BA 380 Lecture Notes Packet 2008

Lecture Notes to Accompany

Operations Management, 10th EditionStevenson (McGraw-Hill 2009)

For

BA 380: Operations Management

Summer 2010

Prepared by: Rene Leo E. Ordonez, PhDProfessor and ChairSchool of BusinessSouthern Oregon UniversityAshland, Oregon

Prepared by: Rene Leo E. Ordonez, PhD School of Business, SOUNotes to Accompany Operations Management (Stevenson, 2009)

BA 380: Operations Management Lecture Notes Page 2

BA 380: OPERATIONS MANAGEMENT

GUIDELINES:

read the topics as outlined in the Lecture Notes view the accompanying digitized lectures attempt to work on (solve) the problems presented in the Lecture Notes replicate the computer-assisted solutions to the problems discussed in

the digitized lectures as well as those explained during the in-person sessions

formulate and bring questions about the readings/problems/concepts and digitized lectures to the in-person sessions, or post them on the Discussion Board (under Communication) in Blackboard

visit Blackboard at least three times a week check emails at least once a day post all questions related to the class on the Discussion Board in

Blackboard instead of emailing the question to the instructor. Questions, concerns, or comments that are student-specific may be sent via regular email.

organize study/help groups

Words to remember:Prioritize, not procrastinate. Spread out the work, not put things off until the last minute

Rene Leo E. Ordonez, PhDProfessor and Chair of Business(541) [email protected]

Prepared by Rene Leo E. Ordonez, PhD SOU School of BusinessNotes to Accompany Operations Management, 10th Edition (Stevenson, 2009)

mailto:[email protected]

Lecture Outlines and Digitized Lectures for BA 380: Operation Management

Rene Leo E. Ordonez, PhD School of Business

Southern Oregon UniversitySummer 2010 Edition

Note: The outlines listed below are based on the text Production Operations Management, 108h Edition, by William Stevenson, Irwin-McGraw-Hill. The problems in each section are also taken from the same text. This is a supplement material to the text.

Lecture NotesPage Number

Introduction 2

Productivity, Competitiveness, Strategy 7

Forecasting 9

Reliability 27

Cost Volume Analysis and Capacity Planning 40

Decision Theory 46

Learning Curves 52

Introduction to Quality Control 58

Quality Control 61

Inventory Management 74

Project Management 87

Waiting Lines 96




Introduction

What is Productions and Operations Management?

A field of study involving the planning, coordinating, and executing of all activities that create goods or provide services

Focus: To explore a variety of decision making tools that operations managers can use in the decision making process. These tools are classified as

o Quantitative Queuing techniques Inventory Models Project models (PERT/CPM) Forecasting techniques Statistical models Breakeven analysis

o Analysis of trade-offs In inventory management we balance tradeoff between two

objectives – minimize cost of carrying inventory and maximize customer service level

The models in discussed will reflect tradeoffs between cost and benefit

o System approach Emphasizes interrelationships among subsystems

Main theme: the whole is greater than the sum of its individual parts

From a systems viewpoint, the output and objectives of the organization as a whole takes precedence over those of any on subsystem

o Establishing priorities Recognition of priorities means devoting more attention to

what is most important

Uses the Pareto phenomenon – a relatively few factors are most important – dealing with those will have a disproportionately large impact on the results achieved

80/20 rule



o Ethics Operations managers, like all managers have the

responsibility to make ethical decisions on: Worker safety, product safety, quality, the

environment, the community, hiring and firing workers, worker’s rights

Why study Operations Management (OM)?

Operations management activities at the core of all business organizations

35% or more of all jobs are in OM related areas (customer service, quality assurance, production planning and control, scheduling, job design, inventory management, etc.

Activities in all other areas of business organizations (finance, accounting, marketing, human resource, etc.) are interrelated with OM

POM is all about management – all managers need to possess the knowledge and skill in the content areas in OM – learn and understand the variety of decision making tools in the decision making process

A course that will prepare students in developing business plans (BA 499 –Business Planning is the capstone course for ALL business majors)



Three Basic Functions of Business Organizations

Finance, Production/operations, Marketing

The operations function involves the creation of inputs into outputs


MarketingProduction/Operations

Finance

Inputs Land Labor Capital Information

Transformation/conversion process

Outputs Goods and Services

ControlFeedback

Feedback

Feedback


Examples of Types of Operations

Type of Operation ExamplesGoods producing Farming, mining,

construction, manufacturing, power generation

Storage/transportation Warehousing, trucking, mail service, moving, taxis, buses, hotel, airlines

Exchange Retailing, wholesaling, banking, renting or leasing, library loans

Entertainment Films, radio and TV, plays, concerts, recording

Communication Newspapers, radio and TV newscast, telephone, satellite

Illustrations of the Transformation Process

Food Processing Inputs Processing Output

Raw vegetablesMetal sheetsWaterEnergyLaborBuildingEquipment

CleaningMaking cansCuttingCookingPackingLabeling

Canned vegetables

Hospital Inputs Processing Output

Doctors, nursesHospitalsMedical suppliesEquipmentLaboratories

ExaminationSurgeryMonitoringMedicationTherapy

Healthy patients



Examples of inputs, transformation, and outputs

Inputs Transformation Output

LandHuman Physical IntellectualRaw materials Energy Water Chemical Metals WoodEquipment Machines Computers Trucks ToolsFacilities Hospitals Factories Offices Retail storesOther Information Time

Processes Cutting, drilling Transporting Teaching Farming Mixing Packing Canning Consulting Copying, faxing

Goods Houses Autos Clothing Computers Machines TVs Food products Textbooks Magazines Shoes Electronic items

Services Health care Entertainment Car repair Delivery Gift wrapping Legal Banking Communication

Production Good versus Service Operations

Characteristics Goods Services

OutputCustomer contactUniformity of inputLabor contentUniformity of outputMeasurement of productivityOpportunity to correct quality problems before delivery to customer

