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Managing Capacity
Chapter 6 & 6S
Chapter Objec5ves
Be able to: § Explain what capacity is, how firms measure capacity, and the
difference between theore5cal and rated capacity. § Describe the pros and cons associated with three different
capacity strategies: lead, lag, and match. § Apply a wide variety of analy5cal tools to capacity decisions,
including expected value and break-‐even analysis, decision trees, learning curves, the Theory of Constraints, wai5ng line theory, and LiMle’s Law.
Capacity Decisions § Defining and measuring capacity § Strategic versus tactical capacity § Evaluating capacity alternatives § 6S. Supplement for Chapter 6:
Advanced perspectives § Learning curves § Theory of Constraints § Waiting lines
Defini5ons
§ Capacity – The capability of a worker, a machine, a workcenter, a plant, or an organiza5on to produce output in a 5me period.
§ Capacity decisions – § How is it measured? § Which factors affect capacity? § The impact of the supply chain on the organiza;on’s effec;ve capacity.
© 2010 APICS Dic;onary
Measures of Capacity
§ Theore5cal capacity – The maximum output capability, allowing for no adjustments for preven5ve maintenance, unplanned down5me, or the like.
§ Rated capacity – The long-‐term, expected output capability of a resource or system.
© 2010 APICS Dic;onary
Examples of Capacity
Table 6.1
Indifference Point Examples
Capacity for a PC Assembly Plant
(800 units per line per shiX)×(# of lines)×(# of shiXs)
Controllable Factors Uncontrollable Factors
1 or 2 shiXs? 2 or 3 lines? Employee
training?
Supplier problems? 98% or 100% good? Late or on 5me?
Supply Chain Considerations Capacity of the others chain members?
Strategic versus Tactical Capacity
§ Strategic [Long-term] Capacity: § One or more years out § “Bricks & Mortar” § Future technologies
§ Adjustable [Tactical] Capacity § One year or sooner § Workforce level, inventory, etc.
§ Operation Planning & Control § Detailed Scheduling
C ap
ac ity
Time
Strategic Capacity Planning • “Bricks & mortar” decisions • High-level planning • High risk
Tactical Planning • Workforce, inventory, subcontracting decisions • Intermediate-level planning • Moderate risk
Planning & Control • Limited ability to adjust capacity • Detailed planning • Lowest risk
Days or weeks out Months out Years out
Capacity versus Time
Three Common Capacity Strategies
§ Lead capacity strategy – A capacity strategy in which capacity is added in an5cipa5on of demand.
§ Lag capacity strategy – A capacity strategy in which capacity is added only aXer demand has materialized.
§ Match capacity strategy – A capacity strategy that strikes a balance between the lead and lag capacity strategies by avoiding period of high under or overu5liza5on.
Comparing Strategies
Figure 6.1
Question?
How can capacity change, even when we do not hire new people
or put in new equipment?
How?
§ Make or Buy (e.g., subcontracting) § One extreme: “Virtual” Business
Walden Paddlers (Marketing)
Hardigg Industries (Manufacturing)
General Composites (Design)
Independent Dealers (Direct Sales)
Evalua5ng Capacity Alterna5ves
§ Cost Comparison § Expected Value § Decision Trees § Break-‐Even Analysis § Learning Curves
Cost Comparison
§ Fixed costs – The expenses an organiza5on incurs regardless of the level of business ac5vity.
§ Variable costs – Expenses directly 5ed to the level of business ac5vity.
Cost Comparison
TC = FC + VC * X
TC = Total Cost FC = Fixed Cost
VC = Variable cost per unit of business ac5vity X = amount of business ac5vity
Cost Comparison -‐ Example 6.1
Figure 6.2
Table 6.2
X=11 X=64
Cost Comparison -‐ Example 6.1
Total cost of common carrier op;on = Total cost of contract carrier op;on
$0 + $750X = $5,000 + $300X
X = 11.11 or 11 shipments
Total cost of contract carrier op;on = Total cost of leasing
$5,000 + $300X = $21,000 + $50X
X = 64 shipments
Find the indifference point – the output level at which the two alterna5ves generate equal costs.
