Quantitative Methods for Business

by Anderson,David R.

• ISBN13: 9780324184136
• ISBN10: 0324184131
• Format: Hardcover
• Copyright: 2003-04-04
• Publisher: Cengage Learning

Summary

This revision of QUANTITATIVE METHODS FOR BUSINESS provides students with a conceptual understanding of the role that quantitative methods play in the decision-making process. This text describes the many quantitative methods that have been developed over the years, explains how they work, and shows how the decision-maker can apply and interpret data. Written with the non-mathematician in mind, this text is applications-oriented. Its "Problem-Scenario Approach" motivates and helps students understand and apply mathematical concepts and techniques. In addition, the managerial orientation motivates students by using examples that illustrate situations in which quantitative methods are useful in decision making.

Table of Contents

Preface	xiii
About the Authors	xviii
Introduction	1	(29)
Problem Solving and Decision Making	3	(1)
Quantitative Analysis and Decision Making	4	(2)
Quantitative Analysis	6	(8)
Model Development	7	(3)
Data Preparation	10	(1)
Model Solution	11	(1)
Report Generation	12	(1)
A Note Regarding Implementation	12	(2)
Models of Cost, Revenue, and Profit	14	(3)
Cost and Volume Models	14	(1)
Revenue and Volume Models	15	(1)
Profit and Volume Models	15	(1)
Breakeven Analysis	16	(1)
Quantitative Methods in Practice	17	(13)
Methods Used Most Frequently	17	(2)
Summary	19	(1)
Glossary	19	(1)
Problems	20	(3)
Appendix 1.1 The Management Scientist Software	23	(3)
Appendix 1.2 Using Excel for Breakeven Analysis	26	(4)
Introduction to Probability	30	(30)
Experiments and the Sample Space	32	(1)
Assigning Probabilities to Experimental Outcomes	33	(2)
Classical Method	33	(1)
Relative Frequency Method	34	(1)
Subjective Method	34	(1)
Events and Their Probabilities	35	(1)
Some Basic Relationships of Probability	36	(8)
Complement of an Event	36	(1)
Addition Law	37	(2)
Conditional Probability	39	(4)
Multiplication Law	43	(1)
Bayes' Theorem	44	(16)
The Tabular Approach	48	(2)
Summary	50	(1)
Glossary	50	(1)
Problems	50	(8)
Case Problem Hamilton County Judges	58	(2)
Probability Distributions	60	(38)
Random Variables	61	(1)
Discrete Random Variables	62	(5)
Probability Distribution of a Discrete Random Variable	63	(1)
Expected Value	64	(1)
Variance	65	(2)
Binomial Probability Distribution	67	(4)
Nastke Clothing Store Problem	67	(2)
Expected Value and Variance for the Binomial Distribution	69	(2)
Poisson Probability Distribution	71	(2)
An Example Involving Time Intervals	72	(1)
An Example Involving Length or Distance Intervals	72	(1)
Continuous Random Variables	73	(3)
Applying the Uniform Distribution	74	(1)
Area as a Measure of Probability	75	(1)
Normal Probability Distribution	76	(8)
Standard Normal Distribution	78	(3)
Computing Probabilities for Any Normal Distribution	81	(1)
Grear Tire Company Problem	82	(2)
Exponential Probability Distribution	84	(14)
Computing Probabilities for the Exponential Distribution	85	(1)
Relationship Between the Poisson and Exponential Distributions	86	(1)
Summary	87	(1)
Glossary	87	(1)
Problems	88	(6)
Case Problem Specialty Toys	94	(2)
Appendix 3.1 Computing Discrete Probabilities with Excel	96	(1)
Appendix 3.2 Computing Probabilities for Continuous Distributions with Excel	97	(1)
