Operations Research

History of OR
Britain, WWII (1938). Multi-disciplinary team of scientists explore how to use radar information to deploy and use fighter planes.
United States. Mathematical models (Search Theory) used to develop optimal air search patterns for anti-submarine tactics.
Evolution of OR
OR moves into industrial domain (1950’s), parallels computers’ growth as business planning/management tool.
Focus on development of mathematical modeling techniques to improve or optimize real-world systems.
What is Operations Research?
Before: application of mathematics and the scientific method to military operations
Today: scientific approach to decision making. Seeks to determine best way to design and operate system, usually requiring allocation of scarce resources
Other OR Applications
Other areas where OR techniques have been proven to be useful include
Inventory control
Warehouse design, storage and retrieval, order picking
Vehicle routing
Delivery transport mode selection
Capacity and manpower planning
Production scheduling
…and other resource usage and allocation decisions.
Mathematical Model
An idealized representation of a real world problem
Decision variables
Objective function
Constraints
Goal: Choose values of the decision variables that maximize the objective function subject to the constraints.
Methodology of Operations Research
What are the objectives?
Is the proposed problem too narrow?
Is it too broad?
What data should be collected?
How will data be collected?
How do different components of the system interact with each other?
What kind of model should be used?
Is the model accurate?
Is the model too complex?
Do outputs match current observations for current inputs?
Are outputs reasonable?
Could the model be erroneous?
What if there are conflicting objectives?
Inherently the most difficult step.
This is where software tools will help us!
Users must be trained on the new system.
System must be observed over time to ensure it works properly.
Successful OR Applications
Linear Programming
Linear programming is used to allocate resources, plan production, schedule workers, plan investment portfolios and formulate marketing (and military) strategies.
The versatility and economic impact of linear programming in today’s industrial world is truly awesome.--Eugene Lawler
What is a Linear Program?
A linear program is a mathematical model
that indicates the goal and requirements of an allocation problem.
It has two or more non-negative variables.
Its objective is expressed as a mathematical function. The objective function plots as a
line on a two-dimensional graph.
There are constraints that affect possible levels of the variables. In two dimensions
these plot as lines and ordinarily define areas in which the solution must lie.
Special Problem Types
Infeasible Problems: These arise from contradictions among the constraints. No solution possible until conflict is resolved.
Ties for optimal solution: Multiple optimal solutions can exist. Any linear combination of two optimal corners is also optimal.
Unbounded problems: Feasible solution regions may be open-ended, and the direction of improvement coincides.
Advantages & Limitations of Linear Programming
Scientific Approach to Problem Solving.
Evaluation of All Possible Alternatives- Most of the problems faced by the present organizations are highly complicated - which can not be solved by the traditional approach to decision making. The technique of Linear Programming ensures that’ll possible solutions are generated - out of which the optimal solution can be selected.
Maximum optimal Utilization of Factors of Production. Linear Programming helps in optimal utilization of various existing factors of production such as installed capacity,. labour and raw materials etc.
Limitations of Linear Programming.
Linear Relationship. Linear Programming models can be successfully applied only in those situations where a given problem can clearly be represented in the form of linear relationship between different decision variables.
Flexibility. Once a problem has been properly quantified in terms of objective function and the constraint equations and the tools of Linear Programming are applied to it, it becomes very difficult to incorporate any changes in the system arising on account of any change in the decision parameter. Hence, it lacks the desired operational flexibility.