TangibleLowHighLowHighEasyHigh

IntangibleHighLowHighLowDifficultLow



Productivity, Competitiveness and Strategy

Productivity – an index that measures outputs (goods or services) relative to the input

Some Examples of Different Types of Productivity Measures

Partial measures

Multifactor measures

Total Measures

Factors that Affect Productivity

Methods Capital Quality Technology Management



Strategy Has a long term impact on the nature and characteristics of the

organization Affects the ability of an organization to compete, or in the case of a

nonprofit organization, the ability to serve its intended purpose The nature of an organization’s strategy depends on its mission

Mission The basis of the organization – the reason for its existence

Mission statement Answers the question, “What business are we in?” Serves to guide formulation of strategies for the organization as well as the

decision making at all levels Without it an organization is likely to achieve its true potential because

there is little direction for formulating strategies

Strategies and Tactics Strategies are plans for achieving goals Strategies provide focus

Tactics are the methods and actions to accomplish strategies The “how to” part of the process

Strategy Formulation – the formulation of an effective strategy must take into account:

1) distinctive competencies of the organization – this can be accomplished by doing a SWOT (strengths, weaknesses, opportunities, and threats) analysis

price, quality, time, flexibility, service, location

2) scan the environment – the considering of events and trends that present either threat or opportunities

External factors:economic condition, political condition, legal environment, technology,

competition, markets

Internal factors:Human resources, facilities and equipment, financial resources, customers,

products and services, technology, suppliers



Forecasting

Why forecast?

Features Common to all Forecasts

Conditions in the past will continue in the future Rarely perfect Forecasts for groups tend to be more accurate than forecasts for

individuals Forecast accuracy declines as time horizon increases

Elements of a Good Forecast

Timely Accurate Reliable (should work consistently) Forecast expressed in meaningful units Communicated in writing Simple to understand and use

Steps in Forecasting Process

Determine purpose of the forecast Establish a time horizon Select forecasting technique Gather and analyze the appropriate data Prepare the forecast Monitor the forecast

Types of Forecasts

Qualitativeo Judgment and opiniono Sales forceo Consumer surveyso Delphi technique

Quantitativeo Regression and Correlation (associative)o Time series



Forecasts Based on Time Series Data

What is Time Series? Components (behavior) of Time Series data

o Trendo Cycleo Seasonalo Irregularo Random variations

Naïve Methods

Naïve Forecast – uses a single previous value of a time series as the basis of a forecast.

Techniques for Averaging

What is the purpose of averaging? Common Averaging Techniques

o Moving Averageso Exponential smoothing

Moving Average

Exponential Smoothing



Techniques for Trend

Linear Trend Equation

Curvilinear Trend Equation

Techniques for Seasonality

What is seasonality?

What are seasonal relatives or indexes?

How seasonal indexes are used:o Deseasonalizing datao Seasonalizing data

How indexes are computed (see Example 7 on page 109)



Accuracy and Control of Forecasts

Measures of Accuracyo Mean Absolute Deviation (MAD)o Mean Squared Error (MSE)o Mean Absolute Percentage Error (MAPE)

Forecast Control Measureo Tracking Signal

Mean Absolute Deviation (MAD)

Mean Squared Error (or Deviation) (MSE)

Mean Square Percentage Error (MAPE)

Tracking Signal



Problems:

2 – Plot, Linear, MA, exponential Smoothing5 – Applying a linear trend to forecast15 – Computing seasonal relatives17 – Using indexes to deseasonalize values26 – Using MAD, MSE to measure forecast accuracy



Problem 2 (118)

National Mixer Inc., sells can openers. Monthly sales for a seven-month period were as follows:

MonthSales

(000 units)Feb 19March 18April 15May 20June 18July 22August 20

(a) Plot the monthly data on a sheet of graph paper.

(b) Forecast September sales volume using each of the following:(1) A linear trend equation(2) A five-month moving average(3) Exponential smoothing with a smoothing constant equal to 0.20, assuming March

forecast of 19(000)(4) The Naïve Approach(5) A weighted average using 0.60 for August, 0.30 for July, and 0.10 for June

(c) Which method seems least appropriate? Why?

(d) What does use of the term sales rather than demand presume?



EXCEL SOLUTION

Plot of the monthly data

Click INSERT tab, click LINE option

Right Click on the time series data on the graph

Select Add Trendline





(1) Five-month moving average

(2) Exponential Smoothing with a smoothing constant of 0.20, assuming March forecast of 19(000)

Enter the smoothing factor in D1 Enter “19” in D5 as forecast for March Create the exponential smoothing formula in D6, then copy it onto D7 to D11



(3) The Naïve Approach

(4) A weighted average using 0.60 for August, 0.30 for July, and 0.10 for June



Problem 5 (118)

A cosmetics manufacturer’s marketing department has developed a linear trend equation that can be used to predict annual sales of its popular Hand & Foot Cream.

Ft =80 + 15 t

where: Ft = Annual sales (000 bottles) t0 = 1990

(a) Are the annual sales increasing or decreasing? By how much?

(b) Predict annual sales for the year 2010 using the equation



Problem 15 (120)

Obtain estimates of daily relatives for the number of customers at a restaurant for the evening meal, given the following data. (Hint: Use a seven-day moving average)

Day Number Served

Day Number Served

1 80 15 842 75 16 773 78 17 834 95 18 965 130 19 1356 136 20 1407 40 21 378 82 22 879 77 23 82

10 80 24 9811 94 25 10312 125 26 14413 135 27 14414 42 28 48



Excel Solution

Type a 7-day average formula in E6 ( =average(C3:c9) ) In F6, type the formula =C6/E6 Copy the formulas in E6 and F6 onto cells E7 to E27 Compute the average ratio for Day 1 (see formula in E12) Copy and paste the formula in E12 onto E13 to E18 to complete the indexes for Days 2

to 7



Problem 17 (121) – Using indexes to deseasonalize values

New car sales for a dealer in Cook County, Illinois, for the past year are shown in the following table, along with monthly (seasonal) relatives, which are supplied to the dealer by the regional distributor.