Decision Analysis	98	(57)
Problem Formulation	100	(3)
Influence Diagrams	101	(1)
Payoff Tables	101	(1)
Decision Trees	102	(1)
Decision Making without Probabilities	103	(3)
Optimistic Approach	103	(1)
Conservative Approach	103	(1)
Minimax Regret Approach	104	(2)
Decision Making with Probabilities	106	(4)
Expected Value to Perfect Information	108	(2)
Risk Analysis and Sensitivity Analysis	110	(6)
Risk Analysis	111	(1)
Sensitivity Analysis	111	(5)
Decision Analysis with Sample Information	116	(10)
Influence Diagram	116	(1)
Decision Tree	117	(2)
Decision Strategy	119	(4)
Risk Profile	123	(2)
Expected Value of Sample Information	125	(1)
Efficiency of Sample Information	126	(1)
Computing Branch Probabilities	126	(29)
Summary	130	(2)
Glossary	132	(1)
Problems	133	(13)
Case Problem 1 Property Purchase Strategy	146	(1)
Case Problem 2 Lawsuit Defense Strategy	147	(1)
Appendix 4.1 Decision Analysis with TreePlan	148	(7)
Utility and Decision Making	155	(17)
The Meaning of Utility	156	(1)
Developing Utilities for Monetary Payoffs	157	(4)
The Expected Utility Approach	160	(1)
Summary of Steps for Determining the Utility of Money	161	(1)
Risk Avoiders versus Risk Takers	162	(3)
Expected Monetary Value versus Expected Utility as an Approach to Decision Making	165	(7)
Summary	166	(1)
Glossary	167	(1)
Problems	167	(5)
Forecasting	172	(51)
The Components of a Times Series	175	(2)
Trend Component	175	(1)
Cyclical Component	176	(1)
Seasonal Component	177	(1)
Irregular Component	177	(1)
Smoothing Methods	177	(9)
Moving Averages	177	(3)
Weighted Moving Averages	180	(1)
Exponential Smoothing	181	(5)
Trend Projection	186	(3)
Trend and Seasonal Components	189	(9)
The Multiplicative Model	190	(1)
Calculating the Seasonal Indexes	190	(4)
Deseasonalizing the Time Series	194	(1)
Using the Deseasonalized Time Series to Identify Trend	195	(2)
Seasonal Adjustments	197	(1)
Models Based on Monthly Data	197	(1)
Cyclical Component	198	(1)
Regression Analysis	198	(8)
Using Regression Analysis as a Causal Forecasting Method	198	(6)
Using Regression Analysis with Times Series Data	204	(2)
Qualitative Approaches	206	(17)
Delphi Method	206	(1)
Expert Judgment	206	(1)
Scenario Writing	206	(1)
Intuitive Approaches	206	(1)
Summary	207	(1)
Glossary	207	(1)
Problems	208	(10)
Case Problem 1 Forecasting Sales	218	(1)
Case Problem 2 Forecasting Lost Sales	219	(1)
Appendix 6.1 Using Excel for Forecasting	220	(3)
Introduction to Linear Programming	223	(60)
A Simple Maximization Problem	225	(5)
Problem Formulation	226	(3)
Mathematical Model for the RMC Problem	229	(1)
Graphical Solution Procedure	230	(13)
A Note on Graphing Lines	238	(2)
Summary of the Graphical Solution Procedure for Maximization Problems	240	(1)
Slack Variables	240	(3)
Extreme Points and the Optimal Solution	243	(1)
Computer Solution of the RMC Problem	244	(3)
Interpretation of Computer Output	245	(2)
A Simple Minimization Problem	247	(5)
Summary of the Graphical Solution Procedure for Minimization Problems	249	(1)
Surplus Variables	250	(1)
Computer Solution of the M&D Chemicals Problem	251	(1)
Special Cases	252	(4)
Alternative Optimal Solutions	252	(1)
Infeasibility	253	(2)
Unbounded	255	(1)
General Linear Programming Notation	256	(27)
Summary	258	(1)
Glossary	259	(1)
Problems	260	(13)
Case Problem 1 Advertising Strategy	273	(1)
