Aggregate Planning: used for Medium range capacity
planning (usually 3 to 12 months)
Goal: achieve production plan that will effectively utilize resources to
meet expected demand. Therefore, must make decisions on output rates, employment
levels & changes, inventory levels and changes, backorders and subcontracting
I) Introduction:
A) Longterm decisions 
B) Aggregate decisions

C) Short term decisions 
II) Purpose & Scope of Aggregate Planning
A) Purpose: minimize costs while balancing expected demand & capacity over entire period
Develop
feasible production plan to achieve balance of expected demand & capacity over planning horizon
B)
Inputs to Aggregate Planning:
1) Available resources
over period must be known
2) "Known"/forecast expected
demand
3) Employment policies
C) Demand
& Capacity  pricing changes, promotions, backlogging orders using overtime, part time employees, subcontracting,
+/ extra shifts & stockpiling inventories, pricing & promotions
1) Demand:
a) Pricing  shift demand from peak periods to offpeak periods; consider degree of
price elasticity
b) Promotion  very effective in shifting demand so that it conforms more closely to capacity
c)
Backorders  cost would include lost sales, lost customers & paperwork
d) New
demand/ Counterseasonal Demand
2) Capacity:
a) Hire & Fire workers (Layoffs)
 including recruitment, screening & training; fire: severance pay, realigning workers, worker motivation, loss of moral
b)
Overtime  can be implemented relatively quickly; firm employee
base; may result in lower productivity, poorer quality, safety & payroll costs increasing
c) Parttime workers
 generally cost less than regular workers in both wages & fringe benefits
d) Inventories  use for finished
goods; includes storage costs, cost of insurance, obsolescence, deterioration, spoilage & breakage
e) Subcontracting
 enables planners to acquire temporary capacity; decisions on available capacity, relative expectations on quality &
costs & demand expectations
Ex: Cost Worksheet: Create one feasible plan, given the following
information: regular time cost per unit = $2 /unit, overtime cost per unit = $3 /unit, subcontracting cost per unit = $6 /
unit, inventory carrying cost = $1/unit/period, and backordering cost = $5/unit per period. Regular production produces 300
units per period, overtime can produce 100 units, and subcontracting can be used for an additional 50 units per period.
Period 
1 
2 
3 
4 
Forecast 
200 
200 
300 
400 
Output: 




Regular 




Overtime 




Subcontract 




OutputForecast 




Inventory: 




Beginning 




Ending 




Average 









Costs: 




Regular 




Overtime 




Subcontract 




Inventory 




Backorders 




Total 




Computer Solution:

Demand 
Regular time Capacity 
Overtime Capacity 
Subcontract Capacity 
Regular time production 
Inventory (end PD) 
Initial Inventory 





0 
Period 1 
200 
300 
100 
50 
300 
100 
Period 2 
200 
300 
100 
50 
300 
200 
Period 3 
300 
300 
100 
50 
300 
200 
Period 4 
400 
300 
100 
50 
300 
100 
Total(units) 
1100 
1200 
400 
200 
1200 
600 





@$2 /unit 
@$1 /unit 
Subtotal Costs 




$2,400. 
$600. 
Total Cost 
$3,000. 





III) Basic Strategies for Uneven Demand
1) Level Capacity  maintain steady rate of regular time output while
meeting variations in demand by combinations of options; use subcontracting, backlogging & use of inventories to absorb
fluctuations
2) Chase Demand  match capacity to demand; planned output for a period would be equal to expected
demand for that period;
3) Hybrid – combination of level and chase used over time to balance demand versus capacity
IV) Choosing a strategy:
A) Assumptions:
1)
Regular capacity in all periods
2) Cost is linear function
3) Plans are feasible
4) All costs
associated can be represented by lump sum or unit costs
5) Cost figures
can be reasonably estimated and are constant
6) Inventories change @ uniform
rate
B) Techniques:
1) Informal techniques: graphing
& charting
2) Mathematical techniques:
a) Linear programming/ Transportation Method
 optimal solution; minimize cost or maximize profit;
Ex: Transportation Formulation
Variables:
r = regular production cost per unit
o = overtime cost per
unit
s = subcontracting costs per unit
h = holding costs per unit per period
b = backorder cost per unit per
period
n = # periods in planning horizon
Period 
1 
2 
3 
.... 
End Inv. 
Capacity 
Beg. Inv. 
0 I11 
h I12 
2h I13 

Nh I1n 
Io 
Period 1: Regular 
r R11 
r+h R12 
r +
2h R13 

r +nh
R1n 
R1 
Overtime

O O11 
o+h O12 
o+2h O13 

o+nh O1n 
O1 
Subcontract

s S11 
s+h S12 
s+2h S13 

s+nh S1n 
S1 
Period 2: Regular 
r+b R21 
r R22 
r+h R23 

r+(n1)h R2n 
R2 
Overtime

o+b O21 
o O22 
o+h O23 

o+(n1)h O2n 
O2 
Subcontract

s+b S21 
s S22 
s+h S23 

s+(n1)h S2n 
S2 
. . . 






