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Spreadsheet Models for Managers: Session 3 3/1 Copyright © Richard Brenner Spreadsheet Models for Managers Session 3 Cushioning, Crowding and Quantization Worksheet Functions Circular References Implicit Intersection Last revised: July 6, 2011
Spreadsheet Models for Managers: Session 3 3/2 Copyright © Richard Brenner Review of last time: Analysis and Synthesis Analysis and Synthesis Decomposing and Recombining Arrays often result — array manipulation required Techniques of array manipulation Array arithmetic (+, -, *, /, ^,...) Matrix arithmetic ( MMULT, TRANSPOSE ) Use Matrix arithmetic when you want to perform a synthesis Use Array arithmetic between analysis and synthesis
Spreadsheet Models for Managers: Session 3 3/3 Copyright © Richard Brenner Why conservative modeling? Modeling is inexact The validity of a model is based on plausibility, not proof Parameters of a model are either guessed or measured In either case, true values are rarely known exactly The system you’re modeling is a moving target What was once well-understood may evolve out from underneath your model Some sources of change (there are many more) Competitive environment Legal environment Technological advances Customer behavior and requirements Your own organization For these reasons we often build safety cushions into models
Spreadsheet Models for Managers: Session 3 3/4 Copyright © Richard Brenner Cushioning Even when you can find an optimum solution: You might still want to a safety margin or cushion You might not know the initial conditions exactly Examples Cash reserves greater than the model predicts you need Extra staff, stock or other resources during periods of high volume Leasing more space than needed to allow for faster expansion Cushioning is the practice of including safety margins in models to mitigate the effects of approximations and change
Spreadsheet Models for Managers: Session 3 3/5 Copyright © Richard Brenner Crowding Examples Plan for doubling up in offices Planned shortages in computer equipment Planned shortages of staff — planned overtime Planned wages or salaries below prevailing rates — planned turnover Usually, this is bad business But when you have to do it, it’s good to know how Crowding is the opposite of cushioning — you intentionally plan for resources smaller than needed
Spreadsheet Models for Managers: Session 3 3/6 Copyright © Richard Brenner Quantization Sometimes vendors require orders in discrete units No “odd lots” Full trailer load, full roll of carpet, full cases Also for labor: full week, full shift Buildings, vehicles, people are not available in fractional units (except by time- share) Minimum quantity requirements To get what you need, you must sometimes acquire more (or less) than you need Quantization occurs when resources are available in discrete units, or when attributes change discontinuously
Spreadsheet Models for Managers: Session 3 3/7 Copyright © Richard Brenner Computational issues The difference between what you actually need and what you plan for is the planned margin Planned margins Can be additive or multiplicative Can be constant Size can depend on base value, time, or some other quantity When the model describes temporal behavior Planned margin can vary with time Planned margin can depend on This period Previous, next, or other period When there is dependence on “this period,” watch out for circular reference errors (more on this later)
Spreadsheet Models for Managers: Session 3 3/8 Copyright © Richard Brenner Excel functions for cushions, crowding and quantization CEILING ( number, significance ) Returns nearest integer multiple of significance on other side of number from 0 number and significance must have the same sign FLOOR ( number, significance ) Returns nearest multiple of significance between 0 and number number and significance must have the same sign INT ( number ) Returns most positive integer closest to number ROUND ( number, numberOfDigits ) Returns multiple of 10 -numberOfDigits that is closest to number TRUNC ( number, numberOfDigits ) Returns multiple of 10 -numberOfDigits that is closest to number, between number and 0 MROUND ( number, base ) Returns number rounded to the nearest multiple of base number and base must have the same sign See On Line Help ExcelFunctions
