A manufacturing company must choose between three aggregate production plans to meet demand that fluctuates over a six-month period. Plan I varies the workforce size, Plan II keeps the workforce constant and uses overtime and idle time, and Plan III keeps the workforce constant and allows inventory and stockouts. The costs of each plan are compared. Plan I costs $24,500, Plan II costs $36,600, and Plan III costs $9,600. Plan III, which keeps the workforce constant and allows for inventory and stockouts, is identified as the preferred plan due to having the lowest cost.

1. AGGREGATE PLANNING
WORKED OUT PROBLEM
OPERATIONS MANAGEMENT
J.G.MONKS…PAGE 341

2. PROBLEM
Manufacturing produces a product which has a 6 month demand cycle, as shown. Each unit requires 10
worker-hours to be produced , at a labour cost of $ 6 per hour regular rate (for $ 9 per hour overtime).
The total cost per unit is estimated at $200, but units can be subcontracted at a cost of $208 per unit.
There are currently 20 workers employed in the subject dept., and hiring and training costs for
additional workers are $300 per person, whereas layoff costs are $400 per person. Company policy is to
retain a safety stock equal to 20 percent of monthly forecast., and each month’s safety stock becomes
the beginning inventory for the next month. There are currently 50 units in stock carried at a cost of $2
per unit-month. Stockouts have been assigned a cost of $20 per unit-month.
Description Jan Feb Mar Apr May Jun
Forecast Demand 300 500 400 100 200 300
Workdays 22 19 21 21 22 20
Worker Hour at 8hr/day 176 152 168 168 178 160
Three aggregate plans are proposed.
PLAN I. Vary the work-force size to accommodate demand.
PLAN II: Maintain a constant workforce of 20, and use overtime and idle time to meet demand.
PLAN III: Maintain a constant workforce of 20, and build inventory or incur a stockout cost.The firm must
begin January with the 50 unit inventory on hand.
Compare thre costs of the three plans:

3. Determination of Production Requirements
SOLUTION:
We must first determine what production requirements are adjusted to include a safety stock of 20
percent of next month’s forecast,. Beginning with January inventory of 50, each subsequent month’s
inventory reflects the difference between the forecast demand and the production requirement of the
previous month.
Forecast Cumulative Safety Stock Beginning Production
Month
Demand Demand (20% FD) Inventory Requirement
(1) (2) (3) (4) (1)+(3) -(4)
January 300 300 60 50 310
February 500 800 100 60 540
March 400 1200 80 100 380
April 100 1300 20 80 40
May 200 1500 40 20 220
June 300 1800 60 40 320

4. PLAN –I (VARY WORKFORCE)

5. PLAN-II (USE OVERTIME AND IDLE TIME)

6. USE INVENTORY AND STOCKOUT BASED ON CONSTANT 20
WORKFORCE

7. SUMMARY
• PLAN I : $ 10,500 HIRING + $14000 LAYOFF = $ 24,500
• PLAN II : $ 8400 OVERTIME + $ 28,200 IDLE TIME = $ 36,600
• PLAN III : $ 8640 STOCKOUT + $960 INVENTORY = $9600
• PLAN III IS THE PREFERRED PLAN