Aggregate Planning
Chapter 11
Aggregate Planning
• Aggregate planning
– Intermediate-range capacity planning that typically covers
a time horizon of 2 to 18 months.
– Useful for organizations that experience seasonal, or other
variations in demand.
– “Big-picture” approach. Groups together similar products
(services) and deals with them as though they were a
single products (service).
– Goal:
• Achieve a production plan that will effectively utilize
the organization’s resources to satisfy overall demand
The Planning Sequence
Long-term planning
Intermediateterm planning
Short-term detailed
planning
Aggregate Planning
• The main idea behind aggregate planning:
Aggregate planning translates business plans into rough
labor schedules and production plans
• Issues to consider for aggregate planning
– Production rate: “aggregate units” per worker per unit
time
– Workforce level: available workforce in terms of hours
– Actual production: Production rate x Workforce level
– Inventory: Units carried over from previous periods
– Costs: production, changing workforce, inventory
What does aggregate planning do?
• Given an aggregate demand forecast,
determine production levels, inventory levels,
and workforce levels, in order to minimize
total relevant costs over the planning horizon
Why do organizations need to do
aggregate planning?
• Planning
– It takes time to implement plans (e.g. hiring).
• Aggregation
– It is not possible to predict with accuracy the timing and volume
of demand for individual items.
• Planning is connected to the budgeting process which is
usually done annually on an aggregate (e.g., departmental)
level.
• It can help synchronize flow throughout the supply chain; it
affects costs, equipment utilization; employment levels;
and customer satisfaction
Aggregate Planning Strategies
• Proactive
– Alter demand to match supply (capacity)
– Among other approaches, we can alter demand by
simply changing the price.
• Reactive
– Alter supply (capacity) to match demand
– Through capacity planning and aggregate planning
• Mixed
– Some of each
Demand Options
• Pricing
– Used to shift demand from peak to off-peak periods.
• Airline: night/weekend
• Restaurants: happy hour/early bird
– Price elasticity is important
– Yield (Revenue) Management
• Maximizing revenue by using a variable pricing strategy. Prices are set relative to capacity
availability.
• Promotion
– Advertising and other forms of promotion
– Issue: response rate and response patterns. Less control over timing of demand
(may worsen the problem by bringing demand at the wrong time).
• Back orders (delaying order filling)
– Orders are taken in one period and deliveries promised for a later period
– Possible loss of sales, increased record keeping, lowered customer service level
• New demand
– Very uneven situation
– Offer different products/services during off-peak periods to make use of excess
capacity: fastfood stores offer breakfast.
Supply Options
•
•
•
•
•
Hire and layoff workers
– May have upper or lower limit
– Unions/internal policies may prohibit layoffs
– Skill levels, recruiting costs
– Associated costs (e.g., recruiting, training, severance-pay, morale)
Overtime
– Maintain skilled workforce; Seasonal peaks
– Unions/Overtime may result in lower productivity, poorer quality, more
accidents, increased payroll costs
Part-time workers
– Usually low-to-moderate job skills; Seasonal
– Independent-contractors
Inventories
– Produce in one period and sell in another
– Costs: holding and carrying cost, money tied up in inventory, insurance,
obsolescence, deterioration, spoilage, breakage etc.
SubcontractingNew Demand
– Less control over output. Quality problems.
– Higher costs
Aggregate Planning Supply Strategies
• Level capacity strategy:
– Maintaining a steady rate of regular-time output;
variations in demand are met by using inventories or other
options such as overtime, part-time workers,
subcontracting, and backorders
• Chase demand strategy:
– Matching capacity to demand; the planned output for a
period is set at the expected demand for that period.