Spreadsheet Models for Managers: Session 3 3/9 Copyright © Richard Brenner Modeling techniques for cushions You’re planning purchase of trucks for a utility company fleet. You want to make sure that you always have enough trucks ready to roll. If the number you need is N, you can pad N with: A constant integer N+Pad A computed integer ROUND(N*(1+Pad),0) gives an integer cushion such that result is a constant percentage greater than the computed value A time-dependent pad N+ Here we compute the actual value in
Spreadsheet Models for Managers: Session 3 3/10 Copyright © Richard Brenner Circular reference errors Spreadsheets calculate the value in a cell by first computing values of cells it depends on If this leads back to the original cell, we say there is a “circular reference” Most spreadsheets cannot deal with circular references Excel has an iterative recalculation mode Generally, performance is so poor that you should avoid using it Circular reference errors are more frequent when the cushioning or crowding factor depend on the previous or next period
Spreadsheet Models for Managers: Session 3 3/11 Copyright © Richard Brenner Unwinding circular references Simple case: Y = 3 - X X = 1 + Y These are simple, linear simultaneous equations The solution is X = 2, Y = 1 If you implement X and Y as cells, Excel cannot resolve the solution because you get a circular reference error Best approach: solve the equations, then implement that solution
Spreadsheet Models for Managers: Session 3 3/12 Copyright © Richard Brenner Unwinding circular references, continued In most common cases, dependencies are linear: Cash on hand Cash before interest expense New debt Cumulative prior debt Cash minimum Interest rate per period If new debt is required: If new debt is not required: To eliminate circularity, solve equations symbolically OH C N D CP D MIN C o C N D = 0 N - i(D + CP D ) o C OH C = N - i(D + CP D ) o C OH C =+ MIN C N D = N - i(D + CP D )) o C MIN C N D = - (
Spreadsheet Models for Managers: Session 3 3/13 Copyright © Richard Brenner Examples Ordering fleet vehicles with various planned margin strategies Simple circularity Diagram of a more complex circularity Minimum cash on hand with circularity Example1 Example2 Example3 Example4
Spreadsheet Models for Managers: Session 3 3/14 Copyright © Richard Brenner Implicit intersection Excel interprets non-array formulas that refer to ranges using a technique called “implicit intersection” If the formula is an array formula, the interpretation proceeds normally. Otherwise Excel retrieves the value of the leftmost (topmost) cell in the independent range that is in the same row (column) as the dependent cell If there is no such cell, a #VALUE error occurs ImplicitIntersection
Spreadsheet Models for Managers: Session 3 3/15 Copyright © Richard Brenner Preview of next time: Temporal Response Excel functions for accessing array elements: INDEX, OFFSET References can be combined to produce new references using reference operators: Colon, Comma and Space Time evolution and temporal response model business processes Convolution applies when system behavior is time-independent and additive The Convolve macro implements convolution Also implement convolution with tables Special Note: Read the session notes for Session 4 to prepare
Spreadsheet Models for Managers: Session 2 2/1 Copyright © Richard Brenner Spreadsheet Models for Managers Session 2 Analysis and Synthesis Array.
Spreadsheet Models for Managers: Session 4 4/1 Copyright © Richard Brenner Spreadsheet Models for Managers Session 4 Temporal Response Array.
Spreadsheet Models for Managers: Session 5 5/1 Copyright © Richard Brenner Spreadsheet Models for Managers Session 5 Course Project Proposals.
Formulas, Ranges, and Functions. Formulas n Formulas perform operations such as addition, multiplication, and comparison on worksheet values. n Formulas.
Spreadsheet Models for Managers: Session 14 14/1 Copyright © Richard Brenner Spreadsheet Models for Managers Session 14 Using Macros II Function.
Example 5.8 Non-logistics Network Models | 5.2 | 5.3 | 5.4 | 5.5 | 5.6 | 5.7 | 5.9 | 5.10 | 5.10a a Background Information.
1 1.1 © 2012 Pearson Education, Inc. Linear Equations in Linear Algebra SYSTEMS OF LINEAR EQUATIONS.
Table of Contents Chapter 5 (What-If Analysis for Linear Programming) Continuing the Wyndor Case Study (Section 5.2)5.2 Changes in One Objective Function.
Chapter 4 Linear Programming Models. Example 4.1 – Advertising Model General Flakes Company advertises a low-fat breakfast cereal in a variety of 30 second.
