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**Managing Capacity Chapter 8**

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**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.

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**Capacity Decisions Defining and measuring capacity**

Strategic versus tactical capacity Evaluating capacity alternatives Advanced perspectives Theory of Constraints Waiting lines Learning curves

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**Defining and Measuring Capacity**

Measure of an organization’s ability to provide goods or services Jiffy Lube Oil changes per hour Law firm Billable hours College Student hours per semester

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**Consider: Capacity for a PC Assembly Plant: Controllable Factors**

(800 units/shift/line)×(% Good)×(# of lines)×(# of Shifts) Controllable Factors 1 or 2 shifts? 2 or 3 lines? Employee training? Uncontrollable Factors Supplier problems? 98% or 100% good? Late or on time?

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**Strategic versus Tactical Capacity**

One or more years out “Bricks & Mortar” Future technologies Tactical: One year or sooner Workforce level, schedules, inventory, etc.

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**Capacity versus Time Capacity Time Days or weeks out Months out**

Planning & Control Limited ability to adjust capacity Detailed planning Lowest risk Tactical Planning Workforce, inventory, subcontracting decisions Intermediate-level planning Moderate risk Strategic Capacity Planning “Bricks & mortar” decisions High-level planning High risk Capacity Time Days or weeks out Months out Years out

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**Capacity Strategies: When, How Much, and How?**

Demand Leader Excess Capacity Lost Business Laggard

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**How? Make or Buy (e.g., subcontracting)**

One extreme: “Virtual” Business Walden Paddlers (Marketing) Hardigg Industries (Manufacturing) Independent Dealers (Direct Sales) General Composites (Design)

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**Evaluating Capacity Alternatives**

Economies of scale (EOS) Expected value analysis (EVA) Decision Trees Break-even points (BEP)

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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? X = 1: $200,004 X= 10,000: $24

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**Fixed & Unit Cost Scenarios**

Page 214 in text. Common Carrier: Fixed cost = 0, unit cost = $750 Contract Carrier: Fixed cost = $5,000, unit cost = $300 Private Carrier: Fixed cost = $21,000, unit cost = $50

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Indifference Point Compares 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

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**Expected Value Analysis**

Forecasted demand or volume is uncertain, allows consideration of the variability in the data

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**Capacity cost structure**

Data Requirements Capacity cost structure (alternatives?) Expected demand (multiple scenarios?) EVA Product and service requirements (e.g. time standards)

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**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

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We Know: Average job requires: hours of machine time /3 hours of assembly team time Machines and teams work 2000 hours per year Each machine and team has yearly fixed cost = $200K 3 different capacity scenarios (see next slide!)

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**Number of Machines and Teams Number of Hours Available Each Year**

Effective Capacity Number of Machines and Teams Number of Hours Available Each Year Maximum Jobs per Year Machines Teams Current 3 5 6,000 10,000 3,000 Expanded 9 18,000 5,000 5,400 New Site 7 12 14,000 24,000 7,000 7,200 Effective capacity is limited by machine capacity What is the effective capacity of each capacity alternative?

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**Alternate Demand Scenarios**

Current Level Expanded New Site Demand Revenue Fixed Expenses 2,000 $2,400,000 $1,600,000 $2,800,000 $3,800,000 5,000 $3,600,000 $6,000,000 7,000 $8,400,000 What is the expected contribution if demand = 5000 AND we decide to move to a new site? Why does revenue for current capacity max out at $3.6 million? $2,200,000 Cannot handle a demand greater than 3,000

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**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 $2,200,000 7,000 $4,600,000

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**Expected Value of Each Capacity Alternative:**

Current capacity level (20%) × $800K +(50%) × $2000K +(30%) × $2000K = $1,760,000

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**Expected Value of Each Capacity Alternative:**

Expanded capacity level (20%) × – $400K + (50%) × $3200K + (30%) × $3200K = $2,480,000

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**Expected Value of Each Capacity Alternative:**

New Site capacity level (20%) × – $1400K + (50%) × $2200K + (30%) × $4600K = $2,200,000

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**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 $800,000 Maximax: New site at $4,600,000

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**Visual tool for evaluating choices using expected value analysis**

Decision Trees Visual tool for evaluating choices using expected value analysis Allows use of different outcomes and different probabilities of success for each

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**Decision Tree Requirements**

Decision points represented by Choose the best input — the highest EVA, lowest cost, least risk, etc. Outcome points represented by Summation of all inputs (outcomes) weighted by their respective probabilities. No choice can be made at these points Trees 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

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**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 discussion Different probabilities because of location differences, market size differences, product mix differences, technology differences, etc.

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**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 outcomes Outcomes 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.

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**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

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Self Test EBB 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 = = 267 Net for 250 units = <$2,500> Net for 300 units = $5,000 Net for 350 units = $12,500 EMV = 0.25 x (-$2,500) x $5, x $12,500 = $5,000

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**Advanced Perspectives**

Theory of Constraints Waiting lines Learning curves

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Theory of Constraints Concept 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?

