BA 380 Lecture Notes Packet 2005

This packet contains detailed outlines of chapters and topics in your text, Production Operations Management, 6th Edition (Ste

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 groupsWords to remember:

Prioritize, not procrastinate.

Spread out the work, not put things off until the last minute

Rene Leo E. Ordonez, PhD

Professor and Chair of Business

(541) 552-6720

[email protected] Outlines and Digitized Lectures for

BA 380: Operation Management

Rene Leo E. Ordonez, PhD

School of Business

Southern Oregon University

Spring 2008 EditionNote: The outlines listed below are based on the text Production Operations Management, 98h 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 Notes

Page Number

Introduction2

Productivity, Competitiveness, Strategy7

Forecasting9

Reliability28

Cost Volume Analysis and Capacity Planning41

Decision Theory 47

Learning Curves53

Introduction to Quality Control59

Quality Control62

Inventory Management75

Project Management88

Waiting Lines97

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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

Quantitative

Queuing techniques

Inventory Models

Project models (PERT/CPM)

Forecasting techniques

Statistical models

Breakeven analysis

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

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

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

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, workers 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

Examples of Types of Operations

Type of OperationExamples

Goods producingFarming, mining, construction, manufacturing, power generation

Storage/transportationWarehousing, trucking, mail service, moving, taxis, buses, hotel, airlines

ExchangeRetailing, wholesaling, banking, renting or leasing, library loans

EntertainmentFilms, radio and TV, plays, concerts, recording

CommunicationNewspapers, radio and TV newscast, telephone, satellite

Illustrations of the Transformation Process

Food ProcessingInputsProcessingOutput

Raw vegetables

Metal sheets

Water

Energy

Labor

Building

Equipment

Cleaning

Making cans

Cutting

Cooking

Packing

LabelingCanned vegetables

HospitalInputsProcessingOutput

Doctors, nurses

Hospitals

Medical supplies

Equipment

Laboratories

Examination

Surgery

Monitoring

Medication

TherapyHealthy patients

Examples of inputs, transformation, and outputs

InputsTransformationOutput

Land

Human

Physical

Intellectual

Raw materials

Energy

Water

Chemical

Metals

Wood

Equipment

Machines

Computers

Trucks

Tools

Facilities

Hospitals

Factories

Offices

Retail stores

Other

Information

Time

Processes

Cutting, drilling

Transporting

Teaching

Farming

Mixing

Packing

Canning

Consulting

Copying, faxingGoods

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

CharacteristicsGoodsServices

Output

Customer contact

Uniformity of input

Labor content

Uniformity of output

Measurement of productivity

Opportunity to correct quality problems before delivery to customer

Tangible

Low

High

Low

High

Easy

High

Intangible

High

Low

High

Low

Difficult

Low

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 organizations 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

Qualitative

Judgment and opinion

Sales force

Consumer surveys

Delphi technique

Quantitative

Regression and Correlation (associative)

Time series

Forecasts Based on Time Series Data

What is Time Series?

Components (behavior) of Time Series data

Trend

Cycle

Seasonal

Irregular

Random variations

Nave Methods

Nave 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

Moving Averages

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:

Deseasonalizing data

Seasonalizing data

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

Accuracy and Control of Forecasts

Measures of Accuracy

Mean Absolute Deviation (MAD)

Mean Squared Error (MSE)

Mean Absolute Percentage Error (MAPE)

Forecast Control Measure

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 Smoothing

5 Applying a linear trend to forecast

15 Computing seasonal relatives

17 Using indexes to deseasonalize values

26 Using MAD, MSE to measure forecast accuracy

Problem 2 (113)

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

MonthSales

(000 units)

Feb19

March18

April15

May20

June18

July22

August20

(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 Nave 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

(a) Plot of the monthly data

How to superimpose a trend line on the graph

Click on the graph created above (note that when you do this an item called CHART will appear on the Excel menu bar)

Click on Chart > Add Trend Line Click on the most appropriate Trend Regression Type

Click OK

(b) Forecast September sales volume using:

(1) Linear Trend Equation

Create a column for time period (t) codes (see column B)

Click Tools > Data Analysis > Regression

Fill in the appropriate information in the boxes in the Regression box that appears

(2) Five-month moving average

(3) 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

(4) The Nave Approach

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

Problem 5 (113)

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

yt =80 + 15 t

where: yt = Annual sales (000 bottles)

t0 = 1990(a) Are the annual sales increasing or decreasing? By how much?

(b) Predict annual sales for the year 2006 using the equation

Problem 15 (115)

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)

DayNumber ServedDayNumber Served

1801584

2751677

3781783

4951896

513019135

613620140

7402137

8822287

9772382

10802498

119425103

1212526144

1313527144

14422848

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 (116) 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 SoldIndexMonthUnits SoldIndex

Jan6400.80Jul7650.90

Feb6480.80Aug8051.15

Mar6300.70Sept8401.20

April7610.94Oct8281.20

May7350.89Nov8401.25

Jun8501.00Dec8001.25

(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

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

Problem 26 (118) 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 Demand

PeriodDemandF1F2

1686666

2756868

3707270

4747172

5697274

6727076

7807178

8787480

(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

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 systemProduct 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 DistributionReliability over Time -- Exponential Distribution

Values of e-T/MTBF

T/MTBFe-T/MTBFT/MTBFe-T/MTBFT/MTBFe-T/MTBF

0.100.90482.600.07435.100.0061

0.200.81872.700.06725.200.0055

0.300.74082.800.06085.300.0050

0.400.67032.900.05505.400.0045

0.500.60653.000.04985.500.0041

0.600.54883.100.04505.600.0037

0.700.49663.200.04085.700.0033

0.800.44933.300.03695.800.0030

0.900.40663.400.03345.900.0027

1.000.36793.500.03026.000.0025

1.100.33293.600.02736.100.0022

1.200.30123.700.02476.200.0020

1.300.27253.800.02246.300.0018

1.400.24663.900.02026.400.0017

1.500.22314.000.01836.500.0015

1.600.20194.100.01666.600.0014

1.700.18274.200.01506.700.0012

1.800.16534.300.01366.800.0011

1.900.14964.400.01236.900.0010

2.000.13534.500.01117.000.0009

2.100.12254.600.01017.100.0008

2.200.11084.700.00917.200.0007

2.300.10034.800.00827.300.0007

2.400.09074.900.00747.400.0006

2.500.08215.000.00677.500.0006

Reliability over Time -- Normal Distribution

STANDARD NORMAL DISTRIBUTION

z00.010.020.030.040.050.060.070.080.09

0.00.00000.00400.00800.01200.01600.01990.02390.02790.03190.0359

0.10.03980.04380.04780.05170.05570.05960.06360.06750.07140.0753

0.20.07930.08320.08710.09100.09480.09870.10260.10640.11030.1141

0.30.11790.12170.12550.12930.13310.13680.14060.14430.14800.1517

0.40.15540.15910.16280.16640.17000.17360.17720.18080.18440.1879

0.50.19150.19500.19850.20190.20540.20880.21230.21570.21900.2224

0.60.22570.22910.23240.23570.23890.24220.24540.24860.25170.2549

0.70.25800.26110.26420.26730.27040.27340.27640.27940.28230.2852

0.80.28810.29100.29390.29670.29950.30230.30510.30780.31060.3133

0.90.31590.31860.32120.32380.32640.32890.33150.33400.33650.3389

1.00.34130.34380.34610.34850.35080.35310.35540.35770.35990.3621

1.10.36430.36650.36860.37080.37290.37490.37700.37900.38100.3830

1.20.38490.38690.38880.39070.39250.39440.39620.39800.39970.4015

1.30.40320.40490.40660.40820.40990.41150.41310.41470.41620.4177

1.40.41920.42070.42220.42360.42510.42650.42790.42920.43060.4319

1.50.43320.43450.43570.43700.43820.43940.44060.44180.44290.4441

1.60.44520.44630.44740.44840.44950.45050.45150.45250.45350.4545

1.70.45540.45640.45730.45820.45910.45990.46080.46160.46250.4633

1.80.46410.46490.46560.46640.46710.46780.46860.46930.46990.4706