MIS 373: Basic Operations Management
11
Level strategy
• Capacities are kept constant over the planning
horizon
– Advantages
• Stable output rates and workforce
– Disadvantages
• Greater inventory (or other) costs
MIS 373: Basic Operations Management
12
Chase strategy
• Capacities are adjusted to match demand
requirements over the planning horizon
– Advantages
• Investment in inventory is low
• Labor utilization in high
– Disadvantages
• The cost of adjusting output rates and/or workforce levels
MIS 373: Basic Operations Management
13
Uneven Demand and Two Strategies:
Demand = Supply
Demand < Supply
Demand > Supply
Supply (output) level
11-14
Choosing a Strategy
• Important factors:
– Company policy
• Constraints on the available options
– e.g., discourage layoffs, no subcontracting to protects secrets, union
policies regarding over time
– Flexibility
• Chase flexibility may not be present for companies designed for
high steady output (e.g., refineries, auto assembly)
– Cost
• Alternatives are evaluated in term of cost (while matching demand
within the constraints).
MIS 373: Basic Operations Management
15
Trial-and-Error Techniques
• Trial-and-error approaches consist of developing
simple table or graphs
that enable planners to visually compare projected
demand requirements with existing capacity
• Alternatives are compared based on their total costs
• Disadvantage:
– it does not necessarily result in an optimal aggregate plan
Example #1:
Chase demand
•
•
•
•
•
•
•
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
Firing Cost: $100/worker
Period
1
2
3
4
5
Demand
40
30
20
50
60
MIS 373: Basic Operations Management
17
Example #1: Chase demand
Time Periods
Beginning Inventory
0
Demand
1
2
3
4
5
Total
40
30
20
50
60
200
Production
End
Inventory
# Hired
# Fired
# Hired in the beginning of a period
# Fired in the
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
beginning of a period
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
18
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
# Hired
# Fired
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
19
Firing Cost: $100/worker
Recall the chase strategy:
Capacities are adjusted to match demand
requirements over the planning horizon
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
# Hired
0
# Fired
1
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
20
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
# Hired
0
0
# Fired
1
1
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
21
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
0
# Hired
0
0
0
# Fired
1
1
1
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
22
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
0
0
# Hired
0
0
0
3
# Fired
1
1
1
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
23
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
0
0
0
# Hired
0
0
0
3
1
# Fired
1
1
1
0
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
24
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
0
0
0
0
# Hired
0
0
0
3
1
4
# Fired
1
1
1
0
0
3
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
25
Firing Cost: $100/worker
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
0
0
0
0
# Hired
0
0
0
3
1
4
# Fired
1
1
1
0
0
3
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
26
Firing Cost: $100/worker
One defining characteristics of the chase strategy is
that we don’t have end inventory.
 All we produced are/were sold.
 No holding cost
Example #1: Chase demand
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
30
20
50
60
200
End
Inventory
0
0
0
0
0
0
# Hired
0
0
0
3
1
4
# Fired
1
1
1
0
0
3
TC=Production + Holding
= 200*10 +
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
+ Hiring + Firing
Production Rate: 10 units/worker/period
+ 4*200 + 3*100 = $3,100 Regular Production Costs: $10/unit
Inventory Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
27
Firing Cost: $100/worker
Exercise
• Perform aggregate planning using the chase strategy:
–
–
–
–
–
–
–
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Period
1
2
3
4
5
Demand
50
40
30
30
40
Solution
Beginning Inventory
10
Demand
1
2
3
4
5
Total
50
40
30
30
40
190
Production
End
Inventory
# Hired
# Fired
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
# Hired
# Fired
We only produce 40 units because
there are 10 units beginning inventory
that we can use.
So, we can still meet the demand of
50 units.
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
0
# Hired
0
# Fired
1
The beginning workforce is 5 workers.
Since we only produce 40 units in this period
and each worker can handle 10 units in a period,
we only need 4 works here.
 We hence fire 1 at the beginning of this period.
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
0
0
# Hired
0
0
# Fired
1
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
0
0
0
# Hired
0
0
0
# Fired
1
0
1
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
0
0
0
0
# Hired
0
0
0
0
# Fired
1
0
1
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
0
0
0
0
0
0
# Hired
0
0
0
0
1
1
# Fired
1
0
1
0
0
2
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
40
40
30
30
40
180
End
Inventory
0
0
0
0
0
0
# Hired
0
0
0
0
1
1
# Fired
1
0
1
0
0
2
TC=Production + Holding + Hiring + Firing
= 180*10 +
5*10
+ 1*100 + 2*200
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Example #2: Level Capacity
0
Demand
1
2
3
4
5
Total
40
30
20
50
60
200
Production
End
Inventory
# Hired
# Fired
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
37
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
# Hired
# Fired
Recall the level strategy:
Capacities are kept constant over the planning
horizon. So,
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Total demand=40+30+20+50+60=200
Inventory Holding Costs: $5/unit/period
Production per period=200/5=40
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
38
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
# Hired
0
# Fired
1
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
39
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
# Hired
0
# Fired
1
Fire 1 worker in this period because 4
workers are sufficient to produce 40
units in a period.
