor cost | $ 2,188,800 | ||||||
Overtime labor cost | $ – | ||||||
Inventory holding cost | $ 64,000 | ||||||
Back-order cost | $ – | ||||||
Hiring cost | $ 10,800 | ||||||
Firing cost | $ – | ||||||
Total Cost | $ 2,263,600 |
Table 2: Plan 1 – Level Aggregate Plan
- From the above table, Aggregate Production Rate is 6,080
- The workforce required to produce the aggregate production rate (6,080)
Since the production rate per employee during regular time is 20.666 units per period, the requirement for this plan is 228 employees. Therefore, an additional 18 employees are needed.
- If this plan was implemented, there would be an increase in holding costs in the future as the plan creates a high inventory level after the first three periods.
From Table 2, the various costs are:
Regular-time labor cost = $2,188,800
Inventory holding cost = $64,000
Hiring cost = $10,800
Total Cost = $2,263,600
To Evaluate the plan in terms of cost, customer service, operations, and human resources. Develop a second table for comparison.
Level Aggregate Plan, using inventories and back orders | |||||||
Detailed plan computations | Period | ||||||
1 | 2 | 3 | 4 | 5 | 6 | Total | |
Demand (units) | 5600 | 4800 | 7840 | 5200 | 6560 | 3600 | |
Cumulative demand (units) | 5600 | 10400 | 18240 | 23440 | 30000 | 33600 | |
Cumulative demand/periods | 5600 | 5200 | 6080 | 5860 | 6000 | 5600 | |
Period production (units) | 5600 | 5600 | 5600 | 5600 | 5600 | 5600 | 33600 |
Cumulative production (units) | 5600 | 11200 | 16800 | 22400 | 28000 | 33600 | |
Cum.Dem. Minus Cum.Prod. | 0 | -800 | 1440 | 1040 | 2000 | 0 | |
Ending Inventory (units) | 0 | 800 | 0 | 0 | 0 | 0 | 800 |
Back-orders (units) | 0 | 0 | 1440 | 1040 | 2000 | 0 | 4480 |
Compute Level Production Rate and Workforce Needed | |||||||
Production Rate (units) | 5600 | ||||||
Units per Employee per Period | 26.67 | ||||||
Employees Needed | 210 | ||||||
Number to Hire | 0 | ||||||
Number to Fire | 0 | ||||||
Cost Calculations for Plan B | |||||||
Regular-time labor cost | $ 2,016,000 | ||||||
Overtime labor cost | $ – | ||||||
Inventory holding cost | $ 8,000 | ||||||
Back-order cost | $ 89,600 | ||||||
Hiring cost | $ – | ||||||
Firing cost | $ – | ||||||
Total Cost | $ 2,113,600 |
Table 3. Plan 2 – Aggregate Level Plan
Comparing the two plans:
- There is a decrease in total cost for the second plan compared to the first plan, $2,113,600 compared to $2,263,600.
- The amount of production plan units for the second plan has also reduced from 36,480 units to 33,600 units. This would signify an increased
- The unit cost for the two plans compare as follows:
Unit cost for plan 1=2,263,600/36,480=62.05
Unit cost for plan 2=2,113,600/33,600=62.90
The unit cost for plan 1 is lower, with a better customer service score as there are no back orders.
Aggregate Planning Worksheet For Attached Tables
References
Reid, R. D., & Sanders, N. R. (2016). Operations Management, Binder Ready Version: An Integrated Approach. John Wiley & Sons.
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Question
[u08a2] Unit 8 Assignment 2 Aggregate Planning
Complete problem 2 on page 511 of your textbook. For help on how to complete this problem, see the Solved Problems on pages 504–510.

Aggregate Planning
When completed, submit your answers as an attachment in the assignment area. Be sure to include your work with the answer.
Resources
Aggregate Planning Scoring Guide
- Due Date:Unit 8
Percentage of Course Grade: 2%.
CRITERIA | DISTINGUISHED |
Accurately solves all computation aspects of the aggregate planning problem. 50% |
Accurately solves all computation aspects of the problem and shows work. |
Provides summary, and/or rationale useful in interpreting the aggregate planning results. 50% |
Accurately summarizes salient points with supporting rationale for interpreting results. |
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