ISEN 315
Spring 2011
Dr. Gary Gaukler
Introduction to Aggregate
Planning
• Goal: To plan gross work force levels and set
firm-wide production plans, based on predicted
demand for aggregate units.
Hierarchy of Planning
• Forecast of aggregate demand over time horizon
• Aggregate Production Plan: determine aggregate
production and workforce levels over time horizon
• Master Production Schedule: Disaggregate the
aggregate plan and determine per-item production
levels
• Materials Requirements Planning: Detailed schedule
for production/replenishment activities
Prototype Aggregate Planning Example
The washing machine plant is interested in determining
work force and production levels for the next 8
months.
Forecasted aggregate demands for Jan-Aug. are: 420,
280, 460, 190, 310, 145, 110, 125.
Starting inventory at the end of December is 200 and
the firm would like to have 100 units on hand at the
end of August.
Find monthly production levels.
Step 1: Determine “net” demand.
Month Net Predicted
Demand
1(Jan)
220
2(Feb)
280
3(Mar)
460
4(Apr)
190
5(May)
310
6(June)
145
7(July)
110
8(Aug)
225
Cum. Net
Demand
220
500
960
1150
1460
1605
1715
1940
Constant Work Force Plan
Suppose that we are interested in determining a
production plan that doesn’t change the size
of the workforce over the planning horizon.
How would we do that?
Monthly Production = 1940/8 = 242.2 or
rounded to 243/month.
But: there are stockouts.
How can we have a constant work force
plan with no stockouts?
Using the graph, find a straight line that lies completely
above the cumulative net demand curve:
Constant Work Force Plan With No Stockouts
3000
2500
2000
1500
1000
500
0
1
2
3
4
5
6
7
8
From the previous graph, we see that the cum. net
demand curve is crossed at period 3, so that monthly
production is 960/3 = 320. Ending inventory each
month is found from:
Month
Cum. Net. Dem.
1(Jan)
220
2(Feb)
500
3(Mar)
960
4(Apr.)
1150
5(May)
1460
6(June)
1605
7(July)
1715
8(Aug)
1940
Cum. Prod.
320
640
960
1280
1600
1920
2240
2560
Invent.
100
140
0
130
140
315
525
620
But - may not be realistic for several
reasons:
• It may not be possible to achieve the
production level of 320 unit/mo with an
integer number of workers
• Since all months do not have the same
number of workdays, a constant production
level may not translate to the same number of
workers each month.
To overcome these shortcomings:
• Assume number of workdays per month is given
• K factor computed where K = # of aggregate units
produced by one worker in one day
• Suppose that we are told that over a period of 40
days, the plant had 38 workers who produced 520
units. It follows that:
• K= 520/(38*40) = .3421
= average number of units produced by one worker
in one day.
Computing Constant Work Force
Assume we are given the following # working
days per month: 22, 16, 23, 20, 21, 17, 18,
10. March is still critical month.
Cum. net demand thru March = 960.
Cum # working days = 22+16+23 = 61.
Find 960/61 = 15.7377 units/day implies
15.7377/.3421 = 46 workers required.
Constant Work Force Production Plan
Mo
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
# wk days
22
16
23
20
21
22
21
22
Prod.
Level
346
252
362
315
330
346
330
346
Cum Cum Nt End Inv
Prod Dem
346
220
126
598
500
98
960
960
0
1275 1150
125
1605 1460
145
1951 1605
346
2281 1715
566
2627 1940
687
Addition of Costs
•
•
•
•
•
Holding Cost (per unit per month): $8.50
Hiring Cost per worker: $800
Firing Cost per worker: $1,250
Payroll Cost: $75/worker/day
Shortage Cost: $50 unit short/month
Cost Evaluation of Constant Work Force Plan
• Assume that the work force at end of Dec was
40.
• Cost to hire 6 workers: 6*800 = $4800
• Inventory Cost: accumulate ending inventory:
(126+98+0+. . .+687) = 2093. Add in 100 units
netted out in Aug = 2193.
• Hence Inv. Cost = 2193*8.5=$18,640.50
• Payroll cost: ($75/worker/day) (46 workers)
(167days) = $576,150
• Cost of plan: $576,150 + $18,640.50 + $4800 =
$599,590.50
Cost Reduction in Constant Work Force Plan
Zero Inventory Plan (Chase Strategy)
• Change the workforce each month in order to
reduce ending inventory to nearly zero by
matching the workforce with monthly demand
as closely as possible.
• This is accomplished by computing the #
units produced by one worker each month (by
multiplying K by #days per mo.) and then
taking net demand each month and dividing
by this quantity.
• The resulting ratio is rounded up and possibly
adjusted downward.
Chase vs. Constant
Linear Programming
•
•
•
•
•
Class of optimization problems
Linear objective function
Linear constraints
Real variables
Efficiently solved
Aggregate Planning LP
• Parameters:
– c H, c F
– cI
– cR
– cO, cU, cS
Aggregate Planning LP
• Parameters:
– nt
–K
– I0 ,W0
– Dt
Aggregate Planning LP
• Decision variables:
– Wt
– Pt
– It
– Ht, Ft
Aggregate Planning LP
• Decision variables:
– Ot
– Ut
– St
Aggregate Planning LP
Aggregate Planning LP
• Constraints:
Aggregate Planning LP
• Constraints:
Aggregate Planning LP
• Objective function: