Aggregate Production Planning (APP)

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1. Aggregate Production Planning (APP)
Why aggregate planning
wDetails are hard to gather for longer horizons
nDemand for Christmas turkeys at Tom Thumb’s vsThanksgiving
turkeys
wDetails carry a lot of uncertainty: aggregation reduces
variability
nDemand for meat during Christmas has less variability than the
total variability in the demand for chicken, turkey, beef, etc.
wIf there is variability why bother making detailed plans,
inputs will change anyway
nInstead make plans that carry a lot of flexibility
nFlexibility and aggregation go hand in hand

2. Aggregate Planning
wAggregate planning: General plan
nCombined products = aggregate product
lShort and long sleeve shirts = shirt
wSingle product
nPooled capacities = aggregated capacity
lDedicated machine and general machine = machine
wSingle capacity
nTime periods = time buckets
lConsider all the demand and production of a given month
together
wQuite a few time buckets [Jan/Feb… orIQ/IIQ/…]
refers to intermediate range
planning covering 2 to 24 months …
a “big picture” look at planning
aimed at balancing capacity and
demand
Aggregate Production Planning (APP)

3. Forecast, Production Plan and Inventory
Recall from the forecasting presentation, future demand is forecasted,
6 Month Forecast
1
2
3
4
5
6
Forecast Demand
10
8
12
14
10
8
Production Plan
10
10
10
12
12
10
then a manufacturing production plan is developed,
Inventory
10
10
12
10
8
10
12
resulting in an inventory plan
which can be evaluated against financial objectives.
Aggregate Production Planning Horizon
Group level forecast
Decision Areas
Staff Planning
Production planning
Master production
scheduling
Purchasing (material and
equipment)
Distribution
Short RangeIntermediate Range Long Range
Now 2 months -2 years
APP

4. Planning Sequence
Master schedule
Establishes short range
schedulesfor specific
products
Aggregate Production Plan
Establishes intermediate
rangeproduction capacity
for product groups
Corporate
strategies
and policies
Economic,
competitive,
and political
conditions
Aggregate
demand
forecasts
Business Plan
Establishes long range
production and capacity
strategies

5. Overview of
Manufacturing
Planning
Activities
MonthJ F M A M J J A S
# motors4025 50 30 30 50 30 40 40
MonthJ F M A M J J A S
# AC Motors
5 hp15 - 30 - - 30 - -10
25 hp2025 20 15 15 15 202020
# DC Motors
20 hp- - - - - - 1010 -
# WR motors
10 hp5 - - 15 15 5 -1010
Master Schedule
Aggregate Plan
Note: Aggregate plan expresses the end product as “motors”
Note: Master schedule specifies precisely how many of which type (or size) of motors will be
produced, and when –to plan for the material and capacity requirements
Example

6. Aggregate Production Planning is a planning processwhich establishes a
company-wide game planfor allocating resources (people, equipment,
etc.) and economically meeting demand. APP
. Matchesmarket demand to company resources
.Expressesintermediate range demand, resources, and
capacity in general terms –product groups or families of
products rather than at the detail product level (e.g. televisions
vs 21”, 27”, 32”, etc.)
.Allows planners more time to deal with short range and day-to-
day issues
.Providesinformation to allow for flexibility … because of
forecast inaccuracy intermediate plans do not have to be
“locked in” too soon
Aggregate Production Planning
Supplier capabilities
Storage capacity
Materials availability
Materials
Current machine capacities
Plans for future capacities
Work-force capacities
Current staffing level
Operations
New products
Product design changes
Machine standards
Engineering
Labor-market conditions
Training capacity
Human Resources
Cost data
Financial condition of firm
Accounting & Finance
APP
Customer needs
Demand forecasts
Competition behavior
Distribution & Marketing
Managerial Inputs to APP

7. The Processof APP:
.Use the company forecast to determine demand for each
period
.Determine capacities (regular time, overtime, subcontracting,
etc)for each period
.Identify company or departmental policies that are pertinent
(employment policies, safety stock policies, etc.)
.Determine unit costs for regular time, overtime, subcontracting,
holding inventories, layoffs, and other relevant costs
.Develop alternatives with cost for each
.If satisfactory plans emerge select the one that best satisfies
objectives; otherwise, continue with the previous step.
Aggregate Production Planning Process
PRODUCTION
PLANNING
CAPACITY
WORK FORCE
PRODUCTION
INVENTORY
INTERNAL
EXTERNAL
EXTERNAL
CAPACITY
COMPETITION
RAW MATERIAL
SUPPLY
DEMAND
ECONOMIC
CONDITIONS
Production Planning Environment
Aggregate Planning ProcessAggregate Planning Process

8. No
APP Process
Determine
requirements for
planning horizon
Identify alternatives,
constraints and costs
Prepare prospective
plan for planning
horizon
Is the plan
acceptable?
Yes
Implement and update
the plan
Move ahead to the
next planning session
Aggregate Planning Objectives
The overriding objective of Aggregate Production Planning is to
consider company policies and management inputs related to
operations, distribution & marketing, materials, accounting & finance,
engineering and human resources to
.Minimize costs & maximize profits
.Maximize customer service
.Minimize inventory investment
.Minimize changes in production rates
.Minimize changes in work-force levels
.Maximize utilization of plant and equipment

9. Aggregate Production Planning (APP)
Operations Managers try to determine the best
way to meet forecasted demand by adjusting
various capacity.
Strategiesfor meeting uneven supply & demand
Levelcapacity-maintain a level (steady rate) of production output
while meeting variations in demand –[that is, use inventory to absorb
fluctuations in demand]
Aggregate Planning … balancing demand/capacity
Time
Level
production
capacity
Demand
Units

10. Effect Of “Level Output Strategy”
a leveloutputstrategy–make the same amount each period
6 Month Forecast
Planning Period
1
2
3
4
5
6
Forecasted Demand

10
8
12
14
10
8
Production Plan
10
10
10
10
10
10
inventory is used to “buffer” the difference in capacity and demand
Inventory Position
10
10
12
10
6
6
8
Leveling strategiestry to keep output (production levels) constant and use other
methods for dealing with the fluctuating demand. These strategies may be either
aggressive or reactive, or a combination of both.
One popular way is to build inventory in low demand times and draw it down in
high demand times.
Extreme AP Strategies-Constant
Output and Constant Capacity
Inventory
Demand
Capacity =
Output
Cost
Increased
Inventory Holding Cost/ Back-
Order Cost
Costs
Minimized
Hiring & Firing Cost/
Subcontracting Cost
Overtime-Idle Time Cost
Use When Inventory Holding Cost is
Low
For High Capital Intensive
Operations
Examples Water Purification Plant
Extreme AP Strategy-Variable
Output and Constant Capacity
Idle Time
Overtime
Output Capacity
Demand
Cost
Increase
Overtime and Idle Time Cost
Subcontracting Cost
Costs
Minimized
Inventory Holding Cost
Hiring/ Firing Cost
Use When Inventory is
Impossible or Expensive
For High Skilled Labor
Intensive Operations
ExamplesLaw Firms, Accounting
Service

11. Strategiesfor meeting uneven supply & demand
Chasedemand-match production capacity to demand by adjusting
capacity to the demand for the period
Aggregate Planning … balancing demand/capacity
Time
Units
Production
chases
demand
Demand
Effect Of “Chase Demand Strategy”
a chase demand strategy–production is adjusted to meet demand
6 Month Forecast
Planning Period
1
2
3
4
5
6
Forecasted Demand

10
8
12
14
10
8
Production Plan
10
8
12
14
10
8
inventory remains constant
Inventory Position
10
10
10
10
10
10
10

12. Cost
Increase
Hiring & Firing Cost/ Idle Capacity Cost
Costs
Minimized
Inventory Holding Cost/ Subcontracting Cost
Overtime and Idle Time Cost
Use Inventory is Impossible or Expensive
Low Skilled Labor Operations
There is a match between Labor Availability and
the Need for Labor
Examples Entertainment Center (Disney World), Farm
Workers
Chasedemand (Ideal Case)-change workforce levels so that
production matches demand
Strategiesfor meeting uneven supply & demand
DemandOptions… when capacity and demand are not the same
.Pricing can be adjusted to affect demand (e.g. lower rates in off season)
.Promotions(e.g. advertising, consumer marketing campaigns)
.Back Orders -shift demand to another period by taking orders in one period
and promising deliver in a future period when capacity is available(may not
create a satisfied customer)
.New demand -create a new need for capacity by producing a product
during slack times to utilize resources(e.g. snow blower company
produces leaf blowers in off season) .
Aggregate Planning … balancing demand/capacity

13. Strategiesfor meeting uneven supply & demand
CapacityOptions… when capacity and demand are not the same
.Hire or lay-off workers(may create morale and employment problems
.Use overtime or under-time
.Part-time workers
.Manage capacity with inventory (e.g. let inventories build during periods of
low demand or deplete during periods of high demand)
.Subcontract temporary capacity
Aggregate Planning … balancing demand/capacity
Level
Strategy
Chase
Strategy
Production
equals
demand
Production rate
is constant
Strategy Details

14. APP Strategies -Pure Strategies
Capacity Options —Change Capacity[Reactive
Strategies]
1)changing inventory levels
2)varying work force size by hiring or layoffs
3)varying production capacity through overtime or
idle time
4)subcontracting
5)using part-time workers
The above five pure strategies are called “passive
strategies” because they do not try to change demand but
attempt to absorb the fluctuations in it.

15. Reactive Strategy ExamplesReactive Strategy Examples
wAnticipation inventoryis a reactive strategy. It
can absorb uneven rates of demand or
supply. Thus it is also a leveling strategy .
wWorkforce adjustment(use of overtime,
under-time or subcontracting) is reactive.
nIf you are varying your workforce it is also chase. If
you subcontract, it is leveling.
wSchedulingemployeevacationsfor low
demand times is a reactive strategy.
wUsingbackordersin high-demand times is a
leveling and a reactive strategy.
¨Demand Options —change demand [Proactive
Strategies]
6)influencing demand
7)backordering during high demand periods
8)Counter seasonal product mixing
APP Strategies -Pure Strategies
The above three pure strategies are called “active
strategies” through which firms try to influence the demand
pattern to smooth out its changes over the planning period.

