MS 401
Production and Service Systems Operations
Spring 2009-2010
Aggregate Production Planning (APP)
Slide Set #8
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APP Overview
• APP: A plan devised to determine companywide workforce
and production levels
– how many employees the firm should retain: hire/fire workers
– quantity and mix of the products to be produced
to meet demand for products, considering company strategy
and the capacity constraints
• Considers “macro” production decisions
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Why APP?
• “APP is the top management’s handle on the business”
– where critical trade-offs are resolved based on company strategy
• APP provides links from manufacturing to other functions
– once APP is agreed on, the manufacturing’s duty is to “hit the
schedule”
• Cost of not having an aggregate plan include
–
–
–
–
–
–
extra inventories
poor customer service
excess capacity
long lead times
panic operations
poor response to new opportunities
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Aggregation
• Managing groups of items rather than individual items
– provides a big picture view
– forecasts for aggregate units are more accurate
• Define the “aggregate unit of production”
– should be commonly understood by the other functions
• APP is later disaggregated to individual items
– results in the master production schedule (MPS) for each item
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Aggregate Units of Production: Example
Model Number
A5532
K4242
L9898
L3800
M2624
M3880
Worker-hours
4.2
4.9
5.1
5.2
5.4
5.8
Price
285
345
395
425
525
725
Percentage
%32
%21
%17
%14
%10
%6
• How do we define the aggregate unit to determine the workforce and
production levels in the plant in this example?
• Aggregate unit: 1$ of output? NOT CONSISTENT
• Aggregate unit: A fictitious washing machine that requires
.32*4.2+.21*4.9+.17*5.1+.14*5.2+.10*5.4+.06*5.8 = 4.856 hours of labour
time
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A Sample Aggregation Scheme (Hax-Meal)
1. Items
•
final products to be delivered to the customer
•
SKU (stock-keeping unit)
•
ex: an individual washing machine model
2. Families
•
group of items that share a common manufacturing setup cost
•
ex: all washing machines
3. Types
•
group of families with production quantities that are determined
by a single aggregate production plan
•
ex: large home appliances (washing machines, dishwashers etc.)
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Hierarchy of Production Planning Decisions
Copyright © 2001 by The McGraw-Hill Companies, Inc
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Primary Issues in APP
• Trade-off between
– reacting quickly to anticipated changes in demand
– retaining a stable workforce and/or production level
• Bottlenecks
– where capacity restrictions occur
• Planning horizon
– end-of horizon effect
– rolling schedule
– periods in which decisions are frozen
• Treatment of demand
– assume deterministic demand to focus on the big picture
D1, D2, …, DT
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Relevant Costs
• Smoothing costs
– cost of changing the workforce
– some components may be difficult to measure
• Holding costs
– due to capital tied up in inventory
• Shortage costs
• Regular time costs
– cost of producing one unit during regular working hours
• Overtime costs
– cost of production beyond regular working hours
• Subcontracting costs
– cost of production at a supplier or by some other firm
• Idle time costs
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Example: DensePack
From Nahmias
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Problem Setup
• Currently (end of December) 300 workers employed
• Ending inventory in December: 500 units
• The firm would like to have 600 units at the end of June
• No backlogging, no overtime
• Forecast demand:
Month
Jan
Feb
Mar
Apr
May
Jun
Demand
1280
640
900
1200
2000
1400
• cH: cost of hiring one worker: $500
• cF: cost of firing one worker: $1000
• cI: cost of holding one unit of inventory for one month: $80
(incurred at the end of each period)
• K = 0.14653 : number of aggrg. units produced by one worker per day
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Cumulative Net Demand
Month
Jan
Feb
Mar
Apr
May
Jun
Demand
780
640
900
1200
2000
2000
Cumulative
780
1420
2320
3520
5520
7520
shortages not
permitted
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Three Approaches
1. Chase strategy (zero inventory plan)
2. Constant workforce plan
3. A mixed strategy
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1) Chase Strategy (Zero Inventory Plan)
• Produce what is needed each month
• Keep zero inventory
– inventory level may not be exactly zero due to integer num. of workers
• Hire and fire workers as needed
– assuming sufficient labor pool exists
– may not be possible in all countries
• unions, contracts etc
– may lead to low morale and quality
– may be suitable when low-skilled labor is required
• farming
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1) Chase Strategy
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1) Chase Strategy
Total cost of hiring, firing and holding is
(755)(500) + (145)(1000) + (30)(80) + (600)(80) = $572,000
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2) Constant Workforce Plan
• In the constant workforce plan, the goal is to eliminate completely the
need for hiring and firing
• Calculate the minimum workforce required for each month to make sure
that shortages do not occur
– we use cumulative inventory values because inventory can be carried over
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2) Constant Workforce Plan
The total (over periods) of the ending inventory levels is 5962+600=6562
Total cost of the plan: (6562)(80)+ (111)(500) =$580,460
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3) A Mixed Strategy Alternative
• Suppose we allow a single change in the workforce level
– can we find a strategy that reduces inventory without permitting shortages?
• Other constraints can also be studied
– for ex: limit on the production capacity of the plant: limit on slope
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Solution with Linear Programming
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Linear Programming
• Determine the values of “n” nonnegative decision variables
in order to max/min a linear function of these variables
subject to “m” linear constrains of these variables
• Can be solved efficiently using the Simplex algorithm
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Model Parameters
cH Cost of hiring one worker
cF Cost of firing one worker
cI
Cost of holding one unit of inventory for one period
cR
Cost of producing one unit on regular time
c0
Incremental cost of producing one unit on overtime
cS Cost to subcontract one unit of production
nt
Number of production days in period t
K
Aggregate number of aggregate products produced per worker per day
I0
Initial inventory on hand at the start of the planning horizon
W0 Initial workforce at the start of the planning horizon
Dt
Demand in period t (assumed to be known and deterministic)
T
Number of time periods (planning horizon)
t
Time period
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Decision Variables
Wt
Workforce level (number of workers) in period t
Pt
Production level in period t (regular and overtime)
It
Inventory level in period t
Ht
Number of workers hired in period t
Ft
Number of workers fired in period t
Ot
Overtime production in units
Ut
Worker idle time in production units
St
Number of units produced (procured) via subcontracting
Thus,
KntWt : the number of units produced by the entire workforce in period t
Ot= Pt- KntWt or Ut= KntWt-Pt
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Problem Constraints
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The LP Formulation
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The DensePack Example
W0=300
I0=500
I6=600
All decision variables >=0
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Aggregate Plan Obtained from LP
• The cost of this plan is only $379,500
– considerably less than the cost achieved with the chase strategy or the
constant workforce plan
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