MonthUnits Sold Index Month

Units Sold Index

Jan 640 0.80 Jul 765 0.90Feb 648 0.80 Aug 805 1.15Mar 630 0.70 Sept 840 1.20April 761 0.94 Oct 828 1.20May 735 0.89 Nov 840 1.25Jun 850 1.00 Dec 800 1.25

(a) Plot the data. Does there seem to be a trend?

(b) Deseasonalize car sales

(c) Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs.



Excel Solution

(a) Plot of original data (seasonalized car sales)

(b) Deseasonalized Car Sales


Create formula in F6 (see circled formula), then copy onto F7 to F17


(c) Graph of seasonalized car sales versus deseasonalized car sales



Problem 22 (123) – Using MAD, MSE, and MAPE to measure forecast accuracy

Two different forecasting techniques (F1 and F2) were used to forecast demand for cases of bottled water. Actual demand and the two sets of forecasts are as follows:

Predicted DemandPeriod Demand F1 F21 68 66 662 75 68 683 70 72 704 74 71 725 69 72 746 72 70 767 80 71 788 78 74 80

(a) Compute MAD for each set of forecasts. Given your results, which forecast appears to be the most accurate? Explain.

(b) Compute MSE for each set of forecasts. Given your results, which forecast appears to be the most accurate? Explain.

(c) In practice, either MAD or MSE would be employed to compute forecast errors. What factors might lead you to choose one rather than the other?

(d) Compute MAPE for each data set. Which forecast appears to be more accurate?



Excel Solution


=SUM(J8:J15)/(COUNT(J8:J15)-1)=AVERAGE(G8:G15)

=ABS(c8-d8) =(c8-d8)^2 =ABS(c8-d8)/c8

=AVERAGE(M8:M15)


Reliability

What is reliability?

Measures the ability of a product, part, or system to perform its intended function under a prescribed set of conditions

Failure – situation in which the item does not perform as intended

Reliabilities always specified with respect to certain conditions a.k.a. normal operating conditions e.g. temp, humidity, maintenance

How can reliability be improved? By improving the following:

Design Production techniques Testing Using backups Preventive maintenance procedures Education System design

Quantifying Reliability: Using Probability as a Measure

(1) The probability that a product or system will function when activated – a point in time

(2) The probability that the product or system will function for a given length of time -- product life used for warranty determination



Product Reliability at a Point in Time

Considers the reliability of the components/parts of a product or system

Product Reliability over time

Focuses on the length of service of the product (mean time between failures)

Failure rate is a function of time and can follow an exponential distribution (see page 159)

Or, can follow the Normal Distribution

Reliability over Time -- Exponential Distribution


Time

f(T)

1 – e-T/MTBF

Reliability = e-T/MTBF


Values of e-T/MTBF

T/MTBF e-T/MTBF T/MTBF e-T/MTBF T/MTBF e-T/MTBF

0.10 0.9048 2.60 0.0743 5.10 0.00610.20 0.8187 2.70 0.0672 5.20 0.00550.30 0.7408 2.80 0.0608 5.30 0.00500.40 0.6703 2.90 0.0550 5.40 0.00450.50 0.6065 3.00 0.0498 5.50 0.00410.60 0.5488 3.10 0.0450 5.60 0.00370.70 0.4966 3.20 0.0408 5.70 0.00330.80 0.4493 3.30 0.0369 5.80 0.00300.90 0.4066 3.40 0.0334 5.90 0.00271.00 0.3679 3.50 0.0302 6.00 0.00251.10 0.3329 3.60 0.0273 6.10 0.00221.20 0.3012 3.70 0.0247 6.20 0.00201.30 0.2725 3.80 0.0224 6.30 0.00181.40 0.2466 3.90 0.0202 6.40 0.00171.50 0.2231 4.00 0.0183 6.50 0.00151.60 0.2019 4.10 0.0166 6.60 0.00141.70 0.1827 4.20 0.0150 6.70 0.00121.80 0.1653 4.30 0.0136 6.80 0.00111.90 0.1496 4.40 0.0123 6.90 0.00102.00 0.1353 4.50 0.0111 7.00 0.00092.10 0.1225 4.60 0.0101 7.10 0.00082.20 0.1108 4.70 0.0091 7.20 0.00072.30 0.1003 4.80 0.0082 7.30 0.00072.40 0.0907 4.90 0.0074 7.40 0.00062.50 0.0821 5.00 0.0067 7.50 0.0006



Reliability over Time -- Normal Distribution


Reliability = P(Z > z)


STANDARD NORMAL DISTRIBUTION

z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359

0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753

0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141

0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517

0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879

0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224

0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549

0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852

0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133

0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389

1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621

1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830

1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015

1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319

1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545

1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633

1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706

1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767

2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817

2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857

2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890

2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916

2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936

2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952

2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964

2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974

2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981

2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986

3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990



Availability

Measures the fraction of time a piece of equipment is expected to be operational

Availability ranges between 0 and 1

Problems:

1– system reliability2 – system reliability4 – reliability and cost7 – comparing reliabilities of 2 systems12 – product life – exponential distribution17 – product life – normal distribution18 – product life – normal distribution



Problem 1 (p180)

Consider the following system:

Determine the probability that the system will operate under each of these conditions:

(a) The system as shown

(b) Each component has a backup with a probability of 0.90 and a switch that is 100 percent reliable.

(c) Backups with 0.90 reliability and a switch that is 99 percent reliable


.90 .90


Problem 2 (180)

A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts each have a 0.96 probability of functioning, and two each have a probability of 0.99. What is the overall probability that the product will function properly?