1.90.47130.47190.47260.47320.47380.47440.47500.47560.47610.4767

2.00.47720.47780.47830.47880.47930.47980.48030.48080.48120.4817

2.10.48210.48260.48300.48340.48380.48420.48460.48500.48540.4857

2.20.48610.48640.48680.48710.48750.48780.48810.48840.48870.4890

2.30.48930.48960.48980.49010.49040.49060.49090.49110.49130.4916

2.40.49180.49200.49220.49250.49270.49290.49310.49320.49340.4936

2.50.49380.49400.49410.49430.49450.49460.49480.49490.49510.4952

2.60.49530.49550.49560.49570.49590.49600.49610.49620.49630.4964

2.70.49650.49660.49670.49680.49690.49700.49710.49720.49730.4974

2.80.49740.49750.49760.49770.49770.49780.49790.49790.49800.4981

2.90.49810.49820.49820.49830.49840.49840.49850.49850.49860.4986

3.00.49870.49870.49870.49880.49880.49890.49890.49890.49900.4990

Availability

Measures the fraction of time a piece of equipment is expected to be operational Availability ranges between 0 and 1

Problems:

1 system reliability

2 system reliability

4 reliability and cost

7 comparing reliabilities of 2 systems

12 product life exponential distribution

17 product life normal distribution

18 product life normal distribution

Problem 1 (p172)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

Problem 2 (173)

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 0.96 probability of 0.99. What is the overall probability that the product will function properly?

Problem 4 (p173)

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 (173)

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 (174)

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 (174)

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 (174)

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)

Problem 3 (p 201)

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 201)

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Tow 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.

a. Determine each alternatives 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 201)

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 B2Decision TheoryThe 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 from

3) a known payoff for each alternative under each possible future condition

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

1) identify the future conditions

2) develop a list of possible alternatives

3) determine/estimate the payoff associated with each alternative

4) if possible, estimate the likelihood of each possible future condition

5) 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. Maximin

b. Maximax

c. Laplace

d. 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 (220)A small building contractor has recently experienced two successive years in which work opportunities exceeded the firms 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 Years Demand

AlternativeLowHigh

Do Nothing$50$60

Expand2080

Subcontract4070

(Profit in $thousands)

Problem 2 (220)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 (220)

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 (220)

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 unitsUse the Multipliers on Table below

LEARNING CURVE COEFFICIENTS

70%75%80%85%90%

Unit NumberUnit TimeTotal TimeUnit TimeTotal TimeUnit TimeTotal TimeUnit TimeTotal TimeUnit TimeTotal Time