Lesson 08 Linear Programming A mathematical approach to determine optimal (maximum or minimum) solutions to problems which involve restrictions.
Chapter 9: Simulation Spreadsheet-Based Decision Support Systems Prof. Name Position (123) University Name.
Spreadsheets Objective 6.02 Explain advanced spreadsheet concepts and functions Advanced Calculations.
Chapter 3 MATLAB Fundamentals Working with Arrays in MATLAB Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Pre-defined System Functions Simple IF & VLOOKUP.
Cost Behavior Cost Objects An item for which managers want cost information For manufacturing or merchandising firms, it is usually the tangible.
Hashing General idea: Get a large array Design a hash function h which converts keys into array indices. Insert (key, value) in the array at h(key) position.
1 Compiler Construction (CS-636) Muhammad Bilal Bashir UIIT, Rawalpindi.
Syntax MROUND(number,multiple) Number is the value to round. Multiple is the multiple to which you want to round number. Remark MROUND rounds up, away.
Computer Programming (TKK-2144) 13/14 Semester 1 Instructor: Rama Oktavian Office Hr.: M.13-15, W Th , F
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Blank & Tarquin: 5 th edition. Ch.13 Authored by Dr. Don Smith,
2 Explain advanced spreadsheet concepts and functions Advanced Calculations 1 Sabbir Saleh_Lecture_17_Computer Application_BBA.
Chapter 4 Linear Regression 1. Introduction Managerial decisions are often based on the relationship between two or more variables. For example, after.
Linear Programming McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
4-2 How can you create matrices ? How do the back-slash \ and * operators work with matrices? Understand how to subscript matrices. Use the built-in functions.
Aggregate Planning. Session Break Up Aggregate Planning Master Production Schedule.
Cost-Volume-Profit Relationships. Learning Objective 1 Explain how changes in activity affect contribution margin and net operating income.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 8.3.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.1 Modeling and Equation Solving.
Chapter 3 Economic Order Quantity. Defining the economic order quantity.
MNG221- Management Science – Inventory Management.
EXCEL DECISION MAKING TOOLS AND CHARTS BASIC FORMULAE - REGRESSION - GOAL SEEK - SOLVER.
Microsoft Office XP Microsoft Excel. Entering Text and Numbers Formatting Text and Performing Mathematical Calculations Numbers and Mathematical Calculations.
2. Solving Schrödinger’s Equation Superposition Given a few solutions of Schrödinger’s equation, we can make more of them Let 1 and 2 be two solutions.
Chapter 5 Working with Multiple Worksheets and Workbooks Microsoft Excel 2013.
© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license.
Maths & Trig, Statistical functions. ABS Returns the absolute value of a number The absolute value of a number is the number without its sign Syntax ◦
Copyright © Cengage Learning. All rights reserved. Systems of Linear Equations and Inequalities in Two Variables 7.
Example 15.1 Daily Scheduling of Postal Employees Workforce Scheduling Models.
Chapter 1 Computing Tools Data Representation, Accuracy and Precision Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction.
Spreadsheet Models for Managers: Session 10 10/1 Copyright © Richard Brenner Spreadsheet Models for Managers Session 10 Capital Leases II: Modeling.
Excel Features That Would Help You Prepare Class Result.
CS212: DATA STRUCTURES Lecture 10:Hashing 1. Outline 2 Map Abstract Data type Map Abstract Data type methods What is hash Hash tables Bucket.
Jeopardy Moving Around Formulas Mean, Median, Mode, Range Final Jeopardy Function Words Mixed Bag $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.
30S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Personal Finance Lesson: Net Pay Net Pay Learning Outcome B-1 PF-L2 Objectives: Calculate.
Computational Biology, Part 17 Biochemical Kinetics I Robert F. Murphy Copyright 1996, All rights reserved.
Chapter 7 Matrix Mathematics Matrix Mathematics in MATLAB and Excel Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or.
1) the value you want to look up Vlookups are really easy......just remember you need 4 things: 2) The table range you want to look up to 3) The column.
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