Capacity Planning Investment in Facilities and Equipment

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Capacity Planning Investment in Facilities and
Equipment

• Average utilization
• defined as average output rate / capacity
• may become unfavorable if capacity planning is
  done poorly
• too much capacity gt poor cost performance
• too little capacity gt poor service quality
• Absolute capacity is normally stated in terms of
  maximums
• outputs processed (product focused firms)
• inputs consumed (process focused firms)

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What is the capacity of this facility?

• Assume this chart represents the hourly output
  capacity of a 6 machine assembly line.
• Assume this chart represents the hourly input
  consumption of a 6 machine jobshop.

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Capacity Strategy

• A long-term capacity strategy tries to address
  when and by how much the company should alter
  capacity.
• Important variables in the decision include
• predicted growth of demand
• variability of demand
• cost of expanding
• direction of technological evolution
• response of competitors, suppliers and customers

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Major Dimensions of Capacity Strategy

• Sizing of capacity cushions
• Firms that hold large cushions have
• limited ability to satisfy demand with inventory
• limited ability to manage demand
• requirement for excellent customer service
• low resource flexibility
• capacity purchased cheaply in big chunks
• Firms that hold small cushions
• must hold down costs to remain competitive
• unused capacity is costly
• unused capacity hides inefficiency
• Timing and Sizing Expansion

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Capacity Strategy

• Expansionist Strategy
• Looking to capture strong economies of scale
• Positive learning

Planned Capacity
Capacity
Expected Demand
Time
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Capacity Strategy

• Build-to-Forecast Strategy
• Trying to match capacity and demand

Planned Capacity
Capacity
Expected Demand
Time
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Capacity Strategy

• The Maximize Utilization Strategy
• Maintains little or no capacity cushion

Expected Demand
Capacity
Planned Capacity
Time
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Systems approach to capacity planning

• Audit and evaluate existing facilities
• Estimate future capacity requirements
• Identify capacity discrepancies
• Develop alternatives
• Evaluate alternatives
• Implement
• Audit results

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Short Term Capacity Planning Problem (only mfg
would consider lowest demand level optimistic)
Processing time in hours / unit
Setup time in hours / setup
Batch size in units / batch
1696 0.2(4000)5.6(4000/25)
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Processing and setup time for each part
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67
PT
38
66
83
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We may be able to reduce our capacity
requirements by building larger batches
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Bigger batches more productivity
Given a 20 capacity cushion, a batch of product
E takes more than a week to produce!
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Inventory Requirements
Rough Approximation if hourly demand .57
units and a batch takes 15.6 hours to produce,
we need 8.91 units in finished goods inventory to
cover demand over leadtime.
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What if setup time were not fixed?
Two machines required!
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What happens to flowtime?
100
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Without setups, are batches necessary?
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Any flowtime improvements?
How much work-in-process inventory is needed?
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Investment in finished goods?
Have we found the perfect system?
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Factors in a Location Decision

• Customer proximity
• Competitors location
• Geographic factors
• Environmental suitability
• Business climate
• Communication systems
• Transportation network
• Personal desires

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A decision-making framework for locating a single
facility

• Decision is made to locate a new facility rather
  than expand on site
• Identify location and proximity factors
• Narrow geographic search (point on a plane tools)
• Search for potential new locations
• Evaluate feasibility of locations
• Evaluate costs (network tools)
• Site selection

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Point on a Plane Measuring Distances
C
The load-distance method is useful when the most
important location factors are related to distance
A
B
Squared Euclidean 6400.00 12800.00 6400.00
Euclidean 80.00 113.14 80.00
Rectilinear 80.00 160.00 80.00
A to B A to C B to C
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Center of Gravity Approach
If we were to locate a facility so that it was
proximate to a number of preexisting locations -
we may first search for the location that
minimizes the total distance traveled from the
new (unidentified) location to the existing sites.
(100,100)
(10,30)
(30,10)
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Center of Gravity Example
Management would like to locate a grain
distribution facility to serve several dairy
farms. An important objective is to minimize the
distance to each farm to encourage use. Given
only this criterion, where would be the optimal
location for the grain facility?
Farm A B C D E F G Total
X 10 7 60 25 55 40 65 262
Y 70 35 75 4 40 30 7 261
X 262/737.43
Y 261/737.29
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Center of Gravity (cont.)
Deliveries (load) 3 6 2 12 8 2 10 43
Farm A B C D E F G Total
X 10 7 60 25 55 40 65 262
Y 70 35 75 4 40 30 7 261
X(load) 30 42 120 300 440 80 650 1662
Y(load) 210 210 150 48 320 60 70 1068
X 1662/43 38.65 Y 1068/43 24.84
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Calling Population
Service system
Queue
Server
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Poisson Distribution

• Number of events that occur in an interval of
  time
• Example Number of customers that arrive in 15
  min.
• Mean ? (e.g., 5/hr.)
• Probability

? 0.5
? 6.0
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Negative Exponential Distribution

• Service time and time between arrivals
• Example Service time is 20 min.
• Mean service rate ?
• e.g., customers/hr.
• Mean service time 1/?
• Equation

