Aggregate Production Planning (APP)

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

Aggregate Planning
w Aggregate planning: General plan
n Combined products = aggregate product
l Short and long sleeve shirts = shirt
w Single product
n Pooled capacities = aggregated capacity
l Dedicated machine and general machine = machine
w Single capacity
n Time periods = time buckets
l Consider all the demand and production of a given month
together
w Quite a few time buckets [Jan/Feb… or IQ/IIQ/…]
refers to intermediate range
planning covering 2 to 24 months …
a “big picture” look at planning
aimed at balancing capacity and
demand

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 Range Intermediate Range Long Range
Now 2 months - 2 years
APP

Planning Sequence
Master schedule
Establishes short range
schedules for specific
products
Aggregate Production Plan
Establishes intermediate
range production 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

Overview of
Manufacturing
Planning
Activities
Month J F M A M J J A S
# motors 40 25 50 30 30 50 30 40 40
Month J F M A M J J A S
# AC Motors
5 hp 15 - 30 - - 30 - - 10
25 hp 20 25 20 15 15 15 20 20 20
# DC Motors
20 hp - - - - - - 10 10 -
# WR motors
10 hp 5 - - 15 15 5 - 10 10
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

Aggregate Production Planning is a planning process which establishes a
company-wide game plan for allocating resources (people, equipment,
etc.) and economically meeting demand. APP
. Matches market demand to company resources
. Expresses intermediate 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
. Provides information 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

The Process of 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 Process
Aggregate Planning Process

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

Operations Managers try to determine the best
way to meet forecasted demand by adjusting
various capacity.
Strategies for meeting uneven supply & demand
Level capacity - 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

Effect Of “Level Output Strategy”
a level output strategy – 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
inventory is used to “buffer” the difference in capacity and demand
Inventory Position 10 10 12 10 6 6 8
Leveling strategies try 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
Examples Law Firms, Accounting
Service

Chase demand - match production capacity to demand by adjusting
capacity to the demand for the period
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
inventory remains constant
Inventory Position 10 10 10 10 10 10 10

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
Chase demand (Ideal Case)- change workforce levels so that
production matches demand
Demand Options … 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) .

Capacity Options … 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
Level
Strategy
Chase
Strategy
Production
equals
demand
Production rate
is constant
Strategy Details

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.

Reactive Strategy Examples
Reactive Strategy Examples
w Anticipation inventory is a reactive strategy. It
can absorb uneven rates of demand or
supply. Thus it is also a leveling strategy .
w Workforce adjustment (use of overtime,
under-time or subcontracting) is reactive.
n If you are varying your workforce it is also chase. If
you subcontract, it is leveling.
w Scheduling employee vacations for low
demand times is a reactive strategy.
w Using backorders in 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.

w
w The 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 (level
level) production or
) production or
service flow.
service flow. (
(All aggressive strategies are
All aggressive strategies are leveling
leveling.)
.)
w
w Product 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.
n
n Off
Off-
-season rates: (January retail sales) (slow
season rates: (January retail sales) (slow-
-season
season
resort rates)
resort rates)
w
w Complementary products
Complementary 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.
n
n EG: counter
EG: counter-
-seasonal products or services such as
seasonal products or services such as
seasonal clothing.
seasonal clothing.
Aggressive Strategies
Planning Strategies Summarized
Planning Strategies Summarized
Reactive Strategies
w Hiring & Layoffs (Chase)
w Overtime & Idle time (Chase)
w Subcontracting (Leveling)
w Back Orders (Leveling)
w Inventory Levels (Leveling)
(Creating more inventory in
slow periods and using it to
meet excess demand in high
demand periods.)
w Pricing (Leveling)
w Promotion (Leveling)
w Complementary (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.

Aggregate Scheduling Options/Strategies :
Advantages & Disadvantages
Option Advantage Disadvantage 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
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
Subcontracting Permits
flexibility and
smoothing of the
firm's output
Loss of quality
control; reduced
profits; loss of
future business
Applies mainly
in production
settings

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.
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.

