2 Chapter Objectives Be able to: Explain what capacity is, how firms measure capacity, and the difference between theoretical and rated capacity,Describe the pros and cons associated with three different capacity strategies: lead, lag, and match.Apply a wide variety of analytical tools to capacity decisions, including expected value and break-even analysis, decision trees, waiting line theory, and learning curves.
3 Capacity Decisions Defining and measuring capacity Strategic versus tactical capacityEvaluating capacity alternativesAdvanced perspectivesTheory of ConstraintsWaiting linesLearning curves
4 Defining and Measuring Capacity Measure of an organization’s ability to provide goods or servicesJiffy Lube Oil changes per hour Law firm Billable hours College Student hours per semester
5 Consider: Capacity for a PC Assembly Plant: Controllable Factors (800 units/shift/line)×(% Good)×(# of lines)×(# of Shifts)Controllable Factors1 or 2 shifts? 2 or 3 lines? Employee training?Uncontrollable FactorsSupplier problems? 98% or 100% good? Late or on time?
6 Strategic versus Tactical Capacity One or more years out“Bricks & Mortar”Future technologiesTactical:One year or soonerWorkforce level, schedules, inventory, etc.
7 Capacity versus Time Capacity Time Days or weeks out Months out Planning & ControlLimited abilityto adjustcapacityDetailed planningLowest riskTactical PlanningWorkforce, inventory,subcontracting decisionsIntermediate-levelplanningModerate riskStrategic Capacity Planning“Bricks &mortar” decisionsHigh-level planningHigh riskCapacityTimeDays or weeks outMonths outYears out
8 Capacity Strategies: When, How Much, and How? DemandLeaderExcessCapacityLost BusinessLaggard
9 How? Make or Buy (e.g., subcontracting) One extreme: “Virtual” BusinessWalden Paddlers(Marketing)Hardigg Industries(Manufacturing)Independent Dealers(Direct Sales)General Composites(Design)
10 Evaluating Capacity Alternatives Economies of scale (EOS)Expected value analysis (EVA)Decision TreesBreak-even points (BEP)
11 Economies of ScaleTotal Cost for Fictional Line: Fixed cost + (Variable unit cost)×(X) = $200,000 + $4X Cost per unit for X=1? X=10,000?X = 1: $200,004X= 10,000: $24
12 Fixed & Unit Cost Scenarios Page 214 in text.Common Carrier: Fixed cost = 0, unit cost = $750Contract Carrier: Fixed cost = $5,000, unit cost = $300Private Carrier: Fixed cost = $21,000, unit cost = $50
13 Indifference PointCompares capacity alternatives — at what volume level do they cost the same?Suppose one option has zero fixed cost and $750 per unit cost; the other option has $5,000 fixed cost, but only $300 per unit cost $0 + $750X = $5,000 + $300X What is the volume, X, at the indifference point?X = or about 11
14 Expected Value Analysis Forecasted demand or volume is uncertain, allows consideration of the variability in the data
15 Capacity cost structure Data RequirementsCapacity cost structure(alternatives?)Expected demand(multiple scenarios?)EVAProduct and servicerequirements(e.g. time standards)
16 Expected Value Analysis Pennington Cabinet Company jobs per year (20% likelihood) 5000 jobs per year (50%) jobs per year (30%)Each job = $1,200 revenue
17 We Know:Average job requires: hours of machine time /3 hours of assembly team timeMachines and teams work 2000 hours per yearEach machine and team has yearly fixed cost = $200K3 different capacity scenarios (see next slide!)
18 Number of Machines and Teams Number of Hours Available Each Year Effective CapacityNumber of Machines and TeamsNumber of Hours Available Each YearMaximum Jobs per YearMachinesTeamsCurrent356,00010,0003,000Expanded918,0005,0005,400New Site71214,00024,0007,0007,200Effective capacity is limited by machine capacityWhat is the effective capacityof each capacity alternative?
