OPERATIONS RESERCH(OR)/ MANAGEMENT SCIENCE(MS)

OPERATIONS RESERCH(OR)/ MANAGEMENT SCIENCE(MS) Department of Industrial Engineering and Management 02, 2004 Instructor : Ching-Fang Liaw E-mail Address : cfliaw@mail.cyut.edu.tw Office : E-503 Office Hour : Tue, Thu: 10:30 ~ 12:00

1. Course Description: The purpose of this course is to introduce Operations Research (OR) / Management Science (MS) techniques for manufacturing, services, and public sector. OR/MS includes a variety of techniques used in modeling business applications for both better understanding the system in question and making best decisions.

OR/MS techniques have been applied in many situations, ranging from inventory management in manufacturing firms to capital budgeting in large and small organizations. Public and Private Sector Applications

The main objective of this course is to provide engineers with a variety of decisional tools available for modeling and solving problems in a real business and/or nonprofit context. In this class, each individual will explore how to make various business models and how to solve them effectively.

2. Text andReferences : Text: (1) Hillier and Lieberman Introduction to Operations Research (2001), Seven Edition, McGraw-Hill. （滄海） (2) 潘昭賢葉瑞徽譯作業研究(上) (2003) （滄海）

References : (1) Lawrence and Pasternack Applied Management Science (2001) Second Edition, John Wiley&Sons. （西書） (2) Hillier, Hillier and Lieberman, Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets (2000), McGraw-Hill . （華泰）

3. Grading: Quizzes 40% Midterm 25% Final 25% Homework/Attendance 10% ======================== Total 100%

4. Topic Outline: UnitTopic(s) 1 Introduction and Overview 2 Linear Programming Formulation 3 Solving Linear Programming 4 Theory of Simplex 5 Duality Theory 6 Project Scheduling: PERT-CPM 7 Game Theory

UnitTopic(s) 8 Decision Analysis 9 Markov Chain Model 10 Queuing Theory 11 Inventory Theory 12 Forecasting 13 Simulation

Linear Programming (LP): A mathematical method that consists of an objective function and many constraints. LP involves the planning of activities to obtain an optimal result, using a mathematical model, in which all the functions are expressed by a linear relation.

A standard Linear Programming Problem Maximize subject to Applications: Man Power Design, Portfolio Analysis

Simplex method: A remarkably efficient solution procedure for solving various LP problems. Extensions and variations of the simplex method are used to perform postoptimality analysis (including sensitivity analysis).

(a) Algebraic Form (0) (1) (2) (3) (b) Tabular Form Coefficient of: Basic Variable Eq. Right Side Z (0) 1 -3 -5 0 0 0 0 0 1 0 1 0 0 0 0 2 0 0 1 0 12 0 3 2 0 0 1 18 (1) (2) (3)

Duality Theory: An important discovery in the early development of LP is Duality Theory. Each LP problem, referred to as ” a primal problem” is associated with another LP problem called “a dual problem”. One of the key uses of duality theory lies in the interpretation and implementation of sensitivity analysis.

Primal Problem Dual Problem Maximize Minimize subject to subject to for i = 1, 2,…, m for j = 1, 2,…, n for j = 1, 2,…, n. for i = 1, 2,…, m.

PERT (Program Evaluation and Review Technique)-CPM (Critical Path Method): PERT and CPM have been used extensively to assist project managers in planning, scheduling, and controlling their projects. Applications: Project Management, Project Scheduling

START 0 Critical Path 2 + 4 + 10 + 4 + 5 + 8 + 5 + 6 = 44 weeks A 2 B 4 10 C D 6 I 7 4 E 5 F G 7 8 J H 9 L K 4 5 M 2 N 6 FINISH 0

Game Theory: A mathematical theory that deals with the general features of competitive situations (in which the final outcome depends primarily upon the combination of strategies selected by the opponent).

Each player shows either one finger or two fingers. If the total number is even, player 1 wins the bet $1 to player 2. If the total number is odd, then player 1 pays $1 to player 2. Payoff table for the odds and evens game Player 2 Strategy 1 2 1 2 1 -1 -1 1 Player 1 Applications: Corporate Scheduling, Group Ware, Strategy

Decision Analysis: An important technique for decision making in uncertainty. It divides decision making between the cases of without experimentation and with experimentation. Applications: Decision Making, Planning

decision fork chance fork Drill Oil 0.14 f Unfavorable 0.7 c 0.85 Dry Sell b Do seismic survey Oil 0.5 g Drill 0.3 Favorable 0.5 Dry d Sell a Oil 0.25 h Drill 0.75 Dry e No seismic survey Sell

Markov Chain Model: A special kind of a stochastic process. It has a special property that probabilities, involving how a process will evolve in future, depend only on the present state of the process, and so are independent of events in the past. Applications: Inventory Control, Forecasting

Suppose that two players (A and B), each having $2, agree to keep playing the game and betting $1 at a time until one player is broke. The probability of A winning: The probability of B winning: State 0 1 2 3 4 0 1 2 3 4

Queueing Theory: This theory studies queueing systems by formulating mathematical models of their operation and then using these models to derive measures of performance.

This analysis provides vital information for effectively designing queueing systems that achieve an appropriate balance between the cost of providing a service and the cost associated with waiting for the service.

Served customers Queueing system Queue S S Service S facility S C C C C Customers C C C C C C Served customers Applications: Waiting Line Design, Banking, Network Design

Inventory Theory: This theory is used by both wholesalers and retailers to maintain inventories of goods to be available for purchase by customers. The just-in-time inventory system is such an example that emphasizes planning and scheduling so that the needed materials arrive “just-in-time” for their use. Applications: Inventory Analysis, Warehouse Design

Economic Order Quantity (EOQ) model Inventory level Batch size Time t

Forecasting: When historical sales data are available, statistical forecasting methods have been developed for using these data to forecast future demand. Several judgmental forecasting methods use expert judgment. Applications: Future Prediction, Inventory Analysis

The evolution of the monthly sales of a product illustrates a time series 10,000 8,000 6,000 4,000 2,000 0 Monthly sales (units sold) 1/99 4/99 7/99 10/99 1/00 4/00 7/00

Simulation: This technique is widely used for estimating the performance of complex stochastic systems if contemplated designs or operating policies are to be used. Applications: Risk Analysis, Future Prediction

Outcome of the simulation run for a queueing system 4 3 2 1 0 Number of customers Cycle 1 C.2 Cycle 3 C.4 C.5 Time

Introduction to MS/OR MS: Management Science OR: Operations Research Key components: (a) Modeling/Formulation (b) Algorithm (c) Application

OR/MS: (1) A discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. (2) OR/MS is based upon mathematics, computer science and other social sciences like economics and business.

General Steps of OR/MS: Step 1: Define problem and gather data Step 2: Formulate a mathematical model to represent the problem Step 3: Develop a computer based procedure for deriving a solution(s) to the problem

Step 4: Test the model and refine it as needed Step 5: Apply the model to analyze the problem and make recommendation for management Step 6: Help implementation

Origin of OR/MS: WWII: The British and U.S. Military Operations The Simplex Method: George Dantzig, 1947 Computer Revolution (Hardware/Software).

OPERATIONS RESERCH(OR)/ MANAGEMENT SCIENCE(MS)