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**Theory of Constraints Pipeline analogy**

Which piece of the pipe is restricting the flow? Would making parts A or D bigger help?

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**Dealing with a Constraint**

Identify the constraint Exploit the constraint Keep it busy! Subordinate everything to the constraint Make supporting it the overall priority Elevate the constraint Try to increase its capacity — more hours, screen out defective parts from previous step, … Find the new constraint and repeat As 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?

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**Waiting Lines Waiting lines and services Waiting Line Theory**

Waiting and customer satisfaction Factors affecting satisfaction Waiting Line Theory Terminology and assumptions Illustrative example

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**Waiting at Outback Steakhouse...**

Waiting outside or in bar Waiting to get food... Leaving restaurant Waiting to pay bill ...

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**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

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**Waiting and Customer Satisfaction**

Cost of service Cost of waiting Lost customers COST Waiting time

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**Cost of Waiting = f(Satisfaction)**

Factors Affecting Satisfaction Firm-related factors Customer-related factors

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**Firm-Related Factors “Unfair” versus “fair” waits**

Uncomfortable versus comfortable waits Initial versus subsequent waits Capacity decisions

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**Waiting Line (Queuing) Theory**

Application of statistics to allow us to perform a detailed analysis of system Utilization levels, line lengths, etc. Terminology and assumptions

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**Terminology and Assumptions I**

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**Terminology and Assumptions II**

Single-Channel Single-Phase Multiple-Channel Single-Phase

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**Terminology and Assumptions III**

Complex service environment ... How would you describe this?

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**Terminology and Assumptions IV**

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 Priority rules (aka “Queue Discipline”) Permissible queue length

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**Example A single drive-in window for Bank Arrival rate Service rate**

15 per hour, on average Service rate 20 per hour, on average How many channels? Phases? What kinds of questions might we have?

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** = arrival rate = 15 cars per hour **

Drive-In Bank = arrival rate = 15 cars per hour = service rate = 20 cars per hour Average utilization of the system: = = 0.75

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**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.

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Drive-In Bank Average number of cars in the system: (waiting plus being served)

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Drive-In Bank Average number of cars waiting:

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Drive-In Bank Average time spent in the system: (waiting plus being served) (How do we know the answer is in hours?)

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**Drive-In Bank Average time spent in the line:**

(How do we know the answer is in hours?)

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**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

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**One Answer: Average number of cars waiting:**

Implications? What are we assuming here?

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**Other Types of Systems (Discussed in the supplement to Chapter 8)**

Single-channel, single-phase with constant service time Example: Automatic car wash Multiple-channel, multiple-phase (hospital) Usually best handled using simulation analysis

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Self Test I Look 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

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Self Test II Look back at the Outback Steakhouse example. What kind of queuing system is it?

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Question? How can capacity change, even when we do not hire new people or put in new equipment?

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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

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**A Formal Definition 80% learning curve -**

For every doubling of cumulative output, there will be a set percentage improvement in time per unit or some other measure of input 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?

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**A Formal Definition (cont’d)**

Where: Tn = time for the nth unit T1 = time for the first unit b = ln(learning percent) / ln2 Explain to students that ln represents the natural logarithm

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**Example Reservation clerk at Delta Airlines**

First call (while training) takes 8 minutes Second call takes 6 minutes What 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 = minutes 16th call is x 8 min = minutes 32nd call is x 8 min = min or 0.75 of 16th call time = x 0.75 = min

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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!

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**How could learning curves be used in long-term purchasing contracts?**

Another Question . . . How could learning curves be used in long-term purchasing contracts?

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Johnston Controls I Johnston 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 materials Second unit took 3,500 hrs. to produce and $200K of materials Labor costs are $30/hour

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Johnston Controls II The customer has asked Johnston Controls to prepare a bid for an additional 10 units. What are Johnston’s expected costs?

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Johnston Controls III Labor learning rate: hours / 5000 hours = 70% Materials learning rate: $200K / $250K = 80%

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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 hrs 5.501 is sum of nb for 12 units 1.7 is the sum of nb for the first two units Refer to Table 8.6 in textbook for 70% learning curve data

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Johnston Controls V Total material for units 3 through 12: = $250,000 × (7.227 – 1.8) = $1,356,750 Refer to Table 8.6 in textbook for 80% learning curve data

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Johnston Controls VI Total cost for “additional 10 units”: = $30 × (19,005 hours) + $1,356, = $1,926,900 What if there is a significant delay before the second contract?

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Self-Test Assume 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 = $739,800 Materials cost will be $250,000 x = $1,578,750 Total cost will $2,318,550 compared to cost of $1,926,200 if we order right away, a savings of $392,350!

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**Case Study in Managing Capacity**

Forster’s Market

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PowerPoint Slides © Michael R. Ward, UTA 2014

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