19 Alternate Demand Scenarios Current LevelExpandedNew SiteDemandRevenueFixedExpenses2,000$2,400,000$1,600,000$2,800,000$3,800,0005,000$3,600,000$6,000,0007,000$8,400,000What is the expected contribution if demand = 5000AND we decide to move to a new site?Why does revenue for current capacity max out at $3.6 million?$2,200,000Cannot handle a demand greater than 3,000
20 Net Revenue Table Demand Current Expanded New Site 3,000 $800,000 ($400,000)($1,400,000)5,000$2,000,000$3,200,000$2,200,0007,000$4,600,000
21 Expected Value of Each Capacity Alternative: Current capacity level (20%) × $800K +(50%) × $2000K +(30%) × $2000K = $1,760,000
22 Expected Value of Each Capacity Alternative: Expanded capacity level (20%) × – $400K + (50%) × $3200K + (30%) × $3200K = $2,480,000
23 Expected Value of Each Capacity Alternative: New Site capacity level (20%) × – $1400K + (50%) × $2200K + (30%) × $4600K = $2,200,000
24 Conclusions for Pennington Which alternative would you choose if you wanted to minimize the worst possible outcome (Maximin)? Maximize the best possible outcome (Maximax)?Why is it important to know effective capacity? How could this help future capacity decisions?Maximin: Current site at $800,000Maximax: New site at $4,600,000
25 Visual tool for evaluating choices using expected value analysis Decision TreesVisual tool for evaluating choices using expected value analysisAllows use of different outcomes and different probabilities of success for each
26 Decision Tree Requirements Decision points represented byChoose the best input — the highest EVA, lowest cost, least risk, etc.Outcome points represented bySummation of all inputs (outcomes) weighted by their respective probabilities. No choice can be made at these pointsTrees drawn from final decision to the outcomes affecting that decision, then on to lower level decisions that might affect the those outcomes, then the lower level outcomes affecting those lower level decisions, and so on
27 Ellison Seafood Example Here the probabilities affecting the demand level are the same for the three options considered.But the decision tree does allow them to be different, can you think of situations where this might be true?Refer students to the text, Example 8.3, Figures 8.4 and 8.5, for this discussionDifferent probabilities because of location differences, market size differences, product mix differences, technology differences, etc.
28 Decision Tree Criteria Book example illustrates selecting highest revenue option.Other option choices can be on basis of:Using total cost for outcomes (useful when selling price is not known)Using estimated risk for outcomesOutcomes reflecting a desired result (choose highest EVA) Can you think of an example?Outcomes reflecting undesirable results (choose lowest EVA) Can you think of an example?Desirable examples: Market share, potential market size, product volume times price, projected reliability, project completion time…Undesirable examples: yield loss, projected failure rate, holding costs, quality costs, time-to-market, etc.
29 Break-Even Point (BEP) Considers revenue and costs, at what volume level are they equal?Suppose each unit sells for $100, the fixed cost is $200,000 and the variable cost is $ BEP $100X = $200,000 + $4X What is the breakeven volume, X?BEP: X = 2,084
30 Self TestEBB Industries must decide whether to invest in a new machine which has a yearly fixed cost of $40,000 and a variable cost of $50 per unit.What is the break even point (BEP) if each unit sells for $200?What is the expected value, given the following demand probabilities: units (25%), 300 units (50%), 350 units (25%)BEP at ($200 - $50)X = $40,000, that is, X = = 267Net for 250 units = <$2,500>Net for 300 units = $5,000Net for 350 units = $12,500EMV = 0.25 x (-$2,500) x $5, x $12,500 = $5,000
31 Advanced Perspectives Theory of ConstraintsWaiting linesLearning curves
32 Theory of ConstraintsConcept that the throughput of a supply chain is limited (constrained) by the process step with the lowest capacity.Sounds logical, but what does this mean for managing the other process steps?
33 Theory of Constraints Pipeline analogy Which piece of the pipe is restricting the flow?Would making parts A or D bigger help?
34 Dealing with a Constraint Identify the constraintExploit the constraintKeep it busy!Subordinate everything to the constraintMake supporting it the overall priorityElevate the constraintTry to increase its capacity — more hours, screen out defective parts from previous step, …Find the new constraint and repeatAs one step is removed as a constraint, a new one will emerge. Which piece of the pipe on the previous slide would be the new constraint if Part C was increased in diameter?
35 Waiting Lines Waiting lines and services Waiting Line Theory Waiting and customer satisfactionFactors affecting satisfactionWaiting Line TheoryTerminology and assumptionsIllustrative example
36 Waiting at Outback Steakhouse... Waiting outside or in barWaiting to get food...LeavingrestaurantWaiting to pay bill ...
37 Key Points Waiting time DECREASES value-added experience On the other hand, adding serving capacity INCREASES costsBusinesses must have a way to analyze the impact of capacity decisions in environments where waiting occurs
38 Waiting and Customer Satisfaction Cost ofserviceCost ofwaitingLost customersCOSTWaiting time
43 Terminology and Assumptions II Single-ChannelSingle-PhaseMultiple-ChannelSingle-Phase
44 Terminology and Assumptions III Complex service environment ...Howwouldyoudescribethis?
45 Terminology and Assumptions IV Population: Infinite or FiniteArrival rates: Random or constant rateRandom rates typically defined by Poisson distribution for infinite populationService Rates: Random or constantRandom service rates typically described by exponential distributionPriority rules (aka “Queue Discipline”)Permissible queue length
46 Example A single drive-in window for Bank Arrival rate Service rate 15 per hour, on averageService rate20 per hour, on averageHow many channels? Phases?What kinds of questions might we have?