11.000111111111

20.7001.7000.7501.7500.8001.8000.8501.8500.9001.900

30.5682.2680.6342.3840.7022.5020.7732.6230.8462.746

40.4902.7580.5632.9460.6403.1420.7233.3450.8103.556

50.4373.1950.5133.4590.5963.7380.6864.0310.7834.339

60.3983.5930.4753.9340.5624.2990.6574.6880.7625.101

70.3673.9600.4464.3800.5344.8340.6345.3220.7445.845

80.3434.3030.4224.8020.5125.3460.6145.9360.7296.574

90.3234.6260.4025.2040.4935.8390.5976.5330.7167.290

100.3064.9320.3855.5890.4776.3150.5837.1160.7057.994

110.2915.2230.3705.9580.4626.7770.5707.6860.6958.689

120.2785.5010.3576.3150.4497.2270.5588.2440.6859.374

130.2675.7690.3456.6600.4387.6650.5488.7920.67710.052

140.2576.0260.3346.9940.4288.0920.5399.3310.67010.721

150.2486.2740.3257.3190.4188.5110.5309.8610.66311.384

160.2406.5140.3167.6350.4108.9200.52210.3830.65612.040

170.2336.7470.3097.9440.4029.3220.51510.8980.65012.690

180.2266.9730.3018.2450.3949.7160.50811.4050.64413.334

190.2207.1920.2958.5400.38810.1040.50111.9070.63913.974

200.2147.4070.2888.8280.38110.4850.49512.4020.63414.608

210.2097.6150.2839.1110.37510.8600.49012.8920.63015.237

220.2047.8190.2779.3880.37011.2300.48413.3760.62515.862

230.1998.0180.2729.6600.36411.5940.47913.8560.62116.483

240.1958.2130.2679.9280.35911.9540.47514.3310.61717.100

250.1918.4040.26310.1910.35512.3090.47014.8010.61317.713

260.1878.5910.25910.4490.35012.6590.46615.2670.60918.323

270.1838.7740.25510.7040.34613.0050.46215.7280.60618.929

280.1808.9540.25110.9550.34213.3470.45816.1860.60319.531

290.1779.1310.24711.2020.33813.6850.45416.6400.59920.131

300.1749.3050.24411.4460.33514.0200.45017.0910.59620.727

Problem 1 (357)

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 (357)

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 (357)

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)

146

239

335

433

532

630

Introduction to Quality

What is QUALITY?

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

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

2) Special features - refers to the extra characteristics

3) Conformance - refers to how well a product or service corresponds to a customer's expectations

4) Reliability - consistency of performance without breakdown

5) Durability - refers to the useful life of the product or service

6) Service after sale - handling of complaints, or checking on customer satisfaction

7) Aesthetics - pleasing to look at

8) 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 achieved

2) How well it conforms to design - the degree to which goods and services conform to the intent of the designer

3)Ease of use - instruction on how to use the product must be easy to understand, injuries caused to consumer can end up in litigation

4) 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 points

i. appreciation for system

ii. a theory of variation

iii. a theory of knowledge

iv. 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 improvement1. 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:

common cause variation - inherent in system

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 Charts

1. At what points in the process to use control charts

2. What size samples to take

3. 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 Chart

Number of Observations in SubgroupFactor for x-bar ChartLower Control LimitUpper Control Limit

nA2D3D4

21.880.003.27

31.020.002.57

40.730.002.28

50.580.002.11

60.480.002.00

70.420.081.92

80.370.141.86

90.340.181.82

100.310.221.78

110.290.261.74

120.270.281.72

130.250.311.69

140.240.331.67

150.220.351.65

160.210.361.64

170.200.381.62

180.190.391.61

190.190.401.60

200.180.411.59

Problems

4 Control charts for Variables Mean and Range charts

6 Control chart for Attributes p-chart

7 Control chart for Attributes c-chart

8 How many to produce given a certain production survival rate

Problem 10.4 (p. 482)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.SAMPLE

123456

79.280.579.878.980.579.7

78.878.779.479.479.680.6

80.081.080.479.780.480.5

78.480.480.379.480.880.0

81.080.180.880.678.881.1

Excel Solution

Problem 10.6 (482)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.

SAMPLE

12345678910111213

Number of defectives1220212027321

Excel Solution

PROBLEM NO. 10 7 (483)

The postmaster of a small western city receives a certain number of complaints each day

about mail delivery. Assume that the distribution of daily complaints is Poisson. Construct

a control chart with three sigma limits using the following data. Is the process in control?

SAMPLE

1234567891011121314

Number of complaints4101489651213764210

Excel Solution

Problem 18 (485)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, and

2. The impact that inventories have on daily operations of an organization

Definitions:

Inventory a stock or store of goods

Independent 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 demand

2. To smooth production requirements

3. To decouple components of the production

4. To protect against stockouts

5. To take advantage of order cycles

6. To hedge against price increases, or to take advantage of quantity discounts

7. To permit operations (work in process)

Objectives of Inventory Control

1. Maximize level of customer service

2. 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 costs

Holding cost

Ordering cost

Stockout cost

(5) A classification system for inventory items

ABC 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 ROP

1. rate of demand

2. lead time

3. extent of demand and/or lead time variability

4. 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 Classification

3 Basic EOQ

4 Basic EOQ

11 EOQ with Non-instantaneous Delivery

13 EOQ with Discount

28 EOQ, ROP, Shortages

33 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 progressPlanning 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 Activity on Node (AON) 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 start

EF earliest time an activity can finish

LS latest time an activity can start

LF 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.