Case Problem 2 Production Strategy	274	(1)
Case Problem 3 Hart Venture Capital	275	(1)
Appendix 7.1 Solving Linear Programs with The Management Scientist	276	(1)
Appendix 7.2 Solving Linear Programs with LINDO®	277	(1)
Appendix 7.3 Solving Linear Programs with Excel	278	(5)
Linear Programming: Sensitivity Analysis and Interpretation of Solution	283	(55)
Introduction to Sensitivity Analysis	285	(1)
Objective Function Coefficients	286	(5)
Simultaneous Changes	290	(1)
Right-Hand Sides	291	(8)
Simultaneous Changes	294	(2)
A Second Example	296	(2)
Cautionary Note on the Interpretation of Dual Prices	298	(1)
More Than Two Decisions Variables	299	(9)
Modified RMC Problem	299	(4)
Bluegrass Farms Problem	303	(5)
Electronic Communications Problem	308	(30)
Problem Formulation	309	(1)
Computer Solution and Interpretation	310	(3)
Summary	313	(1)
Glossary	314	(1)
Problems	315	(17)
Case Problem 1 Product Mix	332	(1)
Case Problem 2 Investment Strategy	333	(1)
Case Problem 3 Truck Leasing Strategy	334	(1)
Appendix 8.1 Sensitivity Analysis with Excel	335	(3)
Linear Programming Applications	338	(79)
Marketing Applications	339	(7)
Media Selection	340	(3)
Marketing Research	343	(3)
Financial Applications	346	(8)
Portfolio Selection	346	(4)
Financial Planning	350	(4)
Production Management Applications	354	(16)
A Make-or-Buy Decision	354	(4)
Production Scheduling	358	(8)
Workforce Assignment	366	(4)
Blending Problems	370	(4)
Data Envelopment Analysis	374	(8)
Evaluating the Performance of Hospitals	375	(1)
Overview of the DEA Approach	376	(1)
DEA Linear Programming Model	377	(5)
Summary of the DEA Approach	382	(1)
Revenue Management	382	(35)
Summary	388	(1)
Glossary	388	(1)
Problems	389	(15)
Case Problem 1 Environmental Protection	404	(2)
Case Problem 2 Phoenix Computer	406	(1)
Case Problem 3 Textile Mill Scheduling	407	(1)
Case Problem 4 Workforce Scheduling	408	(2)
Case Problem 5 Cinergy Coal Allocation	410	(3)
Appendix 9.1 Excel Solution of Hewlitt Corporation Financial Planning Problem	413	(4)
Transportation, Assignment, and Transshipment Problems	417	(49)
The Transportation Problem: The Network Model and a Linear Programming Formulation	418	(7)
Problem Variations	421	(3)
A General Linear Programming Model of the Transportation Problem	424	(1)
The Assignment Problem: The Network Model and a Linear Programming Formulation	425	(6)
Problem Variations	428	(1)
A General Linear Programming Model of the Assignment Problem	429	(1)
Multiple Assignments	429	(2)
The Transshipment Problem: The Network Model and a Linear Programming Formulation	431	(7)
Problem Variations	436	(1)
A General Linear Programming Model of the Transshipment Problem	437	(1)
A Production and Inventory Application	438	(28)
Summary	441	(1)
Glossary	442	(1)
Problems	442	(15)
Case Problem Distribution System Design	457	(2)
Appendix 10.1 Excel Solution of Transportation, Assignment, and Transshipment Problems	459	(7)
Integer Linear Programming	466	(47)
Types of Integer Linear Programming Models	468	(2)
Graphical and Computer Solutions for an All-Integer Program	470	(4)
Graphical Solution of the LP Relaxation	471	(1)
Rounding to Obtain an Integer Solution	471	(1)
Graphical Solution to the All-Integer Problem	472	(1)
Using the LP Relaxation to Establish Bounds	472	(2)
Computer Solution	474	(1)
Application Involving 0--1 Variables	474	(17)
Capital Budgeting	475	(1)