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Simple (M/M/1) Model Equations
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Simple (M/M/1) Model Equations cont.
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Example of an M/M/1 System
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Model B (M/M/S) Equations
Probability of zero people or units in the system
Average number of people or units in the system
Average time a unit spends in the system
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Model B (M/M/S) Equations
Average number of people or units waiting for
service
Average time a person or unit spends in the queue
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Tools for capacity planning Queuing Analysis
Big Jims Sandwich Shop has been experiencing
rapid growth in demand. Jim feels that his
ability to serve customers is largely a function
of seating. Currently, Jim has seating for 30.
Current average demand 30 per hour In 6
months average demand forecast 50 per hour In
12 months average demand forecast 57 per hour
It takes each customer an average of 1/2 hour
to complete service. What are Jims assumptions
if he is willing to model his shop as an M/M/30?
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System Performance Summary for Big Jim current
demand 1 System M/M/30 From Formula 2 Customer
arrival rate (lambda) per hour 30.0000 3 Service
rate per server (mu) per hour 2.0000 4 Overall
system effective arrival rate per hour
30.0000 5 Overall system effective service rate
per hour 30.0000 6 Overall system utilization
50.0000 7 Average number of customers in the
system (L) 15.0004 8 Average number of customers
in the queue (Lq) 0.0004 9 Average number of
customers in the queue for a busy system (Lb)
1.0000 10 Average time customer spends in the
system (W) 0.5000 hours 11 Average time customer
spends in the queue (Wq) 0.0000 hours 12 Average
time customer spends in the queue for a busy
system (Wb) 0.0333 hours 13 The probability that
all servers are idle (Po) 0.0000 14 The
probability an arriving customer waits (Pw or Pb)
0.0442
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System Performance Summary for Big Jim 6 month
forecast demand 1 System M/M/30 From
Formula 2 Customer arrival rate (lambda) per hour
50.0000 3 Service rate per server (mu) per hour
2.0000 4 Overall system effective arrival rate
per hour 50.0000 5 Overall system effective
service rate per hour 50.0000 6 Overall system
utilization 83.3333 7 Average number of
customers in the system (L) 26.2495 8 Average
number of customers in the queue (Lq)
1.2495 9 Average number of customers in the
queue for a busy system (Lb) 5.0000 10 Average
time customer spends in the system (W) 0.5250
hours 11 Average time customer spends in the
queue (Wq) 0.0250 hours 12 Average time customer
spends in the queue for a busy system (Wb)
0.1000 hours 13 The probability that all
servers are idle (Po) 0.0000 14 The
probability an arriving customer waits (Pw or Pb)
24.9893
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System Performance Summary for Big Jim 12 month
forecast demand 1 System M/M/30 From
Formula 2 Customer arrival rate (lambda) per hour
57.0000 3 Service rate per server (mu) per hour
2.0000 4 Overall system effective arrival rate
per hour 57.0000 5 Overall system effective
service rate per hour 57.0000 6 Overall system
utilization 95.0000 7 Average number of
customers in the system (L) 41.8861 8 Average
number of customers in the queue (Lq)
13.3861 9 Average number of customers in the
queue for a busy system (Lb) 19.0000 10 Average
time customer spends in the system (W) 0.7348
hours 11 Average time customer spends in the
queue (Wq) 0.2348 hours 12 Average time customer
spends in the queue for a busy system (Wb)
0.3333 hours 13 The probability that all
servers are idle (Po) 0.0000 14 The
probability an arriving customer waits (Pw or Pb)
70.4530
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Capacity Utilization at Big Jimswithout
capacity improvements
1.0
0.9
Capacity Cushion
0.8
Utilization
0.7
Utilization
0.6
30
35
40
45
50
55
60
Average Hourly Demand
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Customers Waiting at Big Jimswithout capacity
improvements
50
40
M/M/30
30
Customers Waiting (Lq)
20
10
30
35
40
45
50
55
60
Average Hourly Demand
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Capacity Utilization at Big Jimswithout waiting
65
60
Lost sales
Demand
55
50
45
Customers Served
40
Customers
35
30
25
20
30
35
40
45
50
55
60
Average Hourly Demand
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Capacity Utilization at Big Jimswithout waiting

• By estimating lost sales per hour one can begin
  to access the dollar impact of poor customer
  service.

Sales lost per hour
Average Hourly Demand
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Capacity Utilization at Big Jims30 and 40 seat
facility
1.0
M/M/30
0.9
0.8
0.7
Additional Capacity Cushion
0.6
M/M/40
Utilization
0.5
0.4
0.3
0.2
0.1
30
35
40
45
50
55
60
Average Hourly Demand
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Customers Waiting at Big Jims30 and 40 seat
facility
50
40
M/M/30
30
Customers Waiting (Lq)
M/M/40
20
10
30
35
40
45
50
55
60
Average Hourly Demand
50
Capacity Utilization at Big Jims30 40 seat
facility, and faster service
1.0
0.9
M/M/30 (30)
M/M/30 (25)
0.8
0.7
M/M/40 (30)
0.6
Utilization
0.5
0.4
0.3
0.2
0.1
30
35
40
45
50
55
60
Average Hourly Demand
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Customers Waiting at Big Jims30 40 seat
facility, and faster service
1.0
M/M/30 (25)
0.8
0.6
Customers Waiting (Lq)
0.4
0.2
M/M/40 (30)
30
35
40
45
50
55
60
Average Hourly Demand
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Lost Sales at Big Jims (no waiting)with current
and faster service times

• The tradeoff between system cost and poor-
  service cost may come into clearer focus.

Sales Lost Per Hour
Average Hourly Demand