ImmediateEstimatedEstimated

ActivityPredecessorTime (days)ActivityPrecedesTime (days)

a--15aB15

bA12bC,D12

cB6cE6

dB5dEnd5

eC3eEnd3

f--8fG,H8

gF8gI8

hF9hJ9

iG7iEnd7

jH14jK14

kJ6kEnd6

EndD,E,I,K

Problem 7 (804)

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 Predecessortotmtp

A--567

B--8811

CA6811

D--91215

EC569

FD567

GF237

HB445

IH578

EndE,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

(c)Suppose it is now the end of the seventh day and that activities A and B have been completed. Time estimates for the completion of activity D are 5, 6, and 7. Activity C and H are ready to begin. Determine the probability of finishing the project by day 24 and the probability of finishing by day 21.

Problem 11(805)

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.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 source

Infinite source

Finite source

1) Number of servers (channels)

Single

Multiple

2) Arrival and service patterns

Probability distribution (exponential, Poisson, etc)

3) Queue discipline (order of service)

First-come-first-served

Queuing Models:

Infinite Sources

Assumptions: Poisson arrival rate 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 Models

5) Single channel, exponential service time6) Single channel, constant service time7) Multiple channel, exponential service time8) Multiple priority service, exponential service timeFinite 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 textFive Typical Measures of System Performance

Operations 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 line

5) The probability that an arrival will have to wait for service

Infinite-source Symbols

Problem 1 (844)

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 (844)

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 0.8 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

Excel Solution

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

=AVERAGE(M8:M15)

=ABS(c7-d7)/c7

=(c7-d7)^2

EMBED Equation.3

EMBED SmartDraw.2

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Excel.Sheet.8

EMBED Excel.Sheet.8

EMBED Excel.Sheet.8

Where:

TR total revenue

TC total cost

vc variable cost per unit

Q units produced and sold

P total profit

R revenue per unit

FC total fixed cost

.90

.90

EMBED MinitabGraph.Document

z

Reliability = P(Z > z)

Time

f(T)

1 e-T/MTBF

Reliability = e-T/MTBF

=SUM(J8:J15)/(COUNT(J8:J15)-1)

=AVERAGE(G8:G15)

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

Coded time period

Sales data

Coded time period

EMBED Excel.Sheet.8

EMBED Excel.Sheet.8

Marketing

Production/

Operations

Finance

Inputs

Land

Labor

Capital

Information

Transformation/

conversion process

Outputs

Goods and

Services

Control

Feedback

Feedback

Feedback

=ABS(c7-d7)

Prepared by: Rene Leo E. Ordonez, PhD

School of Business, SOU

Notes to Accompany Operations Management (Stevenson, 2007Prepared by Rene Leo E. Ordonez, PhD

SOU School of Business

Notes to Accompany Operations Management, 9th Edition (Stevenson, 2007)