16. wwThe purpose of aggressive strategies is to influence The purpose of aggressive strategies is to influence
demand in order to smooth out (demand in order to smooth out (levellevel) production or ) production or
service flow. service flow. ((All aggressive strategies are All aggressive strategies are levelingleveling.).)
wwProduct Promotions Product Promotions are designed to increase sales using are designed to increase sales using
creative pricing. Doing so in a low demand period is a creative pricing. Doing so in a low demand period is a
leveling leveling strategy.strategy.
nnOffOff--season rates: (January retail sales) (slowseason rates: (January retail sales) (slow--season season
resort rates)resort rates)
wwComplementary productsComplementary products: Services or products that have : Services or products that have
similar resource requirements but different demand cycles similar resource requirements but different demand cycles
allow allow leveling leveling of output.of output.
nnEG: counterEG: counter--seasonal products or services such as seasonal products or services such as
seasonal clothing.seasonal clothing.
Aggressive StrategiesAggressive Strategies
Planning Strategies SummarizedPlanning Strategies Summarized
Reactive Strategies
wHiring & Layoffs (Chase)
wOvertime & Idle time (Chase)
wSubcontracting (Leveling)
wBack Orders (Leveling)
wInventory Levels (Leveling)
(Creating more inventory in
slow periods and using it to
meet excess demand in high
demand periods.)
Aggressive Strategies
wPricing (Leveling)
wPromotion (Leveling)
wComplementary (counter-
seasonal) Products
(Leveling)
Most planning strategies are not Pure (one kind). They are usually Hybrid
Strategies with a combination of techniques, often using leveling and chase.

17. Aggregate Scheduling Options/Strategies :
Advantages & Disadvantages
Option AdvantageDisadvantage Some
Comments
Changing
inventory levels
Changes in
human resources
are gradual, not
abrupt
production
changes
Inventory
holding costs;
Shortages may
result in lost
sales
Applies mainly
to production,
not service,
operations
Varying
workforce size
by hiring or
layoffs
Avoids use of
other alternatives
Hiring, layoff,
and training
costs
Used where size
of labor pool is
large
Aggregate Scheduling Options/Strategies :
Advantages & Disadvantages
Option Advantage DisadvantageSome
Comments
Varying
production rates
through overtime
or idle time
Matches seasonal
fluctuations
without
hiring/training
costs
Overtime
premiums, tired
workers, may not
meet demand
Allows
flexibility within
the aggregate
plan
SubcontractingPermits
flexibility and
smoothing of the
firm's output
Loss of quality
control; reduced
profits; loss of
future business
Applies mainly
in production
settings

18. Aggregate Scheduling Options/Strategies :
Advantages & Disadvantages
Option Advantage DisadvantageSome
Comments
Using part-time
workers
Less costly and
more flexible
than full-time
workers
High
turnover/training
costs; quality
suffers;
scheduling
difficult
Good for
unskilled jobs in
areas with large
temporary labor
pools
Influencing
demand
Tries to use
excess capacity.
Discounts draw
new customers.
Uncertainty in
demand. Hard to
match demand to
supply exactly.
Creates
marketing ideas.
Overbooking
used in some
businesses.
Aggregate Scheduling Options/Strategies :
Advantages & Disadvantages
Option Advantage Disadvantage Some
Comments
Back ordering
during high-
demand periods
May avoid
overtime. Keeps
capacity constant
Customer must
be willing to
wait, but
goodwill is lost.
Many companies
backorder.
Counterseasonal
products and
service mixing
Fully utilizes
resources; allows
stable workforce.
May require
skills or
equipment
outside a firm's
areas of
expertise.
Risky finding
products or
services with
opposite demand
patterns.

19. The Reality of Planning StrategyThe Reality of Planning Strategy
wMost Aggregate Planning (Production and Staffing) is
Trial and Error planning.
wProcess-Focused firmsare more apt to use Chase
strategies. (Chasing/reacting to demand)
nProcess-focused firms are smaller and more
adaptableto changing demand and more flexible in
making capacity change. (Wait-and-see capacity
planning)
wProduct-Focused Firmsare more apt to use Leveling
strategies. (Keeping output level)
nHigh volume, lower inventories, lower margins and
higher equipment-utilization needs make it more
difficult and costly to vary production rates.
No allowances are made for holidays, different number of workdays
Cost is a linear function composed of unit cost & number of units
Plans are feasible(e.g. sufficient inventory storage space is available,
subcontractors are available to produce quantity and quality of
products, changes in output can be made as needed)
Cost figures can be reasonably estimated and are constant for the
planning horizon
Inventories are built and drawn downat a uniform rate and output
occurs at a uniform rate though out
Aggregate Planning assumptions

20. 1. Informal, trial and error methods. In practice, these techniques are more
commonly used.
2. Mathematical techniques -such as linear programming, linear decision rules
or simulation. Although not widely used, they serve as a basis for
comparing theeffectiveness of alternative techniques for aggregate
planning.
General Procedure for Aggregate Planning
1. Determine demand and production requirements for each period.
2. Determine production capacity (regular time, overtime, subcontracting) for
each period.
3.Determine company or departmental policies that are pertinent.
For example, maintain a safety stock of 5 percent of demand, or maintain a
reasonably stable work force.
4. Determine unit costs for regular time, overtime, subcontracting, holding
inventories, back orders and other relevant costs.
5. Develop alternative plans and compute the cost of each.
6. If satisfactory plans emerge, select the one that best satisfies objectives
(such as cost minimization). Otherwise, return to step 5.
Techniques for Aggregate Production Planning
Simple tables or worksheets can be developed to evaluate demand, aggregate group
level production plans and inventory. We will look at some examples to illustrate the
concept of aggregate planning. The assumptions for these examples simplify the
computations but can be easily modified to “real situations”.
Aggregate Planning –Informal Techniques

