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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_1155038269.xlsChart3
0.004432
0.005953
0.007915
0.010421
0.013583
0.017528
0.022395
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0.035475
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0.053991
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0.396953
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0.381388
0.36827
0.352065
0.333225
0.312254
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0.241971
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0.035475
0.028327
0.022395
0.017528
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0.010421
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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)
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 (590)
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
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?
_1227943321.unknown
_1227942299.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 (589)
A 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 carrying costs are $0.40 per roll.
a year. Lead time is three days.
(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
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?
_1227942266.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
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 (586)
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 per unit per 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?
_1227942242.xlsPr 2(603)
Problem 2(585)
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?
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
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?
_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
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