_1044962139.unknown

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_1093161112.unknown

_1155038269.xlsChart3

0.004432

0.005953

0.007915

0.010421

0.013583

0.017528

0.022395

0.028327

0.035475

0.043984

0.053991

0.065616

0.07895

0.094049

0.110921

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0.149727

0.171369

0.194186

0.217852

0.241971

0.266085

0.289692

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0.333225

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0.381388

0.391043

0.396953

0.398942

0.396953

0.391043

0.381388

0.36827

0.352065

0.333225

0.312254

0.289692

0.266085

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0.035475

0.028327

0.022395

0.017528

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0.007915

0.005953

0.004432

Tmtbf

T/MTBFe-T/MTBFT/MTBFe-T/MTBFT/MTBFe-T/MTBF

0.100.90482.600.07435.100.0061

0.200.81872.700.06725.200.0055

0.300.74082.800.06085.300.0050

0.400.67032.900.05505.400.0045

0.500.60653.000.04985.500.0041

0.600.54883.100.04505.600.0037

0.700.49663.200.04085.700.0033

0.800.44933.300.03695.800.0030

0.900.40663.400.03345.900.0027

1.000.36793.500.03026.000.0025

1.100.33293.600.02736.100.0022

1.200.30123.700.02476.200.0020

1.300.27253.800.02246.300.0018

1.400.24663.900.02026.400.0017

1.500.22314.000.01836.500.0015

1.600.20194.100.01666.600.0014

1.700.18274.200.01506.700.0012

1.800.16534.300.01366.800.0011

1.900.14964.400.01236.900.0010

2.000.13534.500.01117.000.0009

2.100.12254.600.01017.100.0008

2.200.11084.700.00917.200.0007

2.300.10034.800.00827.300.0007

2.400.09074.900.00747.400.0006

2.500.08215.000.00677.500.0006

exponential

MEAN5

0.2442808782120

0.2983657373219

0.3644252218318

0.4451105661417

0.54366516

0.6640287113615

0.8110475838714

0.9906170803813

1.2099440519912

1.4778309781011

1.80502924591110

2.2046706471129

2.6927944095138

3.2889909162147

4.0171879475156

4.9066109992165

5.9929562201174

7.3198230432183

8.9404640075192

10.9199219977201

13.337640679210

16.29065289322-1

19.897474978423-2

24.302863311524-3

29.683623966325-4

36.255708657926-5

exponential

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Normal

Mean1

Sigma0

-30.004432

-2.90.005953

-2.80.007915

-2.70.010421

-2.60.013583

-2.50.017528

-2.40.022395

-2.30.028327

-2.20.035475

-2.10.043984

-20.053991

-1.90.065616

-1.80.07895

-1.70.094049

-1.60.110921

-1.50.129518

-1.40.149727

-1.30.171369

-1.20.194186

-1.10.217852

-10.241971

-0.90.266085

-0.80.289692

-0.70.312254

-0.60.333225

-0.50.352065

-0.40.36827

-0.30.381388

-0.20.391043

-0.10.396953

00.398942

0.10.396953

0.20.391043

0.30.381388

0.40.36827

0.50.352065

0.60.333225

0.70.312254

0.80.289692

0.90.266085

10.241971

1.10.217852

1.20.194186

1.30.171369

1.40.149727

1.50.129518

1.60.110921

1.70.094049

1.80.07895

1.90.065616

20.053991

2.10.043984

2.20.035475

2.30.028327

2.40.022395

2.50.017528

2.60.013583

2.70.010421

2.80.007915

2.90.005953

30.004432

Normal

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

_1227942284.xlsPr 2(603)

Problem 2(603)

The following classification table contains figures on the monthly volume

and unit costs for a random sample of 16 units from a list of 2,000

inventory items at a health care facility.

ItemUnit CostUsage

K3410200

K3525600

K3636150

M101625

M202080

Z4580200

F1420300

F9530800

F992060

D4510550

D481290

D5215110

D5740120

N083040

P0516500

P091030

Pr 3 (603)

Problem 3(603)

A large bakery buys flour in 25-lb bags. The bakery uses an average of 4,680 bags

a year. Preparing an order and receiving a shipment of flour involves a cost of $4

per order. Annual carrying costs are $30 per bag.

(a) Determine the economic order quantity

(b) What is the average number of bags on hand?

(c ) How many order per year will there be?

(d) Compute the total cost of ordering and carrying flour.

(e) If annual cost were to increase by $1 per order, how much would that affect

the minimum total cost?

Pr 40 (610)

Problem 40 (610)

Demand for rug-cleaning mahines at Clyde's U-Rent-It is shown in the following table.

Machines are rented by the day only. Profit on the rug cleaners is $10 per day.

Clyde has four rug-cleaning machines.

DemandFrequency

00.30

10.20

20.20

30.15

40.10

40.05

1.00

(a) Assuming that Clyde's stocking decision is optimal, what is the implied

range of excess cost per machine?