21. Aggregate Planning –Informal Techniques
Aggregate Planning -formula’s
Number of workers in period= Number of workers at end of the
previous period + Number of new workers at the start of a period -Number
of laid-off workers at the start of a period
Inventory at the end of a period = Inventory at the end of the previous period
+ Production in the current period -Amount used to satisfy demand in the
current period
Average Inventory for a period = (Beginning Inventory + Ending Inventory) / 2
Cost for a period = Output Cost+ Hire/Lay-off Cost + Inventory Cost +
Backorder Cost where Output Cost = Regular Time Cost + Overtime Cost +
Subcontractor Cost
How To Calculate Costs …
RegularCosts
. Output cost = Regular cost per unit * Quantity of regular output
.Overtime cost = Overtime cost per unit * Overtime quantity
.Subcontract cost = Subcontract cost per unit * Subcontract quantity
Hire-Layoff Costs
.Hire cost = Cost per hire * Number hired
.Lay-off cost = Cost per lay-off * Number laid off
Inventory Costs
.Carrying cost per unit * Average inventory
Back Order Costs
.Back order cost per unit * Backorder quantity

22. Aggregate Production Planning Illustration
Giventhe following information:
6 month production planning period
10 labour-hours per unit required
Labour cost = $10/hour regular
= $15/hour overtime
Total unit cost = $200 / unit
= $228/unitsubcontract
Current workforce=20 employees
Hiring cost= $500 / employee
Layoff cost= $800 / employee
Safety stock=20% of monthly forecast
Beginninginventory = 50 units
Inventory carrying cost = $10/unit/month
Stockout cost = $50/unit/month
Additional information available:
Sales Work Work Hours
Month ForecastDays at 8 Hrs. / Day
Jan. 300 22 176
Feb. 500 19 152
Mar. 400 21 168
Apr. 100 21 168
May. 200 22 176
June 300 20 160
First Step: Calculate Production Requirement
Sales Safety Production
Month Forecast Stock Required
Jan. 300 60 300+60-50=310
Feb. 500 100500+100-60=540
Mar. 400 80 400+80-100=380
Apr. 100 20 100+20-80=40
May. 200 40 200+40-20=220
June 300 60 300+60-40=320
Safety Stock of the period t will be an Beginni9ng Inventory of the period (t+1)
Production
Required
310
540
380
40
220
320
Hours
Required
3100
5400
3800
400
2200
3200
Hrs. Avail.
per Worker
176
152
168
168
176
160
Workers
Required
18
36
23
3
13
20
Workers
Hired
18
10
7
Workers
Fired
2
13
20
Hire/Fire
Costs
$1600
9000
10400
16000
5000
3500
Total Cost = $45,500
Production
Required
310
540
380
40
220
320
Hours
Required
3100
5400
3800
400
2200
3200
Total Hrs.
Available
3520
3040
3360
3360
3520
3200
Overtime
Hours
2360
440
Undertime
Hours
420
2960
1320
OT/ UT
Costs
$4200
11800
2200
14800
6600
0
Plan #2 -Exact Production; Vary Production Rate
Total Cost = $61,000
Month
Jan.
Feb.
Mar.
Apr.
May
June
Month
Jan.
Feb.
Mar.
Apr.
May
June
Plan #1-Exact Production; Vary Work Force
Aggregate Production Planning Illustration –Contd.

23. Cum. Prod.
Required
310
850
1230
1270
1490
1810
Total
Production
352
304
336
336
352
320
Cumulative
Production
352
656
992
1328
1680
2000
Inventory
Level
42
58
190
190
Stockout
Level
194
238
Inv. / SO
Costs
$420
9700
11900
580
1900
1900
Total Cost = $26,400
Hours
Available
3520
3040
3360
3360
3520
3200
Total Cost = $7,160+ $ 21,000 = $28,160
Cum. Prod.
Required
310
850
1230
1270
1490
1810
Hours
Available
3520(20)
4560(30)
5040(30)
1680(10)
1760(10)
1600(10)
Total
Production
352
456
504
168
176
160
Cumulative
Production
352
808
1312
1480
1656
1816
Inv. / (SO)
Level
42
(42)
82
210
166
6
Inv. / SO
Costs
$420
2100
820
2100
1660
60
Hire/Fire
Costs
5000
16000
$7,160 $21,000
Month
Jan.
Feb.
Mar.
Apr.
May
June
Month
Jan.
Feb.
Mar.
Apr.
May
June
Plan #3-Exact Production; Vary Inventory Level With 20 Employees
Aggregate Production Planning Illustration –Contd.
Plan #4-Exact Production; Vary Workforce Level; Vary Inventory Level
Plan
Costs
45,500
61,000
26,400
28,160
Plan
1
2
3
4
Production
Costs
362,000
362,000
400,000
363,200
Total
Costs
407,500
446,500
426,400
391,360
Units
Produced
1810
1810
2000
1816
Cost
per Unit
$225.14
$233.70
$213.20
$215.51
Final Cost Analysis:
Decision: Go with Plan #3 on the basis of lowest cost per unit.
Aggregate Production Planning Illustration -Contd.