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
40
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
# Hired
0
0
# Fired
1
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
41
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
30
# Hired
0
0
0
# Fired
1
0
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
42
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
30
20
# Hired
0
0
0
0
# Fired
1
0
0
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
43
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
30
20
0
# Hired
0
0
0
0
0
# Fired
1
0
0
0
0
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
44
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
30
20
0
60
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
45
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
30
20
0
60
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
One defining characteristics of the level strategy is
that we don’t need to adjust capacity (here, labor
force), except for the initial period.
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
46
Firing Cost: $100/worker
Example #2: Level Capacity
0
1
2
3
4
5
Total
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
End
Inventory
0
10
30
20
0
60
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
TC=Production + Holding + Hiring + Firing
Beginning Inventory: 0 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
But, how to calculate the holding cost?
Regular Production Costs: $10/unit
Inventory Holding Costs: $5/unit/period
 Average inventory in a period
Hiring Cost: $200/worker
MIS 373: Basic Operations Management
47
Firing Cost: $100/worker
Example #2: Level Capacity
1
2
3
4
5
Total
Regular Production
Costs: $10/unit
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
Inventory Holding
Costs:
$5/unit/period
End
Inventory
0
10
30
20
0
60
Hiring Cost:
$200/worker
Firing Cost:
$100/worker
0
Average
Inventory
0
5
20
# Hired
# Fired
25
10
60
=(0+10)/2
=(10+30)/2
0
0
0
0
0
0
1
0
0
0
0
1
We can estimate the holding cost by considering the average
inventory in each period.
MIS 373: Basic Operations Management
48
Example #2: Level Capacity
1
2
3
4
5
Total
Regular Production
Costs: $10/unit
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
Inventory Holding
Costs:
$5/unit/period
End
Inventory
0
10
30
20
0
60
Hiring Cost:
$200/worker
Firing Cost:
$100/worker
0
Average
Inventory
0
5
20
# Hired
# Fired
25
10
60
=(0+10)/2
=(10+30)/2
0
0
0
0
0
0
1
0
0
0
0
1
TC=Production + Holding + Hiring + Firing
TC= 200*10 + 60*5 + 0*200 + 1*100 = $2,400
MIS 373: Basic Operations Management
49
Example #2: Level Capacity
1
2
3
4
5
Total
Regular Production
Costs: $10/unit
Demand
40
30
20
50
60
200
Production
40
40
40
40
40
200
Inventory Holding
Costs:
$5/unit/period
End
Inventory
0
10
30
20
0
60
Hiring Cost:
$200/worker
Firing Cost:
$100/worker
0
Average
Inventory
0
5
20
# Hired
# Fired
25
10
60
=(0+10)/2
=(10+30)/2
0
0
0
0
0
0
1
0
0
0
0
1
TC=Production + Holding + Hiring + Firing
TC= 200*10 + 60*5 + 0*200 + 1*100 = $2,400
MIS 373: Basic Operations Management
50
Exercise
• Perform aggregate planning using the level strategy:
•
•
•
•
•
•
•
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Period
1
2
3
4
5
Demand
50
40
30
30
40
Two additional assumptions:
1. Unmet demands in a period can be held and fulfilled in a future period.
2. There is no cost associated with unmet demands.
Solution
Beginning Inventory
10
Demand
1
2
3
4
5
Total
50
40
30
30
40
190
Production
End Inventory
Avg. Inventory
# Hired
# Fired
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
Avg. Inventory
# Hired
# Fired
Total demand=190
Total demand=190 – 10 = 180
Production per period=180/5=36
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
Avg. Inventory
3
# Hired
0
# Fired
1
By assumption #1, unmet demands in a period can
be held and fulfilled in a future period. So, we keep
track on the unmet demands, and try to fulfill them in
a future period.