(b) Your answers from part a has been presented to Clyde, who protests that the

amount is too low. Does this suggest an increase or decrease in the number of

rug machines he stocks? Explain.

Suppose now that the $10 mentioned as profit is instead the excess cost per day for

each machine and that the shortage cost is unknown. Assuming that the optimal

number of machines is four, what is the implied range of shortage cost per machine?

Pr 33 (609)

Problem 33 (609)

Given the following list of items,

ItemEstimated Annual DemandOrdering CostHolding Cost (%)Unit Price

DSP

H4-010200005020%2.5

H5-201602006020%4

P6-40098008030%28.5

P6-401163005030%12

P7-10062505030%9

P9-10345005040%22

TS-300210004025%45

TS-400450004025%40

TS-0418004025%20

V1-001261002535%40

(a) Classify the items as A, B, and C

(b) Determine the EOQ for each item (round to the nearest whole unit)

Pr 28 (608)

Problem 28 (608)

Regional supermarket is open 360 days per year. Daily use of cash register tape

averages 10 rolls. Usage appears normally distributed with a standard deviation of 2

rolls per day. The cost of ordering tape is $1, and acrrying costs are $0.40 per roll.

a year. Lead time is three dayss.

(a) What is the EOQ?

(b) What ROP will provide a lead time service level of 96%?

What is the expected number of units short per cycle with 96%? Per year?

(d) What is the annual service level?

Pr 13 (605)

Problem 13 (587)

A mail-order house uses 18,000 boxes a year. Carrying costs are 20 cents per year per box,

and ordering costs are $32. The following price schedule applies. Determine:

Number of BoxesPrice per Box

1000 to 19991.25

2000 to 49991.2

5000 to 99991.18

10000 or more1.15

(a) The optimal order quantity

(b) The number of orders per year

Pr 11 (605)

Problem 11 (605)

A company is about to begin production of a new product. The manager of the

department that will produce one of the components for the product wants to know

how often the machine used to produce the item will be available for other work.

The machine will produce the item at a rate of 200 units per day. Eighty units will

be used daily in assembling the final product . Assembly will take place 5 days a

week, 50 weeks per year. The manager estimates that it will take almost a full day

to get the machine ready for production run, at a cost of $60.

Inventory holding costs will be $2 a year.

(a) What run quantity should be used to minimize total annual cost?

(b) What is the length of a production run in days?

During production, at what rate will inventory build up?

(d) If the manager wants to run another job between runs of this item, and

needs a minimum of 10 days per cycle for the other work, will there be enough time?

_1227942322.xlsPr 2(603)

Problem 2(603)




ItemUnit CostUsage

K3410200

K3525600

K3636150

M101625

M202080

Z4580200

F1420300

F9530800

F992060

D4510550

D481290

D5215110

D5740120

N083040

P0516500

P091030

Pr 3 (603)

Problem 3(603)










Pr 40 (610)

Problem 40 (610)




DemandFrequency

00.30

10.20

20.20

30.15

40.10

40.05

1.00









Pr 33 (609)

Problem 33 (590)



DSP

H4-010200005020%2.5

H5-201602006020%4

P6-40098008030%28.5

P6-401163005030%12

P7-10062505030%9

P9-10345005040%22

TS-300210004025%45

TS-400450004025%40

TS-0418004025%20

V1-001261002535%40



Pr 28 (608)

Problem 28 (608)









Pr 13 (605)

Problem 13




1000 to 19991.25

2000 to 49991.2

5000 to 99991.18

10000 or more1.15



Pr 11 (605)

Problem 11 (605)














_1227943321.unknown

_1227942299.xlsPr 2(603)

Problem 2(603)




ItemUnit CostUsage

K3410200

K3525600

K3636150

M101625

M202080

Z4580200

F1420300

F9530800

F992060

D4510550

D481290

D5215110

D5740120

N083040

P0516500

P091030

Pr 3 (603)

Problem 3(603)