24. Example 2: Planners for a company that makes several models of tractors are
about to prepare an aggregate plan that will cover 6 periods. The have
assembled the following cost information ($):
Output Costs
Regular time 2 per tractor
Overtime 3 per tractor
Subcontract6 per tractor
Inventory Costs
1 per tractor on average inventory
Back Order Costs 5 per tractor per period
The forecasted demand by period is:
Aggregate Planning –Example 2
Planning Period
1
2
3
4
5
6
Total
Forecasted Demand
200
200
300
400
500
200
1800

25. Aggregate Planning
Total cost of plan is
$4,700
Inventory
Backorder
Costs
Production Schedule
Cumulative
Forecast&
Production
Cost
ComponentsNotice the backorder
cost in period 5
Example 2: After reviewing the plan the planners need to develop an
alternative based on the news that one of the regular time workers has decided
to retire.
Rather than replace that person they would rather stay with a smaller work
force and use overtime to make up for the lost output.
The maximum overtime output is 40 units.
Aggregate Planning –Example 2
First the regular time output of 300 units per 15 people must be adjusted for 14
people. Therefore 300/15*14 = 280 = adjusted regular time output for 14
people.

26. We are 120 tractors
short.
Where do we
manufacture them?
Aggregate Planning
Why did we put
manufacture them
here?
Does manufacturing
them in other
periods produce a
lower cost?
Total cost of plan is
$4,640
Aggregate Planning
Notice the backorder
cost in period 5

27. Example 3: A third option is to use temporary workers rather than overtime to
fill in for the retiring worker.
Suppose that it costs an additional $100 to hire and train a temporary worker
and that a temporary worker can produce 15 tractors per period.
Aggregate Planning –Example 2
First of all 120 units are needed to replace the retired worker’s output (see
output from Example 2).
Therefore 120/15 = 8 means that 8 temporary worker periods are needed to
create the 120 units.
Noting that periods 4 and 5 have the heaviest demand, using 4 temporary
workers during those periods seems reasonable. This means that we only
have to hire 4 temporary workers for two months.
Why is the hire/train
cost only $400?
Total cost of plan is
$4,860
Aggregate Planning
Notice the backorder
cost in period 5
Notice the
Hire/Layoff cost in
period 4

28. Pure Strategies
Hiring costHiring cost= $100 per worker= $100 per worker
Firing costFiring cost= $500 per worker= $500 per worker
Regular production cost per pound = $2.00Regular production cost per pound = $2.00
Inventory carrying costInventory carrying cost= $0.50 pound per quarter= $0.50 pound per quarter
Production per employeeProduction per employee= 1,000 pounds per quarter= 1,000 pounds per quarter
Beginning work forceBeginning work force= 100 workers= 100 workers
QUARTERQUARTER SALES FORECAST (LB)SALES FORECAST (LB)
SpringSpring 80,00080,000
SummerSummer 50,00050,000
FallFall 120,000120,000
WinterWinter 150,000150,000
Example:Example:
Level Production Strategy
Level production
= 100,000 pounds
(80,000 + 50,000 + 120,000 + 150,000)
4
SpringSpring 80,00080,000 100,000100,000 20,00020,000
SummerSummer 50,00050,000 100,000100,000 70,00070,000
FallFall 120,000120,000 100,000100,000 50,00050,000
WinterWinter 150,000150,000 100,000100,000 00
400,000400,000 140,000140,000
Cost of Level Production Strategy:
(400,000 X $2.00) + (140,00 X $.50) = $870,000
SALESSALES PRODUCTIONPRODUCTION
QUARTERQUARTER FORECASTFORECAST PLANPLAN INVENTORYINVENTORY

29. Chase Demand Strategy
SpringSpring 80,00080,000 80,00080,000 8080 00 2020
SummerSummer 50,00050,000 50,00050,000 5050 00 3030
FallFall 120,000120,000 120,000120,000 120120 7070 00
WinterWinter 150,000150,000 150,000150,000 150150 3030 00
100100 5050
SALESSALES PRODUCTIONPRODUCTION WORKERSWORKERS WORKERSWORKERS WORKERSWORKERS
QUARTERQUARTER FORECASTFORECAST PLANPLAN NEEDEDNEEDED HIREDHIRED FIREDFIRED
Cost of Chase Demand Strategy
(400,000 X $2.00) + (100 x $100) + (50 x $500) = $835,000
Previous SpringSummer FallWinter
Beginning Inventory
0
10,000
40,000
30,000
Demand Forecast
80,000
50,000
120,000
150,000
Production Plan
90,000
80,000
110,000
120,000
Ending Inventory
0
10,000
40,000
30,000
0
Work-force Size
100
90
80
110
120
Total Demand Forecast=
400,000
Total Production Plan=
400,000
Inventory Cost (.50/lb)
$5,000$20,000$15,000 $0
Work-force Cost $5,000$5,000$3,000$1,000
Total Cost $54,000
Quarter
Mixed Strategy
Initial Inv (t) = End Inv (t-1)

