Chapter 1 Introduction

1.1 What Is Management Science? Management Science is the discipline that adapts the scientific approach for problem solving to help managers make informed decisions. The goal of management science is to recommend the course of action that is expected to yield the best outcome with what is available.

1.1 What Is Management Science? The basic steps in the management science problem solving process involves Analyzing business situations and building mathematical models to describe them; Solving the mathematical models; Communicating/implementing recommendations based on the models and their solutions.

The Management Science Approach A scientific method of providing executive departments with a quantitative basis for decisions regarding operations (Philip McCord Morse). Logic and common sense are basic components in supporting the decision making process. The use of techniques such as (US army pamphlet 660-3): Statistical inference Mathematical programming Probabilistic models Network and computer science

Management Science Applications Linear Programming was used by Burger King to find how to best blend cuts of meat to minimize costs. Integer Linear Programming model was used by American Air Lines to determine an optimal flight schedule. The Shortest Route Algorithm was implemented by the Sony Corporation to developed an onboard car navigation system.

Management Science Applications Project Scheduling Techniques were used by a contractor to rebuild Interstate 10 damaged in the 1994 earthquake in the Los Angeles area. Decision Analysis approach was the basis for the development of a comprehensive framework for planning environmental policy in Finland. Queuing models are incorporated into the overall design plans for Disneyland and Disney World, which lead to the development of ‘waiting line entertainment’ in order to improve customer satisfaction.

1.3 Mathematical Modeling Many managerial decision situations lend themselves to quantitative analyses. A constrained mathematical model consists of An objective One or more constraints

1.3 Mathematical Modeling Example NewOffice Furniture produces three products Desks (D) Chairs (C) Molded steel (M) Net profit is $50 per desk $30 per chair $6 per pound of molded steel sold Raw material required 7 pounds of per desk 3 pounds of per chair 1.5 pounds per one pound of molded steel produced. Raw material available 2000 pounds

1.3 Mathematical Modeling Objective: Determine production mix that maximizes the profit under the raw material constraint and other production requirements (detailed next). Maximize 50D + 30C + 6 M Subject to 7D + 3C + 1.5M £ 2000 (raw steel) D ³ 100 (contract ) C £ 500 (cushions available) D, C, M ³ 0 (Non-negativity) D and C are integers

Classification of Mathematical Models Classification by the model purpose Optimization models Prediction models Classification by the degree of certainty of the data in the model Deterministic models Probabilistic (stochastic) models

The Management Science Process Management Science is a discipline that adopts the scientific method to provide management with key information needed in making informed decisions. The team concept calls for the formation of (consulting) teams consisting of members who come from various areas of expertise.

The Management Science Process The four-step management science process (for details click on each button) Problem definition Mathematical modeling Solution of the model Communication/implementation of results

1.6 Using Spreadsheets in Management Science Models Spreadsheets have become a powerful tool in management science modeling. Several reasons for the popularity of spreadsheets: Data are submitted to the modeler in spreadsheets Data can be analyzed easily using statistical and mathematical tools readily available in the spreadsheet. Data and information can easily be displayed using graphical tools.

Basic Excel functions and operators Arithmetic Operations Addition of cells A1and B1: Subtracting cell B1 from A1: Multiplication of cell A1 by B1: Division of cell A1 by B1: Cell A1xraised to the power in cell B1: = A1 + B1 = A1 - B1 = A1 * B1 = A1 / B1 = A1^ B1

Basic Excel functions and operators Relative and absolute addresses All row and column references are considered relative unless preceded by a “$” sign When copied, ‘relative addresses’ change relative to the original cell position. Example: Cell E5 =A1+B$3+$C4+$D$6 Cell G9 = C5+D$3+$C8+$D$6

Basic Excel functions and operators The F4 key Pressing F4 will automatically put a $ sign in highlighted portions of formulas. Specific operations: Press the F4 key once: The sign “$” appears in front of all rows and columns of the highlighted area of the formula. Press the F4 key twice: The “$” sign appears in front of only the row references of the highlighted area of the formula. Press the F4 key third time: The “$” sign appears in front of only the column references of the highlighted area of the formula. Press the F4 key forth time: All the “$” signs are eliminated.

Basic Excel functions and operators Arithmetic functions Sum =SUM(A1:A3) Returns the sum A1+A2+A3 Average =Average(A1:A3) Returns the arithmetic average of cells A1, A2, A3 SUMPRODUCT =SUMPRODUCT(A1:A3,B1:B3) Returns the sum of products A1·B1+A2·B2+A3·B3 ABS =ABS(A3) Returns the absolute value of the entry in cell A3.

Basic Excel functions and operators Arithmetic functions – continued SQRT =SQRT(A3) Returns ÖA3 MAX =MAX(A1:A9) Returns the Maximum of the entries in cells A1 through A9. MIN =MIN(A1:A9) Returns the Minimum of the entries in cells A1 through A9.

Basic Excel functions and operators Statistical functions RAND() =RAND() Generate a random number between 0 and 1 from a uniform distribution. Probabilities and variable values under the normal distribution NORMDIST NORMINV =NORMDIST(25,20,3,TRUE) =NORMINV(.55,20,3) Returns P(X<25) when m = 20 Returns x0,, such that P(X<x0)=.55 and s = 3 when m = 20 and s = 3 NORMSDIST NORMSMINV =NORMSDIST(1.78) =NORMSINV(.55) Returns P(Z<1.78) Returns z0, such that P(Z<z0)=.55

Basic Excel functions and operators Statistical functions Probabilities and variable values under the t- distribution TDIST TINV =TDIST(1.5,12,1) =TINV(.05,15) Returns P(t>1.5) when n=12 Returns t0,, such that P(t<-t0)=.025 and P(t>t0)=.025 when n=15. Note: =TDIST(1.5,12,2) returns P(t<-1.5) + P(t>1.5) when n=12.

Basic Excel functions and operators Statistical functions – Other probability distributions Poisson =POISSON(7,5,TRUE) Returns P(X<7) for Poisson with l = 5. Note: false returns the probability density P(X = 7) EXPONDIST =EXPONDIST(40,1/20,TRUE) Returns P(X<40) for the exponential distribution with 1/m=20 Note: false returns the probability density f(40)=20exp(-20(40))

Basic Excel functions and operators Conditional functions: IF =IF(A4>4,B1+B2, B1 – B2) Returns B1+B2 if A4>4, and B1 – B2 if A4£4. SUMIF =SUMIF(F1:F12, “>60”,G1:G12) Returns G1+G2+…+G12 only if F1+F2+…+F12>60

Basic Excel functions and operators VLOOKUP =VLOOKUP(6.6,A1:E6,4) If the values in column A of a given table [A1:E6] are sorted (in an ascending order), VLOOKUP finds the largest value in column A that is less than or equal to 6.6, identifies the row it belongs to, and returns the value in the fourth column that correspond to this row. Note: If the values in column A are not sorted, =VLOOKUP(6.6,A1:E6,4,FALSE) finds the value 6.6 in column A, identifies the row it belongs to, and returns the value in the fourth column that corresponds to this row.

Basic Excel functions and operators Statistical/Optimization Data Analysis [Selected from the Tools menu]. Useful entries: Descriptive Statistics Regression Exponential Smoothing Anova

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