47 = arrival rate = 15 cars per hour Drive-In Bank = arrival rate = 15 cars per hour = service rate = 20 cars per hourAverage utilization of the system: = = 0.75
48 Drive-In Bank Probability of n arrivals during period T is: e.g., probability of only 4 arrivals during a 45-minute period is:Note: Discuss with students about need to keep time references to the same period. Here, since l is in cars per hour,45 minutes must be converted to 0.75 hours.
49 Drive-In BankAverage number of cars in the system: (waiting plus being served)
51 Drive-In BankAverage time spent in the system: (waiting plus being served)(How do we know the answer is in hours?)
52 Drive-In Bank Average time spent in the line: (How do we know the answer is in hours?)
53 Suppose l is now 19 cars per hour Question? What happens as the arrival rate approaches the service rate?Suppose l is now 19 cars per hour
54 One Answer: Average number of cars waiting: Implications? What are we assuming here?
55 Other Types of Systems (Discussed in the supplement to Chapter 8) Single-channel, single-phase with constant service timeExample: Automatic car washMultiple-channel, multiple-phase (hospital)Usually best handled using simulation analysis
56 Self Test ILook back at the drive-in window example. How can we have an average line length > 1 while the average number of cars being served is < 1?Similarly, what happens as the arrival rate approaches the service rate?Suppose the teller at the drive-in window is given training and can now handle 25 cars an hour (a 25% increase in service rate). What happens to the average length of the line?Length of the line for a service rate of 25 cars per hour is 225/[25(25-15)] =0.9 cars, a decrease from 2.25 cars
57 Self Test IILook back at the Outback Steakhouse example. What kind of queuing system is it?
58 Question?How can capacity change, even when we do not hire new people or put in new equipment?
59 Learning CurvesRecognize that people (and often equipment) become more productive over time due to learning.First observed in aircraft production during World War IIGetting more emphasis as companies outsource more activities
60 A Formal Definition 80% learning curve - For every doubling of cumulative output, there will bea set percentage improvement in time per unit or someother measure of inputOutputTimeperunit10 hrs.8 hrs.6.4 hrs.5.12 hrs.4.096 hrs.80% learning curve -Where does the name come from?
61 A Formal Definition (cont’d) Where: Tn = time for the nth unitT1 = time for the first unitb = ln(learning percent) / ln2Explain to students that ln represents the natural logarithm
62 Example Reservation clerk at Delta Airlines First call (while training) takes 8 minutesSecond call takes 6 minutesWhat is the learning rate?How long would you expect the 4th call to take? The 16th? The 32nd?Learning rate = 6min/8min = 75%Using Table 8.6 in textbook: Learning rate = 6/8 = 75%4th call is x 8 min = minutes16th call is x 8 min = minutes32nd call is x 8 min = min or 0.75 of 16th call time = x 0.75 = min
63 Key PointsQuick improvements early on, followed by more and more gradual improvementsThe lower the percentage, the steeper the learning curvePractically speaking, there is a floorEstimates of effective capacity must consider learning effects!
64 How could learning curves be used in long-term purchasing contracts? Another Question . . .How could learning curves be used in long-term purchasing contracts?
65 Johnston Controls IJohnston Controls won a contract to produce 2 prototype units for a new type of computer.First unit took 5,000 hrs. to produce and $250K of materialsSecond unit took 3,500 hrs. to produce and $200K of materialsLabor costs are $30/hour
66 Johnston Controls IIThe customer has asked Johnston Controls to prepare a bid for an additional 10 units.What are Johnston’s expected costs?
68 Johnston Controls IV“Additional 10 units” means the third through twelfth units.Total labor for units 3 through 12:= 5,000 hours × (5.501 – 1.7)= 19,005 hrs5.501 is sum of nb for 12 units1.7 is the sum of nb for the first two unitsRefer to Table 8.6 in textbook for 70% learning curve data
69 Johnston Controls VTotal material for units 3 through 12: = $250,000 × (7.227 – 1.8) = $1,356,750Refer to Table 8.6 in textbook for 80% learning curve data
70 Johnston Controls VITotal cost for “additional 10 units”: = $30 × (19,005 hours) + $1,356, = $1,926,900What if there is a significant delay before the second contract?
71 Self-TestAssume that there WILL BE a significant delay before Johnston Controls makes the next 10 units. Assuming that Johnston has to “start over” with regard to learning, estimate total cost for these additional 10 units.Assume same learning curve percentages, but start anew.Hence, using sum of nb for first 10 units, hours will be 5,000 x = 24,660 and hours cost will be $30 x 24,660 = $739,800Materials cost will be $250,000 x = $1,578,750Total cost will $2,318,550 compared to cost of $1,926,200 if we order right away, a savings of $392,350!
72 Case Study in Managing Capacity Forster’s Market