2Chapter 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, learning curves, the Theory of Constraints, waiting line theory, and Little’s Law.
6Indifference Point Examples Capacity for a PC Assembly Plant(800 units per line per shift)×(# of lines)×(# of shifts)Controllable FactorsUncontrollable Factors1 or 2 shifts?2 or 3 lines? Employee training?Supplier problems?98% or 100% good?Late or on time?
7Three Common Capacity Strategies Lead capacity strategy – A capacity strategy in which capacity is added in anticipation of demand.Lag capacity strategy – A capacity strategy in which capacity is added only after 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 overutilization.
10Cost ComparisonFixed costs – The expenses an organization incurs regardless of the level of business activity.Variable costs – Expenses directly tied to the level of business activity.
11Cost Comparison TC = FC + VC * X TC = Total Cost FC = Fixed Cost VC = Variable cost per unit of business activityX = amount of business activity
12Cost Comparison - Example 6.1 Table 6.2Figure 6.2
13Cost Comparison - Example 6.1 Total cost of common carrier option = Total cost of contract carrier option$0 + $750X = $5,000 + $300XX = or 11 shipmentsFind the indifference point – the output level at which the two alternatives generate equal costs.Total cost of contract carrier option = Total cost of leasing$5,000 + $300X = $21,000 + $50XX = 64 shipments
14Expected ValueExpected value – A calculation that summarizes the expected costs, revenues, or profits of a capacity alternative, based on several demand levels with different probabilities.
17Decision TreesDecision tree – A visual tool that decision makers use to evaluate capacity decisions to enable users to see the interrelationships between decisions and possible outcomes.
18Decision Tree RulesDraw the tree from left to right starting 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 calculating weighted averages for the branches based on their probabilities.
19Decision Trees – Example 6.3 Original Expected Value ExampleFigure 6.4
20Break-Even AnalysisBreak-even point – The volume level for a business at which total revenues cover total costs.Where:BEP = break-even pointFC = fixed costsVC = variable cost per unit of business activityR = revenue per unit of business activity
21Break-Even Analysis – Example 6.4 Suppose the firm makes $1,000 profit on each shipment before transportation costs are considered. What is the break-even point for each shipping option?Contracting: BEP = $5,000 / $700 = 7.1 or 8 shipmentsCommon: BEP = $0 / $250 = 0 shipmentsLeasing: BEP = $21,000 / $950 = 22.1 or 23 shipments
22Learning CurvesLearning curve theory – A theory that suggests that productivity levels can improve at a predictable rate as people and even systems “learn” to do tasks more efficiently.For every doubling of cumulative output, thereis a set percentage reduction in the amountof inputs required.
24Learning Curve – Example 6.5 What is the learning percentage?4/5 = 80% or .80
25Learning Curve – Example 6.5 How long will it take to answer the 25th call?Figure 6.6
26Other Capacity Considerations The strategic importance of an activity to a firm.The desired degree of managerial control.The need for flexibility.
27The 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 that limits throughput for the entire chain.Figure 6.7
28The Theory of Constraints 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.
29Theory of Constraints – Example 6.6 Table 6.5Where is the Bottleneck? Cut and Style
30Theory of Constraints – Example 6.6 Current ProcessFigure 6.9
31Theory of Constraints – Example 6.6 Adding a Second StylistFigure 6.10
32Theory of Constraints – Example 6.6 Adding One Shampooerand Two StylistsFigure 6.11
33Waiting Line TheoryWaiting Line Theory – A theory that helps managers evaluate the relationship between capacity decisions and important performance issues such as waiting times and line lengths.Figure 6.12
34Waiting Line Theory Waiting Line Concerns: What percentage of the time 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?
35Waiting Lines – Example 6.7 The probability of arrivals in a time period =Example: Customers arrive at a drive-up window at a rate of 3 per minute. If the number of arrivals follows a Poisson distribution, what is the probability that two or fewer customers would arrive in a minute?P(< 2) = P(0) + P(1) + P(2) = = .423 or 42.3%
36Waiting Lines – Example 6.7 The average utilization of the system:Example: Suppose that customers arrive at a rate of four per minute and that the worker at the window is able to handle on average 5 customers per minute. The average utilization of the system is:
37Waiting Lines – Example 6.8 The average number of customers waiting in the system (CW) =The average number of customers in the system (CS) =Example: Given an arrival rate of four customers per minute and a service rate of five customers per minute:Average number of customers waiting:Average number in the system:
38Waiting Lines – Example 6.9 The average time spent waiting (TW) =The average time spent in the system (TS) =Example: Given an arrival rate of four customers per minute and a service rate of five customers per minute:Average time spent waiting:Average time spent in the system:
39Little’s LawLittle’s Law is a law that holds for any system that has reached a steady state that enables us to understand the relationship between inventory, arrival time, and throughput time.I = RT
41Little’s Law - Example 6.11 Average Throughput Time = T = I/R = (25 orders) / (100 orders per day)= .25 days in order processingAverage time an order spends in workcenter A =T = I/R = (14 orders)/(70 orders per day)= .2 days in workcenter AAmount of time the average A order spends in the plant =Order processing time + workcenter A time= .25 days + .2 days = .45 daysAmount of time the average B order spends in the plant =Order processing time + workcenter B time= .25 days days = .30 days
42Little’s Law - Example 6.11Average time an order spends in the plant =70% x .45 days + 30% *.30 days= .405 daysEstimate average throughout time for the entire system =T = I/R = (40.5 orders)/(100 orders per day)= .405 days for the average order
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