Problem 4 (p180)

A product engineer has developed the following equation for the cost of a system component: C=(10P)2, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate for the system to operate. The engineer can spend $173 for the two components. To the nearest two decimal places, what is the largest component reliability that can be purchased?



Problem 7 (180)

A production line has three machines A, B, and C, with reliabilities of .99, .96, and .93, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the line's reliability. Plan 1 involves adding an identical backup line, and Plan 2 involves providing backup for each machine. In either case, three machines (A B, and C) would be used with reliabilities equal to the original three.

(a) Which plan will provide the higher reliability?

(b) Explain why the two alternatives are not the same.

(c) hat other factors might enter into the decision of which plan to adopt?



Problem 12 (181)

An electronic chess game has a useful life that is exponentially distributed with a mean of 30 months. Determine each of the following:

(a) The probability that any given unit will operate for at least:(1) 39 months(2) 48 months(3) 60 months

(b) The probability that any given unit will fail sooner than:(1) 33 months(2) 15 months(3) 6 months

(c) The length of service time after which the percentage of failed units will approximately equal:(1) 50 percent(2) 85 percent(3) 95 percent(4) 99 percent



Problem 17 (181)

A television manufacturer has determined that its 19-inch color TV picture tubes have a mean service life that can be modeled by a Normal distribution with a mean of six years and a standard deviation of one-half year.

(a) What probability can you assign to service lives of at least(1) Five years?(2) Six years?(3) Seven and one-half years?

(b) If the manufacturer offers service contracts of four years on these picture tubes, what percentage can be expected to fail from wear-out during the service period?



Problem 18 (182)Refer to problem 17 above. What service period would achieve an expected wear-out rate of:

(a) 2 percent?

(b) 5 percent?



STRATEGIC CAPACITY PLANNING FOR PRODUCTS AND SERVICES

Cost Volume Analysis (CVA)

What is it?

Focus: relationships between COST, REVENUE, and VOLUME of output Purpose: to estimate income of an organization under different operating

conditions Usefulness: as a tool for comparing capacity alternatives

What does CVA require?

CVA requires the identification of two kinds of costs - Fixed and Variable Fixed cost – cost that does not change when output level is changed

(within a relevant range) Variable cost – cost that changes when the output level changes Mixed – cost items that contain both fixed and variable

Breakeven Analysis

What is it?

A tool used to determine profit level (or for determining breakeven point) for certain output level

Important Equations

TR = R x Q

TC = FC + vcQ

P = TR – TC

P = R x Q - (FC + vcQ)

P = Q (R – VC) – FC

Q = (P + FC)/(R – VC)

QBEP = FC/(R – VC)


Where:TR – total revenueTC – total costvc – variable cost per unitQ – units produced and soldP – total profitR – revenue per unitFC – total fixed cost


Problem 3 (p 211)

A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have fixed costs of $9,200 per month and variable costs of $0.70 per unit produced. Each item is sold to retailers at a price that averages $0.90.

a. What volume per month is required in order to breakeven?

b. What profit would be realized on a monthly volume of 61,000 units? 87,000 units?

c. What volume is needed to provide a profit of $16,000 per month?

d. What volume is needed to provide a revenue of $23,000 per month?

e. Plot the total cost and total revenue lines.



Problem 4 (p 211)

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $40,000 for A and $30,000 for B; variable costs per unit would be $10 for A and $12 for B; and revenue per unit would be $15 for A and $16 for B. (Note: this is somewhat different from the problem found in the textbook).

a. Determine each alternative’s break-even point in units

b. At what volume of output would the two alternatives yield the same profits?

c. If the expected annual demand is 12,000 units, which alternative would yield the higher profits?



Excel Solution



Problem 8 (p 211)

A manager is trying to purchase a certain part or to have it produced internally. Internal production could use either of two processes. One would entail a variable cost of $17 per unit and an annual fixed cost of $200,000; the other would entail a variable cost of $14 per unit and an annual fixed cost of $240,000.

Three vendors are willing to provide the part. Vendor A has a price of $20 per unit for any volume up to 30,000 units. Vendor B has a price of $22 per unit for demand 1,000 units or less, and $18 per unit for larger quantities. Vendor C offers a price of $20 per unit for the first 1,000 units and $19 for additional units.

(d) If the manager anticipates an annual volume of 10,000 units, which alternative would be best from a cost standpoint? For 20,000 units, which alternative would be best?

(e) Determine the range of quantity for which each alternative is best. Are there any alternatives that are never best? Which?



Excel Solution

Errata: “B1” in the formulas above should be “B2”



Decision Theory

The Decision Process

Specify objectives and criteria for making decisions Develop alternatives Analyze and compare alternatives Select the best alternative Implement the chosen alternative Monitor the results to ensure that desired results are achieved

Causes of Poor Decisions

Mistakes in the decision process Bounded rationality Suboptimization

Decision Environments

Certainty Risk Uncertainty

Decision Theory – represents a general approach to decision making and suitable for a wide range of operations management decision (e.g. capacity planning, product and service design, equipment selection, and location planning)

Decision Theory is suitable for decisions characterized by:

1) a set of future conditions exists that will have a bearing on the result of the decision

2) a list of alternatives for the managers to choose from3) a known payoff for each alternative under each possible future condition

To use this approach (Decision Theory), the manager must:

1) identify the future conditions2) develop a list of possible alternatives3) determine/estimate the payoff associated with each alternative4) if possible, estimate the likelihood of each possible future condition5) evaluate alternatives according to some decision criterion



Evaluation of Alternatives Depends on the Degree of Certainty Associated with the Future Condition

1) Decision Making Under Certainty (known future conditions)2) Decision Making Under Uncertainty (no info on how likely future conditions

will be)a. Maximinb. Maximaxc. Laplaced. Minimax Regret

3) Decision Making Under Risk (the likelihood of each future outcome is known)

a. Expected Monetary Value criterion (EMV)b. Expected Value of Perfect Information (EVPI)

Decision Trees

Sensitivity Analysis

Problems:1 – DM under uncertainty2 – DM under risk, EVPI, decision tree3 – Sensitivity analysis4 – DM under risk, EVPI, and decision tree



Problem 1 (229)

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Which alternative should be selected if the decision criterion is:

(a) Maximax?(b) Maximin?(c) Laplace?(d) Minimax Regret?