The Reality of Planning Strategy
The Reality of Planning Strategy
w Most Aggregate Planning (Production and Staffing) is
Trial and Error planning.
w Process-Focused firms are more apt to use Chase
strategies. (Chasing/reacting to demand)
n Process-focused firms are smaller and more
adaptable to changing demand and more flexible in
making capacity change. (Wait-and-see capacity
planning)
w Product-Focused Firms are more apt to use Leveling
strategies. (Keeping output level)
n High 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 down at a uniform rate and output
occurs at a uniform rate though out
Aggregate Planning assumptions

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 the effectiveness 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

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 …
Regular Costs
. 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

Aggregate Production Planning Illustration
Given the 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/unit subcontract
Current workforce = 20 employees
Hiring cost = $500 / employee
Layoff cost = $800 / employee
Safety stock = 20% of monthly forecast
Beginning inventory = 50 units
Inventory carrying cost = $10/unit/month
Stockout cost = $50/unit/month
Additional information available:
Sales Work Work Hours
Month Forecast Days 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. 500 100 500+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
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.

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
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.

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
Subcontract 6 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
They now want to evaluate a plan that calls for a steady rate of regular-time
output.
They intend to start with 0 inventory on hand in the first period.
Prepare an aggregate plan and determine its cost for a level output rate of
300 units per period with 15 workers.

Aggregate Planning
Total cost of plan is
$4,700
Inventory
Backorder
Costs
Production Schedule
Cumulative
Forecast &
Production
Cost
Components Notice 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.
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.

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?
$4,640
Aggregate Planning
Notice the backorder
cost in period 5

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.
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?
$4,860
Aggregate Planning
Notice the backorder
cost in period 5
Notice the
Hire/Layoff cost in
period 4

Pure Strategies
Hiring cost
Hiring cost = $100 per worker
= $100 per worker
Firing cost
Firing cost = $500 per worker
= $500 per worker
Regular production cost per pound = $2.00
Regular production cost per pound = $2.00
Inventory carrying cost
Inventory carrying cost = $0.50 pound per quarter
= $0.50 pound per quarter
Production per employee
Production per employee = 1,000 pounds per quarter
= 1,000 pounds per quarter
Beginning work force
Beginning work force = 100 workers
= 100 workers
QUARTER
QUARTER SALES FORECAST (LB)
SALES FORECAST (LB)
Spring
Spring 80,000
80,000
Summer
Summer 50,000
50,000
Fall
Fall 120,000
120,000
Winter
Winter 150,000
150,000
Example:
Example:
Level Production Strategy
Level production
= 100,000 pounds
(80,000 + 50,000 + 120,000 + 150,000)
4
Spring
Spring 80,000
80,000 100,000
100,000 20,000
20,000
Summer
Summer 50,000
50,000 100,000
100,000 70,000
70,000
Fall
Fall 120,000
120,000 100,000
100,000 50,000
50,000
Winter
Winter 150,000
150,000 100,000
100,000 0
0
400,000
400,000 140,000
140,000
Cost of Level Production Strategy:
(400,000 X $2.00) + (140,00 X $.50) = $870,000
SALES
SALES PRODUCTION
PRODUCTION
QUARTER
QUARTER FORECAST
FORECAST PLAN
PLAN INVENTORY
INVENTORY

Chase Demand Strategy
Spring
Spring 80,000
80,000 80,000
80,000 80
80 0
0 20
20
Summer
Summer 50,000
50,000 50,000
50,000 50
50 0
0 30
30
Fall
Fall 120,000
120,000 120,000
120,000 120
120 70
70 0
0
Winter
Winter 150,000
150,000 150,000
150,000 150
150 30
30 0
0
100
100 50
50
SALES
SALES PRODUCTION
PRODUCTION WORKERS
WORKERS WORKERS
WORKERS WORKERS
WORKERS
QUARTER
QUARTER FORECAST
FORECAST PLAN
PLAN NEEDED
NEEDED HIRED
HIRED FIRED
FIRED
Cost of Chase Demand Strategy
(400,000 X $2.00) + (100 x $100) + (50 x $500) = $835,000
Previous Spring Summer Fall Winter
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)

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)

Mathematical Model
u Data:
– Starting inventory in January: 1,000 units
– Selling price to the retailer: Rs.40/ unit
– Workforce at the beginning of January: 80
– # of working days per month: 20
– Regular work per day per employee: 8 hours
– Maximum overtime allowed per employee per month: 10 hours
– Ending inventory required (at end of June): Minimum 500 units
– Demand forecast:
Month January February March April May June
Demand 1,600 3,000 3,200 3,800 2,200 2,200

