What is �Operations Research?
Operations Management
What is Operations Research?
The first formal activities of Operations Research (OR) were initiated in England during World War II, when a team of British scientists set out to assess the best utilization of war material based on scientific principles rather than on ad hoc rules.
After the war, the ideas advanced in military operations were adapted to improve efficiency and productivity in the civilian sector.
One of the greatest success stories in quantitative methods is the work carried out by the operations research (OR) group at American Airlines.
In 1982, Thomas M. Cook assembled a group of 12 operations research analysts at American Airlines. Under Cook's guidance, the Operations Research group quickly grew to a staff of 75 professionals who developed models and conducted studies to support senior management decision making.
Currently the Operations Research group is called Saber and employs 10,000 professionals worldwide.
One of the most significant applications developed by the Operations Research group emerged due to the deregulation of the airline industry in the late 1970s.
As a result of this deregulation, several low-cost airlines were able to enter the market by selling tickets at a fraction of the price charged by established airlines such as American Airlines.
The Operations Research group suggested offering different kinds of fares (discounted and non-discounted tickets) and in the process created a new area of quantitative methods known as performance or revenue management.
The Operations Research group used forecasting and optimization techniques to determine how many tickets to sell at a discount and how many to keep at full fare.
Although the initial implementation was relatively crude, the group continued to improve the forecasting and optimization models that power the system to obtain better data.
Tom Cook counts at least four basic generations of income management during the period he acquired the load. Each produced a $100 million excess increase in profitability over its predecessor.
Today, American Airlines' revenue management system generates nearly $1 billion a year in increased revenue. Almost all airlines use some type of revenue management system.
The Operations Research group used forecasting and optimization techniques to determine how many tickets to sell at a discount and how many to keep at full fare.
Operations Research Models
Operations Research models are designed to optimize a specific objective criterion subject to a set of constraints, the quality of the resulting solution depends on the degree of completeness of the model in representing the real system.
Operations Research Models
A businessperson has a 5-week commitment traveling between Fayetteville (FYV) and Denver (DEN).
Weekly departure from Fayetteville occurs on Mondays for return on Wednesdays. A regular roundtrip ticket costs $400, but a 20% discount is granted if the roundtrip dates span a weekend.
A one-way ticket in either direction costs 75% of the regular price. How should the tickets be bought for the 5-week period?
Operations Research Models
Three plausible alternatives come to mind:
Operations Research Models
An obvious objective criterion for evaluating the proposed alternatives is the price of the tickets. The alternative that yields the smallest cost is the best. Specifically, we have:
Alternative 1 cost = 5 * $400 = $2,000
Alternative 2 cost = .75 * $400 + 4 * (.8 * $400) + .75 * $400 = $1,880
Alternative 3 cost = 5 * (.8 * $400) = $1,600
Operations Research Models
The general Operation Research Model can be organized in the following general format:
Maximize or minimize Objective Function, subject to Constraints.
Operations Research Models
A home owner is in the process of starting a backyard vegetable garden. The garden must take on a rectangular shape to facilitate row irrigation. To keep critters out, the garden must be fenced. The owner has enough material to build a fence of length L = 100 ft. The goal is to fence the largest possible rectangular area.
w
h
Maximize:
z = wh
Subject to:
2(w+h) = L
w,h > 0
h
w
Operations Research Models
IMPORTANT:
Though Operation Research Models are designed to optimize a specific objective criterion subject to a set of constraints, the quality of the resulting solution depends on the degree of completeness of the model in representing the real system.
Solving the Operation Research Model
The most prominent Operation Research technique is
Linear Programming.
Technique | Description |
Linear programming | It is designed for models with linear objective and constraints functions. |
Integer programming | In which the variables assume integer values. |
Dynamic programming | In which the original model can be decomposed into smaller more manageable subproblems. |
Network programming | In which the problem can be modelled as a network. |
Nonlinear programming | In which functions of the model are nonlinear. |
Solving the Operation Research Model
A peculiarity of most Operation Research techniques is that solutions are not generally obtained in (formula-like) closed forms. Instead, they are determined by algorithms.
An algorithm provides fixed computational rules that are applied repetitively to the problem, with each repetition (called iteration) attempting to move the solution closer to the optimum.
Solving the Operation Research Model
Some mathematical models may be so complex that it becomes impossible to solve them by any of the available optimization algorithms.
In such cases, it may be necessary to abandon the search for the optimal solution and simply seek a good solution using heuristics or metaheuristics, a collection of intelligent search rules of thumb that move the solution point advantageously toward the optimum.
Queueing and simulation models
Queuing and simulation deal with the study of waiting lines. They are not optimization techniques; rather, they determine measures of performance of waiting lines, such as average waiting time in queue, average waiting time for service, and utilization of service facilities, among others.
Queuing models utilize probability and stochastic models to analyse waiting lines, and simulation estimates the measures of performance by “imitating” the behavior of the real system.
Art of Modeling
The model expresses in an amenable manner the mathematical functions that represent the behavior of the assumed real world.
Phases of an Operation Research study
As a decision-making tool, OR is both a science and an art: It is a science by virtue of the mathematical techniques it embodies, and an art because the success of the phases leading to the solution of the mathematical model depends largely on the creativity and experience of the OR team.
The principal phases for implementing OR in practice include the following.
Phases of an Operation Research study
Phase | Description |
Problem definition | Involves delineating the scope of the problem under investigation. This function should be carried out by the entire Operation Research team. The aim is to identify three principal elements of the decision problem:
|
Model construction | Entails an attempt to translate the problem definition into mathematical relationships. If the resulting model fits one of the standard mathematical models, such as linear programming, we can usually reach a solution by using available algorithms. |
Model solution | Is by far the simplest of all Operation Research phases because it entails the use of well-defined optimization algorithms. An important aspect of the model solution phase is sensitivity analysis. It deals with obtaining additional information about the behavior of the optimum solution when the model undergoes some parameter changes. |
Phases of an Operation Research study
Phase | Description |
Model validity | Checks whether or not the proposed model does what it purports to do—that is, does it adequately predict the behavior of the system under study? The model is valid if, under similar input conditions, it reasonably duplicates past performance. Generally, however, there is no guarantee that future performance will continue to duplicate past behavior. |
Implementation | Of the solution of a validated model involves the translation of the results into understandable operating instructions to be issued to the people who will administer the recommended system. The burden of this task lies primarily with the Operation Research team. |