Next Year’s Demand

Alternative Low High

Do Nothing $50 $60

Expand 20 80

Subcontract 40 70

(Profit in $thousands)



Problem 2 (229)

Refer to Problem 1. Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P(low) = .3 and P(high) = .7

(a) Determine the expected profit of each alternative. Which alternative is best? Why?

(b) Analyze the problem using a decision tree. Show the expected profit of each alternative on the tree.

(c) Compute the expected value of perfect information. How could the contractor use this knowledge?



Problem 3 (229)

Refer to Problems 1 and 2. Construct a graph that will enable you to perform sensitivity analysis on the problem. Over what range of P(high) would the alternative of doing nothing be best? Expand? Subcontract?



Problem 4 (229)

A firm that plans to expand its product line must decide whether to build a small or large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be $400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000. If the large facility is built and demand is high, the estimated net present value is $800,000. If demand turns out to be low, the net present value will be -$10,000.

The probability that demand will be high is estimated to be 0.60, and the probability of low demand is estimated to be 0.40

(a) Analyze using a tree diagram

(b) Compute the EVPI. How could this information be used?

(c) Determine over which each alternative would be best in terms of the value of (demand low)



Learning Curves

What is it?

An integral part in corporate strategy, such as decisions concerning pricing, capital investment, and operating costs based on experience curves

Individual learning – the improvement that results when people repeat a process and gain skill or efficiency from the experience

Usefulness: as a tool for estimating operating costs (particularly the labor component)

Manpower planning and scheduling Negotiated purchasing Pricing new products Budgeting, purchasing, and inventory planning Capacity planning

A graph displaying the relationship between unit production time and the cumulative number of units produced (or repetition)



Learning Curve Theory Assumptions:

(1) The amount of time required to complete a given task or unit of a product will be less each time the task is undertaken

(2) The unit time will decrease at a decreasing rate

(3) The reduction in time will follow a predictable pattern – that is, every doubling of repetitions results in a constant percentage decrease in time per repetition

Important: Learning curves are referred to in terms of the complements of their improvement rates. A 100% curve would mean NO improvement at all

Relevant Equations:

(a) For computing the unit time requirement for the nth unit

(b) For computing the cumulative time requirement for n units

Use the Multipliers on Table below



LEARNING CURVE COEFFICIENTS

70% 75% 80% 85% 90%

Unit Number

Unit Time

Total Time

Unit Time

Total Time

Unit Time

Total Time

Unit Time

Total Time

Unit Time

Total Time

1 1.000 1 1 1 1 1 1 1 1 1

2 0.700 1.700 0.750 1.750 0.800 1.800 0.850 1.850 0.900 1.900

3 0.568 2.268 0.634 2.384 0.702 2.502 0.773 2.623 0.846 2.746

4 0.490 2.758 0.563 2.946 0.640 3.142 0.723 3.345 0.810 3.556

5 0.437 3.195 0.513 3.459 0.596 3.738 0.686 4.031 0.783 4.339

6 0.398 3.593 0.475 3.934 0.562 4.299 0.657 4.688 0.762 5.101

7 0.367 3.960 0.446 4.380 0.534 4.834 0.634 5.322 0.744 5.845

8 0.343 4.303 0.422 4.802 0.512 5.346 0.614 5.936 0.729 6.574

9 0.323 4.626 0.402 5.204 0.493 5.839 0.597 6.533 0.716 7.290

10 0.306 4.932 0.385 5.589 0.477 6.315 0.583 7.116 0.705 7.994

11 0.291 5.223 0.370 5.958 0.462 6.777 0.570 7.686 0.695 8.689

12 0.278 5.501 0.357 6.315 0.449 7.227 0.558 8.244 0.685 9.374

13 0.267 5.769 0.345 6.660 0.438 7.665 0.548 8.792 0.677 10.052

14 0.257 6.026 0.334 6.994 0.428 8.092 0.539 9.331 0.670 10.721

15 0.248 6.274 0.325 7.319 0.418 8.511 0.530 9.861 0.663 11.384

16 0.240 6.514 0.316 7.635 0.410 8.920 0.522 10.383 0.656 12.040

17 0.233 6.747 0.309 7.944 0.402 9.322 0.515 10.898 0.650 12.690

18 0.226 6.973 0.301 8.245 0.394 9.716 0.508 11.405 0.644 13.334

19 0.220 7.192 0.295 8.540 0.388 10.104 0.501 11.907 0.639 13.974

20 0.214 7.407 0.288 8.828 0.381 10.485 0.495 12.402 0.634 14.608

21 0.209 7.615 0.283 9.111 0.375 10.860 0.490 12.892 0.630 15.237

22 0.204 7.819 0.277 9.388 0.370 11.230 0.484 13.376 0.625 15.862

23 0.199 8.018 0.272 9.660 0.364 11.594 0.479 13.856 0.621 16.483

24 0.195 8.213 0.267 9.928 0.359 11.954 0.475 14.331 0.617 17.100

25 0.191 8.404 0.263 10.191 0.355 12.309 0.470 14.801 0.613 17.713

26 0.187 8.591 0.259 10.449 0.350 12.659 0.466 15.267 0.609 18.323

27 0.183 8.774 0.255 10.704 0.346 13.005 0.462 15.728 0.606 18.929

28 0.180 8.954 0.251 10.955 0.342 13.347 0.458 16.186 0.603 19.531

29 0.177 9.131 0.247 11.202 0.338 13.685 0.454 16.640 0.599 20.131

30 0.174 9.305 0.244 11.446 0.335 14.020 0.450 17.091 0.596 20.727



Problem 1 (365)

An aircraft company has an order to refurbish the interiors of 18 jet aircraft. The work has a learning curve percentage of 80. On the basis of experience with similar jobs, the industrial engineering department estimates that the first plane will require about 300 hours to refurbish. Estimate the amount of time needed to complete:

(a) The fifth plane

(b) The first five planes

(c) All 18 planes



Problem 3 (365)

A small contractor intends to bid on a job installing 30 in-ground swimming pools. Because this will be a new line of work for the contractor, he believes there will be a learning effect for the job. After reviewing time records from a similar type of activity, the contractor is convinced that an 85 percent curve is appropriate. He estimates that the first pool will take his crew 8 days to install. How many days should the contractor budget for?