Fixed Cost	476	(3)
Distribution System Design	479	(3)
Bank Location	482	(4)
Product Design and Market Share Optimization	486	(5)
Modeling Flexibility Provided by 0--1 Integer Variables	491	(22)
Multiple-Choice and Mutually Exclusive Constraints	491	(1)
k Out of n Alternatives Constraint	492	(1)
Conditional and Corequisite Constraints	492	(2)
A Cautionary Note About Sensitivity Analysis	494	(1)
Summary	494	(1)
Glossary	495	(1)
Problems	496	(10)
Case Problem 1 Textbook Publishing	506	(1)
Case Problem 2 Yeager National Bank	507	(1)
Case Problem 3 Production Scheduling with Changeover Costs	508	(1)
Appendix 11.1 Excel Solution of Integer Linear Programs	509	(4)
Project Scheduling: PERT/CPM	513	(37)
Project Scheduling with Known Activity Times	514	(10)
The Concept of a Critical Path	515	(2)
Determining the Critical Path	517	(5)
Contributions of PERT/CPM	522	(1)
Summary of the PERT/CPM Critical Path Procedure	522	(2)
Project Scheduling with Uncertain Activity Times	524	(8)
The Daugherty Porta-Vac Project	524	(1)
Uncertain Activity Times	524	(3)
The Critical Path	527	(1)
Variability in Project Completion Time	528	(4)
Considering Time-Cost Trade-Offs	532	(18)
Crashing Activity Times	532	(2)
Linear Programming Model for Crashing	534	(3)
Summary	537	(1)
Glossary	538	(1)
Problems	538	(10)
Case Problem R. C. Coleman	548	(2)
Inventory Models	550	(49)
Economic Order Quantity (EOQ) Model	552	(9)
The How-Much-to-Order Decision	556	(1)
The When-to-Order Decision	557	(1)
Sensitivity Analysis for the EOQ Model	558	(1)
Excel Solution of the EOQ Model	559	(1)
Summary of the EOQ Model Assumptions	560	(1)
Economic Production Lot-Size Model	561	(3)
Total Cost Model	562	(2)
Economic Production Lot Size	564	(1)
Inventory Model with Planned Shortages	564	(5)
Quantity Discounts for the EOQ Model	569	(3)
Single-Period Inventory Model with Probabilistic Demand	572	(5)
Johnson Shoe Company	572	(3)
Nationwide Car Rental	575	(2)
Order-Quantity, Reorder Point Model with Probabilistic Demand	577	(4)
The How-Much-to-Order Decision	579	(1)
The When-to-Order Decision	579	(2)
Periodic Review Model with Probabilistic Demand	581	(18)
More Complex Periodic Review Models	584	(2)
Summary	586	(1)
Glossary	586	(1)
Problems	587	(8)
Case Problem 1 Wagner Fabricating Company	595	(1)
Case Problem 2 River City Fire Department	596	(1)
Appendix 13.1 Development of the Optimal Order Quantity (Q) Formula for the EOQ Model	597	(1)
Appendix 13.2 Development of the Optimal Lot-Size (Q*) Formula for the Production Lot-Size Model	598	(1)
Waiting Line Models	599	(41)
Structure of a Waiting Line System	601	(3)
Single-Channel Waiting Line	601	(1)
Distribution of Arrivals	601	(2)
Distribution of Service Times	603	(1)
Queue Discipline	604	(1)
Steady-State Operations	604	(1)
Single-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times	604	(5)
Operating Characteristics	604	(2)
Operating Characteristics for the Burger Dome Problem	606	(1)
Managers' Use of Waiting Line Models	606	(1)
Improving the Waiting Line Operation	607	(1)
Excel Solution of Waiting Line Model	608	(1)
Multiple-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times	609	(5)
Operating Characteristics	610	(1)
Operating Characteristics for the Burger Dome Problem	611	(3)
Some General Relationships for Waiting Line Models	614	(2)
Economic Analysis of Waiting Lines	616	(2)