30. Mixed Strategy
?Combination of Level Production and Chase
Demand strategies
?Examples of management policies
–no more than x% of the workforce can be laid
off in one quarter
–inventory levels cannot exceed x dollars
?Many industries may simply shut down
manufacturing during the low demand season
and schedule employee vacations during that
time
APP Using Mixed Strategies -Exercise
Production per employee= 100 cases per month
Wage rate= $10 per case for regular production
= $15 per case for overtime
= $25 for subcontracting
Hiring cost= $1000 per worker
Firing cost= $500 per worker
Inventory carrying cost= $1.00 case per month
Beginning work force= 10 workers
January 1000 July 500
February 400 August 500
March 400 September 1000
April 400 October 1500
May 400 November 2500
June 400 December 3000
MONTH DEMAND (CASES) MONTH DEMAND (CASES)

31. Mathematical Model
uData:
–St art ing invent ory in January: 1,000 unit s
–Selling price t o t he ret ailer: Rs.40/ unit
–Workforce at t he beginning of January: 80
–# of working days per m ont h: 20
–Regular work per day per em ployee: 8 hours
–Maxim um overt im e allowed per em ployee per m ont h: 10 hours
–Ending invent ory required ( at end of June) : Minim um 500 unit s
–Dem and forecast :
Month JanuaryFebruaryMarch April May June
Demand1,600 3,000 3,200 3,800 2,200 2,200

32. Numerical Example
Item

Cost

Materials

Rs.10/unit

Inventory holding cost

Rs.2/unit/month

Marginal cost of a stockout

Rs.5/unit/month

Hiring and training costs

Rs.300/worker

Layoff cost

Rs.500/worker

Labor hours required

4/unit

Regular time cost

Rs.4/hour

Over time co
st

Rs.6/hour

Cost of subcontracting

Rs.30/unit


(cont…)
uCost Data:
Numerical Example
(Define Decision Variables)
?Th e de cision v a r ia ble s a r e a s follow s:
–W
t= W or k for ce size for m on t h t
–H
t= N u m be r of e m ploye e s h ir e d a t t h e be gin n in g of m ont h t
–L
t= N u m be r of e m ploye e s la id off a t t h e be gin n in g of m on t h t
–P
t= Pr odu ct ion in m on t h t
–I
t= I n v e n t or y a t t h e e n d of m on t h t
–S
t= N u m be r of u n it s st ock e d ou t a t t h e e n d of m on t h t
–C
t= N u m be r of u n it s su bcon t r a ct e d for m on t h t
–O
t= N u m be r of ove r t im e h ou r s w or k e d in m on t h t
( com bin e d for a ll e m ploye e s)
N ot e : For a ll t h e a bove va r ia ble s, t = 1 , 2 , …, 6 givin g a t ot a l of
4 8 de cision va r ia ble s.

33. Numerical Example
(Components of Objective Function)
?Re g u la r t im e la b or cost
Rs. 4 / h ou r * 8 h r / d a y * 2 0 d a y / m on t h = Rs.6 4 0 / m o n t h
Th e r e for e , r e g u la r t im e la b or cost p e r m on t h :
?Ov e r t im e la b or cost
Ov e r t im e la b or cost is Rs.6 / h ou r a n d O
tr e p r e se n t s t h e n u m b e r of ov e r t im e
h ou r s w or k e d in m on t h t( com b in e d for a ll e m p loy e e s)
Th e r e for e , ov e r t im e t im e la b or cost p e r m on t h :
?Cost of h ir in g a n d la y off
Th is cost is ca lcu la t e d a s:
?Cost of h old in g in v e n t or y a n d st ock in g ou t
Th is cost is ca lcu la t e d a s:
?Cost of m a t e r ia ls a n d su b con t r a ct in g ou t
Th is cost is ca lcu la t e d a s: 1 5
å
=
6
1
t
W640
t
å
=
6
1
t
O6
t
åå
==
+
6
1
t
6
1
t
L500H300
tt
åå
==
+
6
1
t
6
1
t
S5I2
tt
åå
==
+
6
1
t
6
1
t C30P10
tt
Numerical Example
(Objective Function)
ååå
åå
ååå
===
==
===
+++
++
++
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
30105
2500
3006640
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
CPS
IL
HOW
uThe obj ective function is:
Minim ize Z =

34. Numerical Example
(Define Constraints Linking Variables)
?W orkforce size, hiring and layoff const raint s:
or
w here t = 1 , 2 , …, 6 and W
0= 8 0
?Capacit y const raint s:
or
w here t = 1 , 2 , …, 6
0LHWW
tt1tt
=++-
-
tt1tt
LHWW -+=
-
ttt O)4/1(W40P +£
0PO)4/1(W40
ttt
³-+
?I nvent ory balance const raint s:
or
w here t = 1 , 2 , …, 6 and I
0= 1 ,0 0 0 , I
6> = 5 0 0 , and S
0= 0 ,
?Overt im e lim it const raint s:
or
w here t = 1 , 2 , …, 6
tt1tttt1-t SISDCPI -++=++
-
0SISDCPI
tt1tttt1-t =+---++
-
tt W10O£
0W10O
tt £-
Numerical Example
(Define Constraints Linking Variables)
(cont…)