Economies of Scale
Total Cost for Fictional Line: Fixed cost + (Variable unit cost)×(X) = $200,000 + $4X Cost per unit for:
X=1? X=10,000? $204,000/unit VS. $24/unit
Expected Value
§ Expected value – A calcula5on that summarizes the expected costs, revenues, or profits of a capacity alterna5ve, based on several demand levels with different probabili5es.
Expected Value – Example 6.2
Expected Value – Example 6.2
C(low demand) = $5,000 + $300(30) = $14,000 C(medium demand) = $5,000 + $300(50) = $20,000 C(high demand) = $5,000 + $300(80) = $29,000
EVContract = (14,000 * 25%) + ($20,000 * 60%) + ($29,000 * 15%)
= $19,850 EVCommon = (22,500 * 25%) + ($37,500 * 60%) + ($60,000 * 15%)
= $37,125 EVLease = (22,500 * 25%) + ($23,500 * 60%) + ($25,000 * 15%)
= $23,475
Expected Value Analysis
States of Nature
Capacity Alternatives
Low Demand
Medium Demand
High Demand
EV
Pr. .25 .60 .15
Common $22,500 $37,500 $60,000 $37,125
Contract $14,000 $20,000 $29,000 $19,850
Private $22,500 $23,500 $25,000 $23,475
Decision Trees
§ Decision tree – A visual tool that decision makers use to evaluate capacity decisions to enable users to see the interrela5onships between decisions and possible outcomes.
Decision Tree Rules
§ Draw the tree from leX to right star5ng with a decision point or an outcome point and develop branches from there.
§ Represent decision points with squares. § Represent outcome points with circles. § For expected value problems, calculate the financial results for each of the smaller branches and move backward by calcula5ng weighted averages for the branches based on their probabili5es.
Decision Trees – Example 6.3
Original Expected Value Example
Figure 6.4
Break-‐Even Analysis
§ Break-‐even point – The volume level for a business at which total revenues cover total costs.
Where: BEP = break-‐even point FC = fixed costs VC = variable cost per unit of business ac;vity R = revenue per unit of business ac;vity
Break-‐Even Analysis – Example 6.4
Suppose the firm makes $1,000 profit on each shipment before transporta;on costs are considered. What is the
break-‐even point for each shipping op;on?
Contrac;ng: BEP = $5,000 / $700 = 7.1 or 8 shipments
Common: BEP = $0 / $250 = 0 shipments
Leasing: BEP = $21,000 / $950 = 22.1 or 23 shipments
Advanced Perspectives
• Learning curves • Theory of Constraints • Waiting lines
Learning Curves
§ Recognize that people (and often equipment) become more productive over time due to learning.
§ First observed in aircraft production during World War II
§ Getting more emphasis as companies outsource more activities
Learning Curves
§ Learning curve theory – A theory that suggests that produc5vity levels can improve at a predictable rate as people and even systems “learn” to do tasks more efficiently.
For every doubling of cumula5ve output, there is a set percentage reduc5on in the amount
of inputs required.
A Formal Definition For every doubling of cumulative output, there will be a set percentage improvement in time per unit or some other measure of input
1 2 4 8 16 Output
Time per unit
10 hrs. 8 hrs.
6.4 hrs. 5.12 hrs.
4.096 hrs.
80% learning curve - Where does the name come from?
Learning Curves
Learning Curve – Example 6.5
What is the learning percentage?
4/5 = 80% or .80
Learning Curve – Example 6.5
How long will it take to answer the 25th call?
Figure 6.6
Key Points
§ Quick improvements early on, followed by more and more gradual improvements
§ The lower the percentage, the steeper the learning curve
§ Practically speaking, there is a floor § Estimates of effective capacity must
consider learning effects!
Other Capacity Considera5ons
§ The strategic importance of an ac5vity to a firm.
§ The desired degree of managerial control. § The need for flexibility.
The Theory of Constraints § Theory of Constraints – An approach to visualizing and
managing capacity which recognizes that nearly all products and services are created through a series of linked processes, and in every case, there is at least one process step [boMleneck or constraint] that limits throughput for the en5re chain of processes. Subordinate all produc5on and capacity decisions to the constraint.