Demand 
D1 
D2 
D3 

End Inv. 

Bowman Formulation:
Min
TC = 0 I11 + h I12 + 2h I13 + r R11 + (r+h) R12 + (r+2h) R13 +
o O11 + (o+h) O12 + (o + 2h) O13 + s S11 + (s+h) S12 +
(s
+ 2h) S13 + …….+ (s+h) S23
st: (rows)
I11 + I12 + I13 = Io
R11 + R12 + R13 = R1
O11 + O12
+ O13 = O1
S11 + S12 + S13 = S1
…..
(columns)
I11 + R11 + O11 + S11 + R21 + O21
+ S21 + …. = D1
I12 + R12 + O12 + S12 + R22 + O22 + S22 + …. = D2
….
(demand = capacity)
D1 + D2 + D3 + …. = Io + R1 + O1 + S1 + R2 + O2 + S2
All
variables > 0
Ex: The demand for "widgets" is 10
in period 1 and 15 in period 2. The capacity to manufacture widgets on regular time is 10 per period and 2 per period on overtime.
There is 1 unit available at the beginning of the period. It costs $2 per unit to produce the product during regular time
and $3 per unit to produce the product during overtime. The cost to hold product in inventory is $1 per unit per period. Cost
to backorder is $100 per unit per period. Given that there is 1 unit in inventory
at the start of period 1, develop (1) solution to this problem, and calculate the total cost to manufacture product in this
manner.
Period 
1 
2 
End Inv. 
Capacity 
Beg. Inv.





Period 1: Regular





Overtime





Period 2: Regular





Overtime





Demand





Computer Solution:
Optimal cost = $55 
Period 1 
Period 2 
End Inv. 
Beg. Inventory 
1 


Period 1: Regular 
9 
1 

Overtime 

2 

Period 2: Regular 

10 

Overtime 

2 
0 
Marginal Costs:

Period 1 
Period 2 
End Inv. 
Beg. Inventory 

0 
0 
Period 1: Regular 


0 
Overtime 
0 

0 
Period 2: Regular 
101 

0 
Overtime 
101 


Shipments with Costs

Period 1 
Period 2 
End Inv. 
Beg. Inventory 
1/$0 


Period 1: Regular 
9/$18 
1/$3 

Overtime 

2/$8 

Period 2: Regular 

10/$20 

Overtime 

2/$6 
0/$0 
Shipping List
From 
To 
Shipment 
Cost per unit 
Shipment cost 
Beg. Inventory 
Period 1 
1 
0 
0 
Period 1: Regular 
Period 1 
9 
2 
18 
Period 1: Regular 
Period 2 
1 
3 
3 
Overtime 
Period 2 
2 
4 
8 
Period 2: Regular 
Period 2 
10 
2 
20 
Overtime 
Period 2 
2 
3 
6 
Overtime 
End Inv. 
0 
4 
0 
V) Disaggregating Aggregate Plan:
Breakdown the
aggregate plan into specific product requirements in order to determine labor requirements, materials & inventory requirements
Master
schedule = quantity & timing of specific end items for schedule horizon; short range planning
Roughcut
capacity planning = approximate balancing of capacity & demand to test feasibility of master schedule
A)
Master Production Schedule (MPS)  quantity & timing of planned production & onhand inventory
a) Inputs =
1) beginning inventory,
2) forecasts for demand
3) customer orders
b) Outputs = projected inventory, production requirements,
uncommitted inventory (available to promise inventory  ATP); can use to provide realistic delivery dates to customers
Projected OnHand Inventory =
Previous Inventory Level 
Current Requirements
Note: Current Requirements = larger of forecast and customer orders
Available to = MPS quantity 
"Current customer orders until build product again"
Promise (ATP)
Demand Time Fence = The point in time inside of which the forecast is no longer included in total demand and projected available
inventory calculations; inside this point, only customer orders are considered.
Planning Time Fence = a point
in time denoted in the planning horizon of the master scheduling process that marks a boundary inside of which changes to
the schedule can manually be made by the master scheduler. The customer requirements within this time fence are the larger
of the forecast or customer orders.
Example: Given the lot size = 100, beginning inventory = 60, demand time fence
is 1 month, and planning time fence is 4 months. Complete the following master production schedule:
Month

1 
2 
3 
4 
Forecast

50 
50 
50 
50 
Customer Orders

10 
20 
25 
60 
Projected OnHand





MPS





ATP