35. Average Inventory and
Average Flow Time
?Average invent ory for a period t :
?Average invent ory over t he planning horizon:
i.e.
?Average flow t im e: ( Average invent ory) / ( Throughput )
)I(I
2
1
t1t+
-
å
=
-
+
T
tT
1
t1t
)I(I
2
11
ú
û
ù
ê
ë
é
++å
-
=
-
1
1
tt1t I)I(I
2
11
T
tT
å
å
=
-
=
- ú
û
ù
ê
ë
é
++
T
t
T
t
T
T
1
t
1
1
tt1t
D
1
I)I(I
2
11
Various Scenarios
?Som e of t he possible scenarios are:
–I ncrease in holding cost ( from Rs.2 t o Rs.6 )
–Overt im e cost drops t o Rs.5 per hour
–I ncreased dem and fluct uat ion
?Your plan w ill change w it h t he change in scenarios
MonthJanuaryFebruaryMarchAprilMay June
Demand1,000 3,000 3,8004,8002,0001,400

36. Transportation Tableau for
Aggregate Planning
?Su p p ose w e h a v e t h e f ollow in g in f or m a t ion
–Be g in n in g I n v e n t or y : I
0
–Re g u la r t im e p r od u ct ion cost p e r u n it : r
–O v e r t im e p r od u ct ion cost p e r u n it : v
–Su b con t r a ct p r od u ct ion cost p e r u n it : s
–H old in g cost p e r u n it p e r p e r iod : h
–Ba ck or d e r cost p e r u n it p e r p e r iod : b
–Sh or t a g e ( u n sa t isf ie d or d e r ) cost p e r u n it p e r p e r iod : c
–U n d e r t im ecost p e r u n it : u
–D e sir e d in v e n t or y le v e l a t t h e e n d of p e r iod 3 : I
e
–Tot a l u n u se d ca p a cit ie s: U
–Tot a l u n sa t isf ie d or d e r s: C
P e r io d s
1 2 3
D e m a n d D
1 D
2 D
3
R e g u la r Ca p a cit y R
1 R
2 R
3
O v e r t im e Ca p a cit y O
1 O
2 O
3
Su b co n t r a ct Ca p a cit y S
1 S
2 S
3
LINEAR PROGRAMMING
(no backorders, supply > demand)
Beg. Inventory
Demand for
Period 1 Period 2 Period 3
Total
Capacity
(supply)
Unused
Capacity
Supply from
v v + h v + 2h
0 h 2h
s s + h s + 2h
v v + h
r r + h r + 2h
v
r r + h
s s + h
s
r
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
I
0
R
1
O
1
S
1
R
2
O
2
S
2
R
3
O
3
S
3
u
u
u
u
u
u
u
u
u
u
Demand D
1 D
2 D
3+ l
e U Grand Total
1
2
3

37. LINEAR PROGRAMMING
(backorders, supply > demand)
Beg. Inventory
Demand for
Period 1 Period 2 Period 3
Total
Capacity
(supply)
Unused
Capacity
Supply from
v v + h v + 2h
0 h 2h
s s + h s + 2h
v + b v v + h
r r + h r + 2h
v + 2b v + b v
r + b r r + h
s + b s s + h
s + 2b s + b s
r + 2b r + b r
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
I
0
R
1
O
1
S
1
R
2
O
2
S
2
R
3
O
3
S
3
u
u
u
u
u
u
u
u
u
u
Demand D
1 D
2 D
3+ l
e U Grand Total
1
2
3
Beg. Inventory
Demand for
Period 1 Period 2 Period 3
Total
Capacity
(supply)
Supply from
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
I
0
R
1
O
1
S
1
R
2
O
2
S
2
R
3
O
3
S
3
C
Demand D
1 D
2 D
3+ l
eGrand Total
v v + h
0 h 2h
s s + h
r r + h
v v + h v + 2h
s s + h s + 2h
r r + h r + 2h
r
v
s
LINEAR PROGRAMMING
(no backorders, demand > supply)
Unsatisfied Demand
c c c
1
2
3

38. Demand
1 2 3 4 5 6 7 8 9 Total
190 230 260 280 210 170 160 260 180 1940
There are 20 full time employees, each can produce 10 units per period at the cost of $6 per unit. Therefore the supply of full time
workers is as follows
1 2 3 4 5 6 7 8 9 Total
200200 200 200 200 200 200 200 200 1800
Overtime cost is $13 per unit.
Inventory carrying cost $5 per unit per period
Backlog cost $10 per unit per period
Maximum over time production is 20 units per period
Formulated the problem as a Linear Programming model.
Exercise
APP by the Transportation Method
1 900 1000 100 500
2 1500 1200 150 500
3 1600 1300 200 500
4 3000 1300 200 500
Regular production cost per unit $20
Overtime production cost per unit $25
Subcontracting cost per unit $28
Inventory holding cost per unit per period$3
Beginning inventory 300 units
EXPECTED REGULAR OVERTIME SUBCONTRACT
QUARTER DEMAND CAPACITY CAPACITY CAPACITY

39. Production Plan for the Example using TP
1 900 1000 100 0 500
2 1500 1200 150 250 600
3 1600 1300 200 500 1000
4 3000 1300 200 500 0
Total7000 4800 650 1250 2100
REGULAR SUB- ENDING
PERIOD DEMAND PRODUCTION OVERTIME CONTRACT INVENTORY
The aggregate plan can not be used for production because it
is at the group level rather than the individual product level.
The aggregate plan must be broken down into specific product
requirements so that specific labor skills, materials, and inventory
plans can be determined. (e.g. 21” TV’s take different parts than 27”
TV’s)
We will discuss this more in MPS, but first let’s take a look at
some general concepts.
The Production Plan

