Operations Research

1. Operations Research The OR Process 2005.9.13 1

2. Lecture 1 – Operations Research • Topics • What is OR? • Modeling and the problem solving process • Deterministic vs. stochastic models • OR techniques • Using the Excel add-ins to find solutions • Solving real problems

3. Systems Approach Include broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered. Optimal Solution A solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. Team A group of individuals bringing various skills and viewpoints to a problem. Operations Research Techniques A collection of general mathematical models, analytical procedures, and algorithms.

4. What is OR? • It is a Process • It assists Decision Makers • It has a set of Tools • It is applicable in many Situations

5. Definition of OR? OR professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.

6. The Process: Recognize the Problem • Manufacturing • Planning • Design • Scheduling • Dealing with Defects • Dealing with Variability • Dealing with Inventory • …

7. Service Industries Logistics Transportation Environment Health Care Situations with complexity Situations with uncertainty Other applications

8. Problem Solving Process Goal: solve a problem Model must be valid Model must be tractable Solution must be useful

9. Define the problem Delimit the system Select measures Determine variables Identify constraints Formulate the Problem

10. The Situation • May involve current operations or proposed expansions due to expected market shifts • May become apparent through consumer complaints or through employee suggestions • May be a conscious effort to improve efficiency or response to an unexpected crisis. Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.

11. Define variables Define constraints Data requirements Problem Formulation • Describe system • Define boundaries • State assumptions • Select performance measures Example: Maximize individual nurse preferences subject to demand requirements.

12. Personnel Planning and Scheduling: Example of Bounding a Problem

13. Construct a Model • Math. Programming Model • Stochastic Model • Statistical Model • Simulation Model

14. Problem statement Formulate the Problem Construct a Model Model Constructing a Model • Problem must be translated from verbal, qualitative terms to logical, quantitative terms • A logical model is a series of rules, usually embodied in a computer program • A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. Example: Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources.

15. Model Find a solution Solution Tools Solving the Mathematical Model • Many tools are available as discussed in this course • Some lead to “optimal” solutions • Others only evaluate candidates  trial and error to find “best” course of action Example: Read nurse profiles and demand requirements, apply algorithm, post-processes results to get monthly schedules.

16. Find a Solution • Linear Programming • Nonlinear Programming • Regression • Direct Search • Stochastic Optimization • Trial and Error

17. Establish a Procedure • Production software • Easy to use • Easy to maintain • Acceptable to the user

18. The Goal is to Solve the Problem • The model must be valid • The model must be tractable • The solution must be useful

19. Implement the Solution • Change for the organization • Change is difficult • Establish controls to recognize change in the situation

20. Implementation • A solution to a problem usually implies changes for some individuals in the organization • Often there is resistance to change, making the implementation difficult • User-friendly system needed • Those affected should go through training Example: Implement nurse scheduling system in one unit at a time. Integrate with existing HR and T&A systems. Provide training sessions during the workday.

21. Components of OR-Based Decision Support System • Data base (nurse profiles, external resources, rules) • Graphical User Interface (GUI); web enabled using java or VBA • Algorithms, pre- and post- processor • What-if analysis • Report generators

22. Problems, Models and Methods Real World Situation Problems Models Methods

23. Operations Research Models Deterministic Models Stochastic Models • Linear Programming • Discrete-Time Markov Chains • Network Optimization • Continuous-Time Markov Chains • Integer Programming • Queueing • Nonlinear Programming • Decision Analysis

24. Deterministic vs. Stochastic Models Deterministic models – 60% of course Stochastic (or probabilistic) models – 40% of course Deterministic models assume all data are known with certainty Stochastic models explicitly represent uncertain data via random variables or stochastic processes. Deterministic models involve optimization Stochastic models characterize / estimate system performance.

25. Examples of OR Applications • Rescheduling aircraft in response to groundings and delays • Planning production for printed circuit board assembly • Scheduling equipment operators in mail processing & distribution centers • Developing routes for propane delivery • Adjusting nurse schedules in light of daily fluctuations in demand

26. Steps in OR Study

27. What you Should Know about Operations Research • How decision-making problems are characterized • OR terminology • What a model is and how to assess its value • How to go from a conceptual problem to a quantitative solution • How to find solutions with the Excel add-ins

28. Operations Research/Management Science OR/MS Professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures. Institute for Operations Research and the Management Sciences 1

29. What is Operations Research? Operations The activities carried out in an organization. Research The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. Model An abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.

30. Philosophy Why are we here? • Theology What is going to become of us? • Science What is it, how and why does it work? • Mathematic How do we prove it? • Engineering How do we make it? • OR/MS How do we get it to work efficiently (optimally)? • Psychology How do we feel about it? • Sociology How does it affect us and how do we affect it? • Politics How can we agree on getting it to work? • Business How do we convert it to an opportunity and make money out of it? • Law How do we create doubt about why it happened so we can win and make big money? • Psychiatry What is the bright side of looking at it? • Medicine How do we get it going again?