Pr 40 (610)

Problem 40 (610)




DemandFrequency

00.30

10.20

20.20

30.15

40.10

40.05

1.00









Pr 33 (609)

Problem 33 (609)



DSP

H4-010200005020%2.5

H5-201602006020%4

P6-40098008030%28.5

P6-401163005030%12

P7-10062505030%9

P9-10345005040%22

TS-300210004025%45

TS-400450004025%40

TS-0418004025%20

V1-001261002535%40



Pr 28 (608)

Problem 28 (589)

A regional supermarket is open 360 days per year. Daily use of cash register tape


rolls per day. The cost of ordering tape is $1, and carrying costs are $0.40 per roll.

a year. Lead time is three days.





Pr 13 (605)

Problem 13




1000 to 19991.25

2000 to 49991.2

5000 to 99991.18

10000 or more1.15



Pr 11 (605)

Problem 11 (605)














_1227942266.xlsPr 2(603)

Problem 2(603)




ItemUnit CostUsage

K3410200

K3525600

K3636150

M101625

M202080

Z4580200

F1420300

F9530800

F992060

D4510550

D481290

D5215110

D5740120

N083040

P0516500

P091030

Pr 3 (603)

Problem 3(603)










Pr 40 (610)

Problem 40 (610)




DemandFrequency

00.30

10.20

20.20

30.15

40.10

40.05

1.00









Pr 33 (609)

Problem 33 (609)



DSP

H4-010200005020%2.5

H5-201602006020%4

P6-40098008030%28.5

P6-401163005030%12

P7-10062505030%9

P9-10345005040%22

TS-300210004025%45

TS-400450004025%40

TS-0418004025%20

V1-001261002535%40



Pr 28 (608)

Problem 28 (608)









Pr 13 (605)

Problem 13




1000 to 19991.25

2000 to 49991.2

5000 to 99991.18

10000 or more1.15



Pr 11 (605)

Problem 11 (586)








Inventory holding costs will be $2 per unit per year.






_1227942242.xlsPr 2(603)

Problem 2(585)




ItemUnit CostUsage

K3410200

K3525600

K3636150

M101625

M202080

Z4580200

F1420300

F9530800

F992060

D4510550

D481290

D5215110

D5740120

N083040

P0516500

P091030

Pr 3 (603)

Problem 3(603)






How many order per year will there be?




Pr 40 (610)

Problem 40 (610)




DemandFrequency

00.30

10.20

20.20

30.15

40.10

40.05

1.00









Pr 33 (609)

Problem 33 (609)



DSP

H4-010200005020%2.5

H5-201602006020%4

P6-40098008030%28.5

P6-401163005030%12

P7-10062505030%9

P9-10345005040%22

TS-300210004025%45

TS-400450004025%40

TS-0418004025%20

V1-001261002535%40



Pr 28 (608)

Problem 28 (608)









Pr 13 (605)

Problem 13




1000 to 19991.25

2000 to 49991.2

5000 to 99991.18

10000 or more1.15



Pr 11 (605)

Problem 11 (605)














_1155033026.unknown

_1093160979.unknown

_1093161004.unknown

_1093160949.unknown

_1093160877.unknown

_1093160910.unknown

_1093086707.xlsChart1

1111

0.70.80.90.99

0.56818033980.70210370280.84620598630.9841967965

0.490.640.810.9801

0.43684642620.59563734360.78298672170.9769340252

0.39772623780.56168296220.76158538770.9743548286

0.36739667390.53448952470.7439478340.972179462

0.3430.5120.7290.970299

0.32282889850.49294960950.71606457130.9686433343

0.30579249840.47650987490.70468804950.9671646849

0.29115701740.46211113870.69455251840.9658290284

0.27840836650.44934636980.68542684890.9646112803

0.26717427210.43791552170.67713796580.9634924165

0.25717767170.42759161970.66955305060.9624576674

0.24820755090.41819918450.66256805110.961495338

0.24010.40960.65610.96059601

0.2327

Documents

BA 380 Lecture Notes Packet 2005