# Operational research

Operational research involves analysis of various operations performed in human and technical systems. It is basic tool used by mathematical theory of decision.

Genesis of this method is connected with a operations research group of experts working at the headquarters of the British army in 1938 and directed by the famous British physicist P.M. Blackett. The group, with representatives from various science areas, developed quantitative solutions to problems related to the organization of military pursuits. After the war, methods used in the military proved to be useful to solving problems in various fields of management. During time decision problems solved by the operational are more and more complex and therefore in these studies managers began to use system approach.They are also the primary area of use of newly emerging in the 40s and 50s of twentieth century computer technology.

In practice, an operational research is a management tool for the analysis and the precise phenomena and processes in the enterprise by using mathematical methods. Operational research is a collection of structured methods and techniques derived from the theory of mathematical programming and econometrics used to describe, analyse and search for optimal solutions for decision making. The subject of operational research are description and the solution based on the use of mathematical models and tools

## Operational research methodology

Operations research methodology includes the following steps:

• Identification of the decision problem.
• Construction of a mathematical model.
• Solution of a developed model.
• Verification of a model.
• The development of the control system.

The basic problems solved using operations research include: inventory management, analysis of structure of production, apportionment, transport, storage handling, ordering, route selection, exchange, competition.

### Linear programming

Linear programming was the earliest method used in operations research for building and solving deterministic models. It is applicable to the analysis of the decision in which both the constraints and the objective function are linear. Due to simplicity, to solve linear programming models managers use graphical methods. Typical decision-making problems analyzed using linear programming include the following:

• Selection of structure of production,
• Compound problem (the problem of diet),
• The problem of cutting,
• Selection of production process,
• The issue of transportation and related issues
• Location of production problems,
• The problem of minimizing empty runs,
• Routing issues.

### Queueing theory

The issue of queues is a typical model of stochastic process involving both probabilistic and statistical models. Typical queuing problems arise when some place is randomly visited by any number of people or objects. This could be, for example, the post office box, the patients coming to the doctor, customers coming in to cash registers at the supermarket, etc. Specifying those persons and other objects as "customers" you will find that they present themselves in time that could not be predicted in advance. It can be represented as a random process which can be described by a suitable probability distribution. Goal of solving the problem of queuing may be, for example, identify and minimize customer waiting time in the queue, specify the amount of service positions, to avoid unnecessary delays resulting from lack of customers.

### Network programming

Methods for network programming. Models of network are used to minimize the duration and costs of complex operations. Network models can be divided into two basic groups - methods for deterministic network logical structure (DAN - Deterministic Activity Networks) and stochastic network logical structure (GAN - Generalized Activity Networks). The networks of deterministic selection order is clearly defined. This group includes the critical path method (CPM - Critical Path Method), its various forms and the method of PERT (Program Evaluation and Review Technique). The CPM method selection activities and their duration is deterministic. The PERT method selection is a deterministic function, and their duration is random. Both the CPM method and the PERT method may be supplemented by an analysis of the time-cost - the method of CPM-COST and PERT-COST.

### Modelling of competition and conflict

Modelling of competition, conflict and negotiation. Issues of competition, conflict and negotiation are modeled using game theory. Currently, game theory is often used to build models of decision-making, which have been identified as a complex. Game theory is sometimes referred to as "interactive decision theory". It concerns the behavior of rational decision makers whose decisions affect each other. Its name stems from the fact that it was originally used in the analysis of games such as chess or poker. Game theory is also used in the description and study of all kinds of conflicts and negotiations.