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Managing Capacity Chapter 6

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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, learning curves, the Theory of Constraints, waiting line theory, and Little’s Law.

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Definitions Capacity – The capability of a worker, a machine, a workcenter, a plant, or an organization to produce output in a time period. Capacity decisions – How is it measured? Which factors affect capacity? The impact of the supply chain on the organization’s effective capacity. © 2010 APICS Dictionary

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Measures of Capacity Theoretical capacity – The maximum output capability, allowing for no adjustments for preventive maintenance, unplanned downtime, or the like. Rated capacity – The long-term, expected output capability of a resource or system. © 2010 APICS Dictionary

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Examples of Capacity Table 6.1

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**Indifference Point Examples**

Capacity for a PC Assembly Plant (800 units per line per shift)×(# of lines)×(# of shifts) Controllable Factors Uncontrollable Factors 1 or 2 shifts? 2 or 3 lines? Employee training? Supplier problems? 98% or 100% good? Late or on time?

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**Three 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.

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Comparing Strategies Figure 6.1

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**Evaluating Capacity Alternatives**

Cost Comparison Expected Value Decision Trees Break-Even Analysis Learning Curves

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Cost Comparison Fixed costs – The expenses an organization incurs regardless of the level of business activity. Variable costs – Expenses directly tied to the level of business activity.

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**Cost Comparison TC = FC + VC * X TC = Total Cost FC = Fixed Cost**

VC = Variable cost per unit of business activity X = amount of business activity

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**Cost Comparison - Example 6.1**

Table 6.2 Figure 6.2

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**Cost Comparison - Example 6.1**

Total cost of common carrier option = Total cost of contract carrier option $0 + $750X = $5,000 + $300X X = or 11 shipments Find 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 + $50X X = 64 shipments

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Expected Value Expected value – A calculation that summarizes the expected costs, revenues, or profits of a capacity alternative, based on several demand levels with different probabilities.

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**Expected Value – Example 6.2**

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**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

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Decision Trees Decision tree – A visual tool that decision makers use to evaluate capacity decisions to enable users to see the interrelationships between decisions and possible outcomes.

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Decision Tree Rules Draw 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.

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**Decision Trees – Example 6.3**

Original Expected Value Example Figure 6.4

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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 activity R = revenue per unit of business activity

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**Break-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 shipments Common: BEP = $0 / $250 = 0 shipments Leasing: BEP = $21,000 / $950 = 22.1 or 23 shipments

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Learning Curves Learning 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, there is a set percentage reduction in the amount of inputs required.

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Learning Curves

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**Learning Curve – Example 6.5**

What is the learning percentage? 4/5 = 80% or .80

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**Learning Curve – Example 6.5**

How long will it take to answer the 25th call? Figure 6.6

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**Other Capacity Considerations**

The strategic importance of an activity to a firm. The desired degree of managerial control. The need for flexibility.

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**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 that limits throughput for the entire chain. Figure 6.7

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**The Theory of Constraints**

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.

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**Theory of Constraints – Example 6.6**

Table 6.5 Where is the Bottleneck? Cut and Style

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**Theory of Constraints – Example 6.6**

Current Process Figure 6.9

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**Theory of Constraints – Example 6.6**

Adding a Second Stylist Figure 6.10

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**Theory of Constraints – Example 6.6**

Adding One Shampooer and Two Stylists Figure 6.11

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Waiting Line Theory Waiting 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

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**Waiting 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?

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**Waiting 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%

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**Waiting 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:

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**Waiting 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:

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**Waiting 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:

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Little’s Law Little’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

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Little’s Law - Example 6.11 Figure 6.14

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**Little’s Law - Example 6.11 Average Throughput Time =**

T = I/R = (25 orders) / (100 orders per day) = .25 days in order processing Average time an order spends in workcenter A = T = I/R = (14 orders)/(70 orders per day) = .2 days in workcenter A Amount of time the average A order spends in the plant = Order processing time + workcenter A time = .25 days + .2 days = .45 days Amount of time the average B order spends in the plant = Order processing time + workcenter B time = .25 days days = .30 days

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Little’s Law - Example 6.11 Average time an order spends in the plant = 70% x .45 days + 30% *.30 days = .405 days Estimate 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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**Managing Capacity Case Study**

Forster’s Market

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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.

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© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 S 7-1 Operations Management Capacity Planning Supplement 7.

© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 S 7-1 Operations Management Capacity Planning Supplement 7.

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