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
Avg. Inventory
3
# Hired
0
# Fired
1
Avg. inventory = [10 + (-4)]/2 = 3
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
-8
Avg. Inventory
3
-6
# Hired
0
0
# Fired
1
0
-8 = (-4) + (-4)
Unmet demand from period #1 and from period #2
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
-8
-2
Avg. Inventory
3
-6
-5
# Hired
0
0
0
# Fired
1
0
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
-8
-2
4
Avg. Inventory
3
-6
-5
1
# Hired
0
0
0
0
# Fired
1
0
0
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
-8
-2
4
0
Avg. Inventory
3
-6
-5
1
2
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
Beginning Inventory
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
-4
-8
-2
4
0
Avg. Inventory
3
-6
-5
1
2
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
Negative Inventory has no meaning!
By assumption #2, there is no cost associated with
unmet demand (i.e., negative inventory has no
Beginning Inventory: 10 units
costs).
Beginning Workforce: 5 workers
TC=Production + Holding
+ Hiring + Firing
= 180*10 + 10*(3+1+2) + 0 + 1*200 = $2,030
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
Avg. Inventory
# Hired
# Fired
Another way to solve this problem.
 Pushing unmet demands to its next period
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40 44
30
30
40
190
Production
36
36
36
36
36
180
End Inventory
0
Avg. Inventory
5
# Hired
0
# Fired
1
Another way to solve this problem.
 Pushing unmet demands to its next period
 Instead of -4 end inventory, here we have 0.
 See that the demand for period #2 increase from 40 to
44.
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40 44
30 38
30
40
190
Production
36
36
36
36
36
180
End Inventory
0
0
Avg. Inventory
5
0
# Hired
0
0
# Fired
1
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40 44
30 38
30 32
40
190
Production
36
36
36
36
36
180
End Inventory
0
0
0
Avg. Inventory
5
0
0
# Hired
0
0
0
# Fired
1
0
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40 44
30 38
30 32
40
190
Production
36
36
36
36
36
180
End Inventory
0
0
0
4
Avg. Inventory
5
0
0
2
# Hired
0
0
0
0
# Fired
1
0
0
0
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40 44
30 38
30 32
40
190
Production
36
36
36
36
36
180
End Inventory
0
0
0
4
0
4
Avg. Inventory
5
0
0
2
2
9
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Solution
10
1
2
3
4
5
Total
Demand
50
40 44
30 38
30 32
40
190
Production
36
36
36
36
36
180
End Inventory
0
0
0
4
0
4
Avg. Inventory
5
0
0
2
2
9
# Hired
0
0
0
0
0
0
# Fired
1
0
0
0
0
1
TC=Production + Holding + Hiring + Firing
= 180*10 + 10*9 + 0 + 1*200 = $2,090
While the TC number is different, this approach seems
more intuitive than the previous approach, especially
on the parts about inventory.
Beginning Inventory: 10 units
Beginning Workforce: 5 workers
Production Rate: 10 units/worker/period
Regular Production Costs: $10/unit
Inventory Costs: $10/unit/period
Hiring Cost: $100/worker
Firing Cost: $200/worker
Aggregate Planning in Services
• The aggregate planning process is different for
services in the following ways:
– Most services cannot be inventoried
– Demand for services is difficult to predict
– Capacity is also difficult to predict
– Service capacity must be provided at the
appropriate place and time
– Labor is usually the most constraining resource for
services
MIS 373: Basic Operations Management
68
Aggregate Planning in Services
• Hospitals:
– allocate funds, staff, and supplies to meet the demands of
patients for their medical services
• Restaurants:
– smoothing the service rate, determining workforce size, and
managing demand to match a fixed capacity
– Perishable inventory
• Airlines:
– complex due to the large number of factors involved (planes,
flight & group personnel, multiple routes, airports etc.)
– Capacity decisions must also take into account the percentage
of seats to be allocated to various fare classes in order to
maximize profit or yield (Revenue Management)
MIS 373: Basic Operations Management
69