(a) The first 10 pools?

(b) The second 10 pools?

(c) The final 10 pools?



Problem 5 (366)

A manager wants to determine an appropriate learning percentage for a certain activity. Toward that end, times have been recorded for completion of each of the first six repetitions. They are:

RepetitionTime

(minutes)1 462 393 354 335 326 30



Introduction to Quality

What is QUALITY?

Broadly defined -- quality refers to the ability of a product or service to consistently meet or exceed customer expectation

The Dimensions of Quality

1) Performance - refers to the main characteristics of the product or service (use)

2) Special features - refers to the extra characteristics3) Conformance - refers to how well a product or service corresponds to

a customer's expectations4) Reliability - consistency of performance without breakdown5) Durability - refers to the useful life of the product or service6) Service after sale - handling of complaints, or checking on customer

satisfaction7) Aesthetics - pleasing to look at8) Safety - safe when use as directed

The determinants of quality (degree to which a product or service successfully satisfies its intended purpose) are:

1) Design - the starting point for the level of quality eventually achieved2) How well it conforms to design - the degree to which goods and

services conform to the intent of the designer3) Ease of use - instruction on how to use the product must be easy to

understand, injuries caused to consumer can end up in litigation4) Service after delivery - technical support/contact from the service

provider

Some of the consequences of poor quality Loss of business Liability Productivity Costs

1. Internal failure costs - failures discovered during production

2. External failure costs - failures discovered after delivery to customer

3. Appraisal costs - cost of activities designed to ensure quality or to uncover defects

4. Prevention costs - cost of preventing defects from occurring



Difference between modern quality management and the formerly traditional approach

Quality Control by prevention vs. Quality Control by detection

Quality Gurus:

1. Deming - a statistics professor at NYU in the 40s, and is credited for Japan's focus in quality and productivity

Known for his 14-point prescription for achieving quality in an organization (see page 426 for list)

Four key elements in Deming's 14 pointsi. appreciation for systemii. a theory of variationiii. a theory of knowledgeiv. psychology

2. Juran - like Deming also taught Japanese manufacturers how to improve quality

Views quality as fitness-for-use

Believes that 80% of quality defects are management controllable

Describes Quality management as trilogy consisting of (1) quality planning, (2) quality control (3) quality improvement

1. Quality planning is necessary to establish processes that are capable of meeting quality standards

2. Quality control is necessary to know when corrective action is needed

3. Quality improvement will help find better ways of doing things

Key element of Juran's philosophy is the commitment of management to continual improvement

3. Crosby - developed the concept of zero defects and popularized the phrase "do it right the first time"

Like Deming and Juran, he believes management's role in achieving quality

Believes in the concept "quality is free"



4. Ishikawa - Key contributions include the development of the cause-and-effect diagram (a.k.a the fishbone diagram)

5. Taguchi - best known for the Taguchi loss function - a formula for determining the cost of poor quality

The idea is that deviation of a part from a standard causes a loss His method is credited with helping Ford Motor Company to reduce its

warranty losses



Quality Control

Purpose of QC

To assure that the process is performing in an acceptable manner Done through monitoring the process via inspection

Quality Assurance Relies on inspection

Inspection after production (acceptance sampling) Inspection during production (statistical process control, or SPC)

Basic Issues in Inspection:1) How much and how often to inspect2) At what points in the process to inspect3) Whether to inspect in a centralized or on-site location4) Whether to inspect attributes (counting something) or variables

(measure something)

Where to inspect:

Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before covering a process

Key Concepts:

Variation is the enemy of quality Every process exhibits some form of variation The degree of this variation is a measure of the capability of the process Process variation can be classified as:

o common cause variation - inherent in systemo special cause variation - presence is detected using SPC



Control Charts

Key tool for monitoring and controlling processes. A control chart is a time-ordered plot of sample statistics

Purpose: used for detecting presence of special cause variation.

Components of a Control Chart(1) Upper Control Limit(2) Middle Value(3) Lower Control Limit

Possible Errors in SPC Type I error Type II error

Managerial Considerations Concerning Control Charts1. At what points in the process to use control charts2. What size samples to take3. What type of control chart



Four Common Types of Charts

A. Control charts for Variables

(1) Mean chart (a.k.a x-bar chart) - used to monitor the average of the process

(2) Range chart (a.k.a. R-chart) - used to monitor the variability of the process



B. Control charts for Attributes

(1) p-chart (proportion chart) - used to monitor the proportion of defectives

(2) c-chart (used when the goal is to control the number of defects per unit



Charts Illustrating a Process Not in Control



Table for A2, D3 and D4

Factor for R

ChartNumber of

Observations in

Subgroup

Factor for x-bar

Chart

Lower Control

Limit

Upper Control

Limitn A2 D3 D4

2 1.88 0.00 3.273 1.02 0.00 2.574 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.8210 0.31 0.22 1.7811 0.29 0.26 1.7412 0.27 0.28 1.7213 0.25 0.31 1.6914 0.24 0.33 1.6715 0.22 0.35 1.6516 0.21 0.36 1.6417 0.20 0.38 1.6218 0.19 0.39 1.6119 0.19 0.40 1.6020 0.18 0.41 1.59

Problems 4 – Control charts for Variables – Mean and Range charts6 – Control chart for Attributes – p-chart7 – Control chart for Attributes – c-chart8 – How many to produce given a certain production survival rate



Problem 10.4 (p. 492)

Computer upgrades have a nominal time of 80 minutes. Samples of 5 observations each have been taken, and the results are listed below. Determine the upper and lower control limits for mean and range charts, and decide if the process is in control.