Figure 6.7
The Theory of Constraints
§ Iden;fy the constraint § Exploit the constraint
§ Keep it busy! § Subordinate everything to the constraint
§ Make suppor;ng it the overall priority § Elevate the constraint
§ Try to increase its capacity — more hours, screen out defec;ve parts from previous step.
§ Find the new constraint and repeat § As one step is removed as a constraint, a new one will emerge.
Theory of Constraints – Example 6.6
Where is the BoMleneck? Cut and Style
Table 6.5
Theory of Constraints – Example 6.6
Current Process Figure 6.9
Theory of Constraints – Example 6.6
Adding a Second Stylist Figure 6.10
Theory of Constraints – Example 6.6
Adding One Shampooer and Two Stylists
Figure 6.11
Wai5ng Line Theory
§ Wai5ng Line Theory – A theory that helps managers evaluate the rela5onship between capacity decisions and important performance issues such as wai5ng 5mes and line lengths.
Figure 6.12
Wai5ng Line Theory
§ Wai5ng Line Concerns: § What percentage of the ;me will the server be busy? § On average, how long will a customer have to wait in line? How long will the customer be in the system?
§ On average, how may customers will be in line? § How will those averages be affected by the arrival rate of customers and the service rate of the workers?
Waiting at Outback Steakhouse...
Waiting to get food...
Waiting to pay bill ...
Leaving restaurant
Waiting outside or in bar
Key Points
§ Waiting time DECREASES value- added experience
§ On the other hand, adding serving capacity INCREASES costs
§ Businesses must have a way to analyze the impact of capacity decisions in environments where waiting occurs
Waiting and Customer Satisfaction
Cost of waiting
Cost of service
C O
S T
Waiting time
Lost customers
Cost of Waiting = f(Satisfaction)
Factors Affecting Satisfaction
1. Firm-related factors
2. Customer-related factors
Firm-Related Factors § “Unfair” versus “fair” waits
§ Uncomfortable versus comfortable waits
§ Initial versus subsequent waits
§ Capacity decisions
Waiting Line (Queuing) Theory
§ Applied statistics to allow us to perform a detailed analysis of system
§ Utilization levels, line lengths, etc.
§ Terminology and assumptions
Terminology and Assumptions I
? Service
System
Line Phase
Alterna5ve Wai5ng Lines
§ Single-‐Channel, Single-‐Phase § Ticket window at theater
§ Mul5ple-‐Channel, Single-‐Phase § Tellers at the bank, windows at post office
§ Single-‐Channel, Mul5ple-‐Phase § Line at the Laundromat, DMV
Single-‐Channel, Single-‐Phase
Figure 6S.1
Mul5ple-‐Channel, Single-‐Phase
Figure 6S.2
Single-‐Channel, Mul5ple-‐Phase
Figure 6S.3
Terminology and Assumptions II
§ Population: Infinite or Finite § Arrival rates: Random or constant rate
§ Random rates typically defined by Poisson distribution for infinite population
§ Service Rates: Random or constant § Random service rates typically described by
exponential distribution
§ Dispatching rules (aka “Queue Discipline”) § Permissible queue length
Comparisons
LiMle’s Law
LiMle’s Law is a law that holds for any system that has reached a steady state that enables us to understand the rela5onship between inventory, arrival 5me, and throughput 5me.
I = RT
LiMle’s Law -‐ Example 6.11
Figure 6.14
LiMle’s Law -‐ Example 6.11 Average Throughput Time =
T = I/R = (25 orders) / (100 orders per day) = .25 days in order processing
Average ;me an order spends in workcenter A =
T = I/R = (14 orders)/(70 orders per day) = .2 days in workcenter A
Amount of ;me the average A order spends in the plant =
Order processing ;me + workcenter A ;me = .25 days + .2 days = .45 days
Amount of ;me the average B order spends in the plant =
Order processing ;me + workcenter B ;me = .25 days + .05 days = .30 days
LiMle’s Law -‐ Example 6.11
Average ;me an order spends in the plant = 70% x .45 days + 30% *.30 days
= .405 days
Es;mate average throughout ;me for the en;re system = T = I/R = (40.5 orders)/(100 orders per day)
= .405 days for the average order