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 cost Rs.6/hour
Cost of subcontracting Rs.30/unit
(cont…)
u Cost Data:
Numerical Example
(Define Decision Variables)
• The decision variables are as follow s:
– W t = W orkforce size for m onth t
– Ht = Num ber of em ployees hired at the beginning of m onth t
– Lt = Num ber of em ployees laid off at the beginning of m onth t
– Pt = Production in m onth t
– I t = I nventory at the end of m onth t
– St = Num ber of units stocked out at the end of m onth t
– Ct = Num ber of units subcontracted for m onth t
– Ot = Num ber of overtim e hours w orked in m onth t
( com bined for all em ployees)
Note: For all the above variables, t = 1 , 2 , …, 6 giving a total of
4 8 decision variables.

Numerical Example
(Components of Objective Function)
• Regular tim e labor cost
Rs. 4 / hour * 8 hr/ day * 2 0 day/ m onth = Rs.6 4 0 / m onth
Therefore, regular tim e labor cost per m onth:
• Overtim e labor cost
Overtim e labor cost is Rs.6 / hour and Ot represents the num ber of overtim e
hours w orked in m onth t ( com bined for all em ployees)
Therefore, overtim e tim e labor cost per m onth:
• Cost of hiring and layoff
This cost is calculated as:
• Cost of holding inventory and stocking out
This cost is calculated as:
• Cost of m aterials and subcontracting out
This cost is calculated as: 1 5
å
=
6
1
t
W
640
t
å
=
6
1
t
O
6
t
å
å =
=
+
6
1
t
6
1
t L
500
H
300
t
t
å
å =
=
+
6
1
t
6
1
t S
5
I
2
t
t
å
å =
=
+
6
1
t
6
1
t C
30
P
10
t
t
Numerical Example
(Objective Function)
å
å
å
å
å
å
å
å
=
=
=
=
=
=
=
=
+
+
+
+
+
+
+
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
30
10
5
2
500
300
6
640
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
t
C
P
S
I
L
H
O
W
u The objective function is:
Minimize Z =

Numerical Example
(Define Constraints Linking Variables)
• W orkforce size, hiring and layoff constraints:
or
w here t = 1 , 2 , …, 6 and W 0 = 8 0
• Capacity constraints:
or
w here t = 1 , 2 , …, 6
0
L
H
W
W t
t
1
t
t =
+
+
- -
t
t
1
t
t L
H
W
W -
+
= -
t
t
t O
)
4
/
1
(
W
40
P +
£
0
P
O
)
4
/
1
(
W
40 t
t
t ³
-
+
• I nventory balance constraints:
or
w here t = 1 , 2 , …, 6 and I 0 = 1 ,00 0 , I 6 > = 5 0 0 , and S0 = 0 ,
• Overtim e lim it constraints:
or
w here t = 1 , 2 , …, 6
t
t
1
t
t
t
t
1
-
t S
I
S
D
C
P
I -
+
+
=
+
+ -
0
S
I
S
D
C
P
I t
t
1
t
t
t
t
1
-
t =
+
-
-
-
+
+ -
t
t W
10
O £
0
W
10
O t
t £
-
Numerical Example
(Define Constraints Linking Variables) (cont…)

Average Inventory and
Average Flow Time
• Average inventory for a period t:
• Average inventory over the planning horizon:
i.e.
• Average flow tim e: ( Average inventory) / ( Throughput)
)
I
(I
2
1
t
1
t +
-
å
=
- +
T
t
T 1
t
1
t )
I
(I
2
1
1
ú
û
ù
ê
ë
é
+
+ å
-
=
-
1
1
t
t
1
t I
)
I
(I
2
1
1 T
t
T
å
å
=
-
=
- ú
û
ù
ê
ë
é
+
+
T
t
T
t
T
T
1
t
1
1
t
t
1
t
D
1
I
)
I
(I
2
1
1
Various Scenarios
• Som e of the possible scenarios are:
– I ncrease in holding cost ( from Rs.2 to Rs.6 )
– Overtim e cost drops to Rs.5 per hour
– I ncreased dem and fluctuation
• Your plan w ill change w ith the change in scenarios
Month January February March April May June
Demand 1,000 3,000 3,800 4,800 2,000 1,400