40. Because different products require different materials, skills, etc. we must manufacture
at the item level rather than the group level. The masterschedule(item level)is
similar to the aggregateplan(group level).
.Master Schedule-is a detailed plan usually done for weekly periods
(sometimes daily)showing the quantity and timing of specific items (e.g.
21” TV’s)for a scheduled horizon and can be used by other functional areas
of the organization.
.Rough-Cut Capacity Planning-is an approximate balancing of the
detailed master production schedule with capacity to test the feasibility of
the master production schedule. It resembles the aggregate planning
process; but, at a detailed product level.
The Production Plan
Master
scheduling
Beginning
Inventory
Forecast
Customer
Orders
Inputs
3 inputs and 3 outputs
Master Scheduling Process
Outputs
Projected
Inventory
Master
Production
Schedule
Available To
Promise
(uncommitted
inventory)

41. Projecteddemandis calculated based on the customer orders
and forecast.
ProjectedDemand= max (forecast, orders)
Inputs To Master Scheduling
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
How can customer orders be more than forecast?
Therefore, the ProjectedInventoryPosition(previous inventory position -projected
demand)without any production can be calculated and is shown below:
Outputs Of Master Scheduling
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
-29
-59
-99
-139
-179
-219

42. If the lot size for this item is 70 units, we can now build the MasterProduction
Schedule. We add our first lot in week/day 3 because this is the first negative
inventory position. We then update our ProjectedInventoryPosition.
Outputs Of Master Scheduling
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
-29
-69
-109
-149
Master Production Schedule (MPS)
70
Outputs Of Master Scheduling
We add our next lot in week/day 5 because this is the next negative inventory position.
We then update our ProjectedInventoryPosition.
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
-39
-79
Master Production Schedule (MPS)
70
70

43. We add our next lot in week/day 7 because this is the next negative inventory position.
We then update our ProjectedInventoryPosition.
Outputs Of Master Scheduling
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
-9
Master Production Schedule (MPS)
70
70
70
We add our next lot in week/day 9 because this is the next negative inventory position.
We then update our ProjectedInventoryPosition, and have completed the second
output of the master scheduling process, the MasterProductionSchedule.
Outputs Of Master Scheduling
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70

44. Outputs Of Master Scheduling
We are now ready to compute our final output of the master scheduling process, the
Availableto Promise (ATP) or uncommitted inventory. This is inventory which is
available to sell and is extremely important to customer service. The ATP is
calculated for week/day 1, 3, 6, 7 and 8.
Think about how Land’s End may use the ATP!
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70
Available To Promise (ATP)
Outputs Of Master Scheduling
The ATP is calculated for week/day 1 by the following:
Week 1 ATP = Beginning inventory -sum of committed
inventory (customer orders) until the first master
scheduled lot
= 64 -(33 + 20) = 11
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70
Available To Promise (ATP)
11

45. The ATP is calculated for week/day 3 by the following:
Week 3 ATP = MPS for week/day 3 -sum of committed
inventory (customer orders)until the next master
scheduled lot
= 70 -(10 + 4) = 56
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70
Available To Promise (ATP)
11
56
Outputs Of Master Scheduling
Outputs Of Master Scheduling
The ATP is calculated for week/day 5 by the following:
Week 5 ATP = MPS for week/day 5 -sum of committed
inventory (customer orders)until the next master
scheduled lot
= 70 -2 = 68
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70
Available To Promise (ATP)
11
56
68

46. Outputs Of Master Scheduling
The ATP is calculated for week/day 7 by the following:
Week 7 ATP = MPS for week/day 7 -sum of committed
inventory (customer orders)until the next master
scheduled lot
= 70 -0 = 70
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70
Available To Promise (ATP)
11
56
68
70
Outputs Of Master Scheduling
The ATP is calculated for week/day 8 by the following:
Week 8 ATP = MPS for week/day 8 -sum of committed
inventory (customer orders)until the next master
scheduled lot
= 70 -0 = 70
Planning Period
1
2
3
4
5
6
7
8
Forecast
30
30
30
30
40
40
40
40
Customer Orders
33
20
10
4
2
Projected Demand
33
30
30
30
40
40
40
40
Projected On Hand Inventory
64
31
1
41
11
41
1
31
61
Master Production Schedule (MPS)
70
70
70
70
Available To Promise (ATP)
11
56
68
70
70

47. Master Scheduling
You can see by these calculations that changes to a Master Schedule can be
disruptive, particularly those in the first few weeks/days of a schedule.
It is difficult to rearrange schedules, materials plans, and labor plans on a short notice.
For these reasons, many schedules have varying degrees of changes that are
allowed. Timefencesare created to indicate the level of change if any that will be
considered .
Stabilizing The Master Schedule
Planning Period
1
2
3
4
5
6
7
8
9
10
11
12

Frozen FullFirm Open

48. Items
Product lines
or families
Individual
products
Components
Manufacturing
operations
Resource level
Plants
Individual
machines
Critical work
centers
Production PlanningCapacity Planning
Resource
Requirements Plan
Rough-Cut
Capacity Plan
Capacity
Requirements Plan
Input/Output
Control
Aggregate
Production Plan
Master Production
Schedule
Material
Requirements Plan
Shop Floor
Schedule
All work
centers
Hierarchical Planning Process