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.

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

21. Available OR_MM 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