Transportation Tableau for
Aggregate Planning
• Suppose w e have the follow ing inform ation
– Beginning I nventory: I 0
– Regular tim e production cost per unit: r
– Overtim e production cost per unit: v
– Subcontract production cost per unit: s
– Holding cost per unit per period: h
– Backorder cost per unit per period: b
– Shortage ( unsatisfied order) cost per unit per period: c
– Undertim e cost per unit: u
– Desired inventory level at the end of period 3 : I e
– Total unused capacities: U
– Total unsatisfied orders: C
Periods
1 2 3
Dem and D1 D2 D3
Regular Capacity R1 R2 R3
Overtim e Capacity O1 O2 O3
Subcontract Capacity S1 S2 S3
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
I0
R1
O1
S1
R2
O2
S2
R3
O3
S3
u
u
u
u
u
u
u
u
u
u
Demand D1 D2 D3 + le U Grand Total
1
2
3

LINEAR PROGRAMMING
(backorders, supply > demand)
Beg. Inventory
Demand for
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
I0
R1
O1
S1
R2
O2
S2
R3
O3
S3
u
u
u
u
u
u
u
u
u
u
Demand D1 D2 D3 + le U Grand Total
1
2
3
Beg. Inventory
Demand for
Total
Capacity
(supply)
Supply from
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
Regular
Overtime
Subcontract
I0
R1
O1
S1
R2
O2
S2
R3
O3
S3
C
Demand D1 D2 D3 + le Grand 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

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
200 200 200 200 200 200 200 200 200 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

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
Total 7000 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

Because different products require different materials, skills, etc. we must manufacture
at the item level rather than the group level. The master schedule (item level) is
similar to the aggregate plan (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)

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

If the lot size for this item is 70 units, we can now build the Master Production
Schedule. We add our first lot in week/day 3 because this is the first negative
inventory position. We then update our Projected Inventory Position.
Forecast 30 30 30 30 40 40 40 40
ProjectedOnHandInventory 64 31 1 41 11 -29 -69 -109 -149
MasterProductionSchedule(MPS) 70
We add our next lot in week/day 5 because this is the next negative inventory position.
We then update our Projected Inventory Position.
Forecast 30 30 30 30 40 40 40 40
ProjectedOnHandInventory 64 31 1 41 11 41 1 -39 -79
MasterProductionSchedule(MPS) 70 70

We then update our Projected Inventory Position.
Forecast 30 30 30 30 40 40 40 40
ProjectedOnHandInventory 64 31 1 41 11 41 1 31 -9
MasterProductionSchedule(MPS) 70 70 70
We then update our Projected Inventory Position, and have completed the second
output of the master scheduling process, the Master Production Schedule.
Forecast 30 30 30 30 40 40 40 40
ProjectedOnHandInventory 64 31 1 41 11 41 1 31 61
MasterProductionSchedule(MPS) 70 70 70 70

We are now ready to compute our final output of the master scheduling process, the
Available to 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!
Forecast 30 30 30 30 40 40 40 40
AvailableToPromise(ATP)
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
Forecast 30 30 30 30 40 40 40 40
AvailableToPromise(ATP) 11

Week 3 ATP = MPS for week/day 3 - sum of committed
inventory (customer orders)until the next master
scheduled lot
= 70 - (10 + 4) = 56
Forecast 30 30 30 30 40 40 40 40
AvailableToPromise(ATP) 11 56
scheduled lot
= 70 - 2 = 68
Forecast 30 30 30 30 40 40 40 40
AvailableToPromise(ATP) 11 56 68

scheduled lot
= 70 - 0 = 70
Forecast 30 30 30 30 40 40 40 40
AvailableToPromise(ATP) 11 56 68 70
scheduled lot
= 70 - 0 = 70
Forecast 30 30 30 30 40 40 40 40
AvailableToPromise(ATP) 11 56 68 70 70

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. Time fences are 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 Full
Firm Open

Items
Product lines
or families
Individual
products
Components
Manufacturing
operations
Resource level
Plants
Individual
machines
Critical work
centers
Production Planning Capacity 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

Aggregate Production Planning (APP)

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