SAMPLE1 2 3 4 5 6

79.2 80.5 79.8 78.9 80.5 79.778.8 78.7 79.4 79.4 79.6 80.680.0 81.0 80.4 79.7 80.4 80.578.4 80.4 80.3 79.4 80.8 80.081.0 80.1 80.8 80.6 78.8 81.1



Excel Solution



Problem 10.6 (493)

A medical facility does MRIs for sports injuries. Occasionally a test yields inconclusive results and must be repeated. Using the following sample data and n=200, determine the upper and lower control limits for the fraction of retests using two-sigma limits.

Is the process in control? If not eliminate any values that are outside the limits and compute the revised limits.

SAMPLE1 2 3 4 5 6 7 8 9 10 11 12 13

Number of defectives 1 2 2 0 2 1 2 0 2 7 3 2 1



Excel Solution



PROBLEM NO. 10 – 7 (493)

The postmaster of a small western city receives a certain number of complaints each dayabout mail delivery. Assume that the distribution of daily complaints is Poisson. Constructa control chart with three sigma limits using the following data. Is the process in control?

SAMPLE1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of complaints 4 10 14 8 9 6 5 12 13 7 6 4 2 10



Excel Solution



Problem 18 (495)

A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 percent for the other two steps.

(a) If the desired daily output is 450 units, how many units must be started to allow for loss due to scrap?

(b) If the scrap rate for each step would be cut in half, how many units would this save in terms of the scrap allowance?

(c ) If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate?



INVENTORY MANAGEMENT

Importance of Inventory Management -- Good inventory management is essential to the successful operation for most organizations because of:

1. The amount of money invested in inventory represents, and2. The impact that inventories have on daily operations of an organization

Definitions:

Inventory – a stock or store of goodsIndependent vs. Dependent demand items

Independent demand items are the finished goods or other end items that are sold to someone

Dependent demand items are typically subassemblies or component parts that will be used in the production of a final or finished product

Our focus: inventory management of finished goods, raw materials, purchased parts, and retail items

Functions of Inventories

1. To meet anticipated demand2. To smooth production requirements3. To decouple components of the production4. To protect against stockouts5. To take advantage of order cycles6. To hedge against price increases, or to take advantage of quantity discounts7. To permit operations (work in process)

Objectives of Inventory Control

1. Maximize level of customer service2. Minimize costs (carrying costs and ordering costs)



Requirements for Effective Inventory Management

(1) A system to keep track of the inventory periodic, perpetual, two-bin, and universal product code (UPC)

(2) A reliable forecast of demand

(3) Knowledge of lead times and lead time variability-lead time time between submitting a purchase order and receiving it-lead time variability reliability of the supplier

(4) Estimates of inventory holding costs, ordering costs, and shortage costsHolding costOrdering costStockout cost

(5) A classification system for inventory itemsABC approach – classifies inventory according to some measure of importance ($ value) where A – very important, C – least important







Formula for EOQ with Non-instantaneous Replenishment

where: D – annual demand S – setup cost

H – Holding (carrying cost) per unit p – production or delivery rate

d – usage rate

C. Quantity Discounts Model

1. Compute the common EOQ

2. Only one of the unit prices will have the EOQ in its feasible range. Identify the range that:

If the feasible EOQ is on the lowest price range, that is the optimal order quantity

If the feasible EOQ is in any other range, compute the total cost for the EOQ and for the price breaks of all lower unit costs. Compare the total costs – EOQ is the one that yields the lowest total cost.



When to Order (reorder points - ROPs) Models

Objective: minimize the risk (probability) of stockouts

4 Determinants of the ROP1. rate of demand2. lead time3. extent of demand and/or lead time variability4. degree of stockout risk acceptable to management

Basic Formula for Computing ROP

A. Constant demand and constant lead time

B. Variability is present in demand during lead time

use this formula if an estimate of expected demand during lead time and its standard deviation are available

use this formula when data on lead time and demand are not readily available



Shortages and Service Levels

The ROP computation does not reveal the expected amount of shortage for a given lead time service level

Information on expected number of shortage per cycle, or per year can be determined using the following:

A. Expected number of units short per cycle, E(n)

B. Expected number of units short per year, E(N)

C. Annual Service Level



Service Level for Single-period Model

Used to handle ordering of perishables(fresh fruits, vegetables, seafood, flowers), and

Items that have a limited useful life(newspaper, magazines)

Analysis focuses on two costs: shortage and excess

Problems:

2 – ABC Inventory Classification3 – Basic EOQ4 – Basic EOQ11– EOQ with Non-instantaneous Delivery13 – EOQ with Discount28 – EOQ, ROP, Shortages33 – EOQ for multiple products











(b) Determine the EOQ for each item.



Project Management

What is a project?