Other Waiting Line Models	618	(1)
Single-Channel Waiting Line Model with Poisson Arrivals and Arbitrary Service Times	619	(2)
Operating Characteristics for the M/G/1 Model	619	(1)
Constant Service Times	620	(1)
Multiple-Channel Model with Poisson Arrivals, Arbitrary Service Times, and No Waiting Line	621	(3)
Operating Characteristics for the M/G/k Model with Blocked Customers Cleared	622	(2)
Waiting Line Models with Finite Calling Populations	624	(16)
Operating Characteristics for the M/M/1 Model with a Finite Calling Population	624	(3)
Summary	627	(1)
Glossary	628	(1)
Problems	629	(7)
Case Problem 1 Regional Airlines	636	(2)
Case Problem 2 Office Equipment, Inc.	638	(2)
Simulation	640	(60)
Risk Analysis	643	(13)
PortaCom Project	643	(1)
What-If Analysis	643	(2)
Simulation	645	(8)
Simulation of the PortaCom Problem	653	(3)
Inventory Simulation	656	(6)
Simulation of the Butler Inventory Problem	659	(3)
Waiting Line Simulation	662	(11)
Hammondsport Savings Bank ATM Waiting Line	662	(1)
Customer Arrival Times	662	(1)
Customer Service Times	663	(1)
Simulation Model	664	(3)
Simulation of the Hammondsport Savings Bank ATM Problem	667	(2)
Simulation with Two ATMs	669	(2)
Simulation Results with Two ATMs	671	(2)
Other Simulation Issues	673	(27)
Computer Implementation	673	(1)
Verification and Validation	674	(1)
Advantages and Disadvantages of Using Simulation	674	(1)
Summary	675	(1)
Glossary	676	(1)
Problems	677	(7)
Case Problem 1 Tri-State Corporation	684	(2)
Case Problem 2 Harbor Dunes Golf Course	686	(2)
Case Problem 3 County Beverage Drive-Thru	688	(1)
Appendix 15.1 Simulation with Excel	689	(6)
Appendix 15.2 Simulation of the PortaCom Problem Using Crystal Ball	695	(5)
Markov Processes	700	(24)
Market Share Analysis	702	(7)
Accounts Receivable Analysis	709	(15)
Fundamental Matrix and Associated Calculations	711	(1)
Establishing the Allowance for Doubtful Accounts	712	(2)
Summary	714	(1)
Glossary	715	(1)
Problems	716	(4)
Appendix 16.1 Matrix Notation and Operations	720	(4)
Multicriteria Decisions	724	(45)
Goal Programming: Formulation and Graphical Solution	725	(8)
Developing the Constraints and the Goal Equations	726	(2)
Developing an Objective Function with Preemptive Priorities	728	(1)
Graphical Solution Procedure	729	(3)
Goal Programming Model	732	(1)
Goal Programming: Solving More Complex Problems	733	(6)
Suncoast Office Supplies Problem	733	(1)
Formulating the Goal Equations	734	(1)
Formulating the Objective Function	735	(1)
Computer Solution	736	(3)
Scoring Models	739	(5)
Analytic Hierarchy Process	744	(2)
Developing the Hierarchy	745	(1)
Establishing Priorities Using AHP	746	(8)
Pairwise Comparisons	746	(2)
Pairwise Comparison Matrix	748	(1)
Synthesization	749	(1)
Consistency	750	(2)
Other Pairwise Comparisons for the Car Selection Problem	752	(2)
Using AHP to Develop an Overall Priority Ranking	754	(15)
Summary	755	(1)
Glossary	756	(1)
Problems	757	(9)
Case Problem EZ Trailers, Inc.	766	(1)
Appendix 17.1 Scoring Models with Excel	767	(2)
Appendixes	769	(47)
Appendix A Binomial Probabilities	770	(7)
Appendix B Poisson Probabilities	777	(6)
Appendix C Areas for the Standard Normal Distribution	783	(1)
Appendix D Values of e-λ	784	(1)
Appendix E References and Bibliography	785	(2)
Appendix F Self-Test Solutions and Answers to Even-Numbered Problems	787	(29)
Index	816