Operations Research for Solving Real-World Problems
Our main focus is the appliance of quantitative O.R. methods on complex, real-world aviation problems
Operations Research (O.R.) is the discipline of applying appropriate analytical methods to help make better decisions. By using techniques such as mathematical modeling to analyze complex situations, Operations Research gives executives the power to make more effective decisions and to build more productive systems.
Operations Research is characterized by:
- Optimization: The underlying objective of the problem shall be optimized (maximized or minimized).
- Model-analytic approach: Model-based thinking and analysis are the basic principles of operations research.
- Problem quantification: The quantification and calculation of the regarded decision problems are a main feature of operations research.
- Decision support: Decisions are not automatically made, but rather supported by supplying decision relevant quantitative information.
Some of the most well-studied examples for the successful appliance of O.R. techniques in the airline industry are:
- Fleet assignment optimization
- Crew pairing and rostering optimization
- Tail assignment optimization
Real-world problems, especially in the airline industry, are often extremely difficult to solve efficiently, because the linear growth of input data leads to an exponential growth of possible solutions. To find an optimal decision regarding both the objective and the necessary effort, empirical considerations are being replaced by scientifically founded planning methods and decision techniques.
The development of optimization solutions is usually based on the following procedure:
- Identifying and abstracting the real problem
- Formulation of a mathematical model
- Solving the mathematical model
- Interpretation of the mathematical solution and suggestion for the real problem
Optimization solutions have to consider the existing operational and organizational structure of an enterprise in order to achieve the optimal efficiency of a human-machine system. This is particularly important to decision support systems that combine the efficiency of computers on well-structured problems with the ability of humans on solving poorly-structured problems in order to support decision makers in making better decisions.
Below you will find some of the most commonly applied O.R. methods and techniques.
Mixed-Integer Linear Programming
Linear Programming is one of the most important and most well-known O.R. instruments. The challenge in practical applications is the development of a mathematical model that is suitable for the real problem and efficiently solvable by a standard solver (e.g. IBM ILOG CPLEX or Gurobi).
Heuristic Implementations for Complex Linear and Non-Linear Problems
The high complexity in practical applications is often increased by the fact that the objective functions are not linear or the size of the problems prevents from solving with a standard solver in an acceptable amount of time. In such cases the development of heuristic procedures is recommended. A heuristic is a method that might not always find the best solution, but is guaranteed to find a good solution in reasonable time.
Configuration and Calibration of Models and Systems
After developing and implementing the models and systems these must be configured and calibrated in order to generate high quality solutions in reasonable time.
The challenge in practical applications is the development of models that are suitable for real problems and efficiently solvable.
Proof-of-Concept Studies and Potential Assessment
We support you in assessing your potential during preliminary studies by developing and executing mathematical models
After many years of practical experience, besides in-depth knowledge in designing mathematical models and efficient algorithms, we have developed a rapid prototyping framework for airline optimization applications.
In the past we have supported our clients in different kinds of potential analysis.
Using Existing Applications
Sometimes potential analysis can be done by manipulating data and configuring existing applications.
Examples we supported by configuration of existing applications:
- Analysis of increasing the number of cabin crew qualifications for crew rostering.
- Analysis of the trade-off between overtime pay and request fulfillment for cockpit crews during crew rostering.
Using Product Benchmarks
Especially during vendor selection processes, benchmarking results based on prepared real data can be used for evaluation.
Examples we supported by using products and benchmark results:
- Business case evaluation by extrapolation of benchmark results for crew pairing and rostering optimizers.
- Product evaluation for supporting several tail assignment tasks related to operations control.
Using Prototype Results
If there are no products on the market available the development of prototypes will help to assess potentials.
Examples we supported by developing and evaluating prototypes:
- Potential assessment for proactive handling of bad weather and crew strike irregularities to minimize passenger impact considering itinerary based passenger re-accommodation options.
- Evaluation of meta-heuristics for the optimization of flight connections at hub airports.
Experience as Crucial Success Factor
The success of O.R. projects depends on structured procedure, mathematical background knowledge as well as problem-specific expertise.
Identifying Optimization Requirements
We support you in identifying your specific requirements to develop or customize optimization applications
When translating your business requirements into IT system requirements the following optimizer specific areas have to be addressed.
After identification of your business tasks to be supported, your process specific optimizer acceptance scenarios and requirements have to be deduced.
Examples where we supported the scoping of optimizers:
- Process analysis and scoping of tail assignment related business tasks, e.g. aircraft crew synchronization and fuel consumption optimization.
- Process analysis and scoping of crew roster maintenance related business tasks, e.g. crew candidate selection and roster maintenance optimization.
Objectives and Rules
Your business constraints and objectives have to be translated into optimizer requirements.
Examples where we supported the description of optimizer rules and objectives:
- Functional specification of a crew rostering optimizer and implementation of crew rostering rules and objectives.
- Functional specification of a tail assignment based optimizer for operations and maintenance control.
- Implementation of objectives and rules during prototyping of an optimizer to minimize passenger impact in proactive cancellation scenarios.
Besides response times, requirements for simple extensibility and user acceptance of optimizer solutions have to be described.
Examples where we supported the description of non-functional optimizer requirements:
- Description of non-functional requirements for a tail assignment related optimizer.
- Description of non-functional requirements for a crew rostering related optimizer.
Specialization in Operations Research
Founded in 2001, we spezialize in providing O.R. services and products to the aviation industry.
System Configuration and Calibration
We support you in configuration, rule implementation and calibration of your optimization applications
In order to achieve goals sustainably, to use resources efficiently and, finally, to ensure high user acceptance, the following configuration aspects of optimization applications have to be managed.
Managing rules is essential to get realistic high-quality solutions. Besides implementation and maintenance, documentation of business rules is an important success factor for optimizers.
Examples where we supported rule management tasks:
- Implementation and documentation of crew rostering rules.
- Documentation and prototypical implementation of tail assignment rules.
Calibration of optimizers is necessary to achieve goals sustainably and to use resources efficiently.
Examples where we calibrated optimizers:
- Implementation and calibration of objectives for crew pairing and rostering optimizers.
- Calibration of objectives for a hub flight connection optimizer.
- Implementation and calibration of objectives for a flight leg cancellation optimizer.
Not only objectives and constraints but also additional application parameters have to be configured, e.g. optimizer algorithm parameters.
Examples where we configured application parameters:
- Configuration of crew rostering and paring optimizers.
- Configuration of a hub flight connection optimizer.
- Configuration of a connection builder model to reduce the number of connections in a huge flight network.