Unique, one-time operations designed to accomplish a set of objectives in a limited time frame

Examples: construction of new buildings, installing a new computer network system, launching a space shuttle, producing a movie, etc

Once underway, projects must be monitored to contain cost and meet timelines

This chapter is devoted to a description of graphical and computational methods that are used for planning and scheduling projects

Key Decisions in Project Management

Deciding which projects to implement Selecting the project manager Selecting the project team Planning and deciding the project Managing and controlling project resources Deciding if and when a project should be terminated

Planning and Scheduling With Gantt Charts

Gantt chart - a popular tool for planning and scheduling simple projects Used to monitor progress over time by comparing planned progress to actual

progress

Planning with PERT/CPM

PERT (program evaluation review technique) and CPM (critical path method) are two of the most widely used techniques for planning and coordinating large-scale projects

By using PERT/CPM, managers are able to obtain:(a) A graphical display of project activities(b) An estimate of how long the project will take(c) An indication of which activities are most critical to timely project

completion(d) An indication of how long an activity can be delayed without lengthening

the project

Network Diagram – a.k.a. precedence diagram is a chart used in PERT that depicts major project activities and their sequential relationships

o Activity on Node (AON)o Activity on Arrow (AOA)



Path – a sequence of activities that leads from the starting node to the finishing nodes

Critical path – the path with the longest time

Critical activities – activities that are on the critical path. They have zero slack

Network conventions



Deterministic vs Probabilistic Time Estimates

Deterministic times – if time estimates can be made with a high degree of confidence that actual time will not differ significantly

Probabilistic times – must include an indication of the extent of probable variation

A Computing Algorithm

ES – earliest time activity can startEF – earliest time an activity can finishLS – latest time an activity can startLF – latest time an activity can finish



Problem 1 (see page 802)



Problem 3 (Not in text)

The information below pertains to a project that is about to commence. As the project manager, which activities would you be concerned with in terms of timely project completion? Explain.

Immediate Estimated Estimated

Activity Precedecessor Time (days) Activity Precedes Time (days)

a -- 15 a B 15

b A 12 b C,D 12

c B 6 c E 6

d B 5 d End 5

e C 3 e End 3

f -- 8 f G,H 8

g F 8 g I 8

h F 9 h J 9

i G 7 i End 7

j H 14 j K 14

k J 6 k End 6

End D,E,I,K



Problem 7 (819)

Three recent college graduates have formed a partnership and have opened an advertising firm. The first project consists of activities in the following table.

ActivityImmediate

Predecessor to tm tpA -- 5 6 7B -- 8 8 11C A 6 8 11D -- 9 12 15E C 5 6 9F D 5 6 7G F 2 3 7H B 4 4 5I H 5 7 8

End E,G,I

(a) Draw the precedence diagram

(b) What is the probability that the project can be completed in 24 days or less? In 21 days or less?



Excel Solution



Problem 11(820)

The following precedence diagram reflects three time estimates for each activity. Determine:

(a) The expected completion time for each path and its variance

(b) The probability that the project will require more than 49 weeks.

(c) The probability that the project can be completed in 46 weeks or less.


1

5

42

3

9

8

7

6

11

10

8 -8 -8(a)

7-1 0-1 2(h )

1 1-1 2-1 4(d )

1 3-1 3-1 3(g)

1 4-1 8-2 6(f )

5 -6 -7(c )

5 - 7-1 0(k)

9-1 0-1 2(e)

1 1-1 2-1 3(b )

8-1 0-1 4( i)

6 -6 -6(m )

1 0-11-1 2( l)


Queuing

What is queuing theory?

The mathematical approach to the analysis of lines

Useful in planning and analysis of service capacity

Goal of queuing -- minimize total cost - costs associated with customers waiting in line for service and those associated with capacity

System Characteristics

1) Population sourceo Infinite sourceo Finite source

1) Number of servers (channels)o Singleo Multiple

2) Arrival and service patternso Probability distribution (exponential, Poisson, etc)

3) Queue discipline (order of service)o First-come-first-served





Queuing Models:

Infinite Sources Assumptions:

o Poisson arrival rateo System operates under steady state (average arrival and

service rates are stable)

Important note: The arrival () and service rates () must be in the same units

Four Basic Models5) Single channel, exponential service time6) Single channel, constant service time7) Multiple channel, exponential service time8) Multiple priority service, exponential service time

Finite Source

(4) Appropriate for cases in which the calling population is limited to a relatively small number of potential calls

(5) Example -- one person may be responsible for handling breakdown on 15 machines

(6) The mathematics of finite-source model can be complex, analysts often use finite queuing tables in conjunction with simple formulas to analyze these systems



Important Note: To solve queuing problems use the Excel templates that accompany the text

Five Typical Measures of System PerformanceOperations Managers Look at

1) Average number of customers waiting (in line or in system)2) Average time customers wait (in line or system)3) System utilization (percentage of capacity used)4) Implied cost of given level of capacity and its related waiting line5) The probability that an arrival will have to wait for service

Infinite-source Symbols



Problem 1 (861)

Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per 8-hour day (assume Poisson).

Determine:

(a) The average number of customers awaiting repairs.

(b) System utilization

(c) The amount of time during an 8-hour day that the repairman is not out on call

(d) The probability of two or more customers in the system.

Excel Solution



Problem 2 (861)

A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson distributed. Determine:

(a) The average number of customer waiting in line

(b) The average time customers spend in the system

(c) The average number in the system

Excel Solution



Problem 4 (844)

A small town with one hospital has two ambulances to supply ambulance service. Requests for ambulances during non-holiday weekends average 0.45 per hour and tend to be Poisson distributed. Travel and assistance time averages one hour per call and follows an exponential distribution. Find:

(a) System utilization

(b) The average number of customers waiting

(c) The average time customers wait for an ambulance

(d) The probability that both ambulances will be busy when a call comes in



Problem 10 (845)

Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentially distributed and has a mean of 14 minutes per machine. The machines operate for an average of 86 minutes between adjustments. While running, each machine can turn out 50 pieces per hour. Find:

(a) The probability that a machine will have to wait for an adjustment

(b) The average number of machines waiting for adjustment

(c) The average number of machines being serviced

(d) The expected hourly output of each machine, taking adjustments into account

(e) Machine downtime represents a cost of $70 per hour; operator cost (including salary and fringe benefits) is $15 per hour. What is the optimum number of operators?

Excel Solution


Documents

BA 380 Lecture Notes Packet 2008