01 intro
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Operations research (OR) aims to provide rational decision making by structuring complex situations using analytical and numerical techniques to develop mathematical models. The problem solving process involves formulating the problem, constructing a model, finding a solution, and implementing it. Models can be deterministic, with known inputs, or stochastic, incorporating uncertainty. OR techniques in Excel add-ins can help solve real problems like nurse scheduling.
01 intro
- 1. 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
- 2. 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.
- 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. Definition of OR s OR professionals aim to provide a rational basis for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. s 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.
- 5. Problem Solving Process Formulate the Problem Situation Problem Implement a Solution Statement Goal: solve a problem • Model must be valid Data • Model must be Construct tractable a Model Implement • Solution must be the Solution useful Model Procedure Find a Solution Establish a Procedure Test the Model and the Solution Solution Tools
- 6. The Situation • May involve current operations or proposed developments due to expected market shifts Situation • May become apparent through consumer complaints or through employee suggestions Data • May be a conscious effort to improve efficiency or respond to an unexpected crisis Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.
- 7. Problem Formulation Formulate the Problem Situation Problem Statement Data • Describe system • Define variables • Define boundaries • Define constraints • State assumptions • Identify data requirements • Select performance measures Example: Maximize individual nurse preferences subject to demand requirements, or minimize nurse dissatisfaction costs.
- 8. Personnel Planning and Scheduling: Example of Bounding a Problem Long-term planning Ð Full & part-timers Ð Shifts Ð Days off Weekly scheduling Ð Vacations, leave Ð Overtime Ð Part-timers, casuals Ð Task assignments Real-time control Ð Emergencies Ð Daily adjustments Ð Sick leave Ð Overtime
- 9. Constructing a Model Situation Problem • Problem must be translated Formulate the statement from verbal, qualitative terms to Problem Data logical, quantitative terms • A logical model is a series of Construct a Model rules, usually embodied in a computer program Model • 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.
- 10. Solving the Mathematical Model • Many tools are available as discussed in this course Model Find a • Some lead to “optimal” solution solutions • Others only evaluate candidates trial and Solution Tools error to find “best” course of action Example: Collect input data -- nurse profiles and demand requirements; apply algorithm; post-process results to get monthly schedules.
- 11. Implementation • A solution to a problem usually implies Situation changes for some individuals in the organization • Often there is resistance to change, making the implementation difficult Implement • A user-friendly system is needed the Procedure • Those affected should go through training Procedure 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.
- 12. Components of OR-Based Decision Support System • Database (nurse profiles, external resources, rules) • Graphical User Interface (GUI); web enabled using java or VBA • Algorithms, pre- and post- processors • “What-if” analysis capability • Report generators
- 13. Problems, Models and Methods Real World Real World Situation Situation Problems TP LP DS Problems Models Models LP NFP TP Methods Methods interior simplex
- 14. Operations Research Models Deterministic Models Stochastic Models • Linear Programming • Discrete-Time Markov Chains • Network Optimization • Continuous-Time Markov Chains • Integer Programming • Queuing • Nonlinear Programming • Decision Analysis
- 15. 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.
- 16. 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
- 17. 1 Problem formulation Steps in OR 2 Study Model building 3 Data collection 4 Data analysis 5 Coding Model No 6 Fine-tune verification and model validation Yes 7 Experimental design 8 Analysis of results
- 20. Activate Excel Add-ins Tools Menu: Add ORMM or Individual Add-ins
- 22. What You Should Know About Operations Research • Components of the decision-making process • 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 load or locate the Excel add-ins