Sample Essay On Linear And Integer Programming Modeling In A Work Place

Introduction

The topic I have chosen is simulation modeling. Simulation modeling (situational simulation) is a technique that allows you to build models that describe the processes as they would take place in reality. Such a model can "played" in time from beginning to the end, for one test as well as for a set of the tests. The results will be determined by the random nature of the processes. According to this data, it is possible to obtain fairly stable statistics. Simulation modeling is a method of investigation, in which the investigated system is replaced by a model with sufficient accuracy to describe the real system with which experiments are conducted to obtain information about the system. Experimentation with a model called imitation (imitation - a comprehension of the essence of the phenomenon, without resorting to experiments on the real object). Simulation modeling is a special case of mathematical modeling. There is a class of objects for which, for various reasons have not been developed analytical model, or not developed methods for solving the resulting model. In this case, an analytical model is replaced by the simulator or simulation model.
Simulation modeling is sometimes called obtaining numerical solutions to partial problems formulated on the basis of analytical solutions or by using numerical methods. Simulation model is a logical-mathematical description of an object, which can be used to experiment on your computer in order to design, analyze and evaluate the functioning of the object.

The Use of Simulation Modeling

Simulation is used when:
It is expensive or impossible to experiment on the real object;
It is impossible to construct an analytical model: the system has time, causality, the effects of non-linearity, stochastic (random) variables;
It is necessary to simulate the behavior of the system over time.
The purpose of the simulation is to reproduce the behavior of the system under study, based on the analysis of the most significant relationships between its elements, or in other words - the development of a simulator study for various experiments.

There are various types of simulation modeling which can be used in a work place:

Agent based modeling - a relatively new (1990s-2000s) direction of simulation which is used to study decentralized systems, the dynamics of the operation of which is not determined by global rules and laws (as in other modeling paradigms), but on the contrary, when these global rules and laws are the result of the activity of individual members of the group. The goal of agent-based models - get an idea about these global rules, the general behavior of the system on the basis of assumptions about the individual, the private behavior of its individual active objects and the interaction of these objects in the system. Agent is an entity possessing activity, autonomous behavior, can make decisions in accordance with a certain set of rules, to interact with the environment, as well as their own change. A good example of the use of agent-based modeling is the consumer market. In a very dynamic, competitive and challenging market environment, the buyer's choice often depends on the individual, inherent activity of the consumer, networking, and external influences, which are best described using agent-based modeling. Another common example is epidemiology. Here agents are people who may be immune, infection carriers, recover from or susceptible to disease. Agent based modeling will be projected into the world of social networking models, diverse contacts between people and eventually obtain objective forecasts of infection. However, we should not think that the agent-based modeling is applicable only to solve the problems of communicative nature. Tasks related to logistics, manufacturing, supply chain and business processes, and solved using agent-based modeling. For example, the behavior of a complex machine can be effectively modeled by a separate object (agent) with maps of states, describing her system timers, internal states, all sorts of reactions in different situations, etc. Such a model may be necessary to recreate the processes at work. The participants of the supply chain (manufacturing companies, wholesalers, retailers) can be represented as agents with individual goals and rules. Agents can also be projects or products within the same company at the same time have their own dynamics and internal states compete for resources companies.
Discrete event simulation - modeling approach offers aside from the continuous nature of the events and consider only the major events of the modeled system, such as "expectation", "Order Processing", "movement with load", "unloading" and others. Discrete event simulation is more developed and has a huge scope of applications - from logistics and queuing systems to transport and production systems. This type of modeling is most suitable for modeling of industrial processes. Jeffrey Gordon founded in the 1960s.
System dynamics - modeling paradigm, where for the system being built graphical charts causal relationships and global influence of some parameters on the other in time, and then created on the basis of these diagrams model is simulated on the computer. In fact, this type of modeling more than any other paradigm helps us to understand what was going on identifying causal relationships between objects and phenomena. System dynamics model is used in building business processes, development of the city, the production model, population dynamics, ecology and development of the epidemic. The method is based Jay Forrester in the 1950s.

The Application of Simulation Modeling in a Work Place

Application of the method of simulation can be demonstrated by the example of a bank branch serving individuals. Assume that it is necessary to determine the minimum number of staff, which provides the required service quality. The criterion of the quality of service we define a rule: the average queue size clients should not exceed N people. It is obvious that for the task must have sufficient knowledge about the system: which customers visit the bank, how many customers come during the working day, as well as how long it takes one customer service. While this task may seem specialized, similar problems arise in many areas that involve human and technical resources. Payment time of the skilled worker and time using sophisticated technology represents a significant share of the costs of companies. Determination of the optimal schedule recourse using allows efficiently perform tasks, reduces costs, and thus increase profitability. In the first stage of solving the problem created a model that corresponds to the structure and business processes of the bank branch. In developing the model takes into account only those parts which have a significant effect on the studied aspects of the system. For example, the presence of separation of corporate services or the credit department does not affect services to individuals, because they are physically and functionally separated from the latter. Schematically, such a model can be represented as a sequence of the following:
http://www.runthemodel.com/models/run.php?popup=1&id=348
In the second stage we input data: the intensity of the arrival of customers, the average customer service time, the number of available staff. Based on these data, the model simulates or reproduces job bank for a predetermined period of time, for example, working hours.
The next stage is to analyze the statistics collected and presented model. If the average queue size exceeds customer selected limit of N people, the number of available staff should be increased and a new experiment.
As a result of a series of experiments on the model, the user can determine the optimal number of staff. The selection process parameters can also be done using the integrated optimizer that automatically checks the various combinations and finds the best solution.

Conclusion

The use of simulation models has many advantages compared with the performance of experiments on the real system and the use of other methods.
Cost. Suppose the company laid off some employees, which further led to a decrease in the quality of service and loss of the customer. Make an informed decision would help the simulation model, the costs of the application of which consist only of the price of the software and the cost of consulting services.
Time. In reality, evaluate the effectiveness of, for example, a new network to distribute products or restructuring of the warehouse can only be months or even years. Simulation model to determine the optimal such changes in a matter of minutes required for the experiment.
Repeatability. Modern life requires organizations to quickly respond to changing market conditions. For example, the production volumes forecast of demand must be made in time, and changes are critical. With the help of the simulation model can hold an unlimited number of experiments with different parameters to determine the best option.
Accuracy. Traditional computational mathematical methods require a high degree of abstraction and do not account for important details. Simulation modeling allows us to describe the structure of the system and its processes in the natural state, without the use of rigorous mathematical formulas and dependencies.
Visibility. Simulation model has the capability process visualization system in time, specify its schematic structure and delivery of results in graphical form. This allows you to visualize the obtained solution and pledged to bring in his ideas to clients and colleagues.
Versatility. Simulation modeling allows solving problems of all sectors: manufacturing, logistics, finance, health and many others. In each case, the model simulates, reproduces real life and allows for a wide range of experiments without affecting the real objects.

Works Cited

Gilbert, G. (n.d.). Agent-based models.
Naldi, G. (2010). Mathematical modeling of collective behavior in socio-economic and life sciences. Boston: Birkhäuser.
Winsberg, E. (n.d.). Simulated Experiments: Methodology for a Virtual World.Philosophy of Science, 105-125.