Basic concepts

Computer Aided Engineering, better known as CAE [1], can be defined as the use of a computer to improve or assist in engineering solutions or product development for a wide range of industries.

When it comes to statistics, there are two types of variables: continuous and discrete. In this article, you'll learn how CAE and discrete variables are related and applied in engineering.

First, understand the differences between continuous and discrete variables.

It can be said that continuous variables are infinite and there is always something between them. Discrete variables are countable and there are no elements between them [2]. To better understand these concepts in practice, take a look at Figure 1.

Figure 1: Analog clock (continuous variable) and digital clock (discrete variable)[3].

There are infinite possibilities for reading the analog clock, since it is not possible to say exactly what position the hands are in. You can also see that there is always something between one reading and the next. These characteristics make it a continuous variable.

On the other hand, the digital clock only has one reading at a time, so there is no reading between one hour and the next. These facts characterize it as a discrete variable.

Based on these concepts of variables, continuous and discrete models are defined. In the former, the state of the system changes continuously as a function of time, while in the latter the state of the system changes only when an event occurs.

Queue Theory

Generally speaking, Queue Theory uses mathematical techniques to study the flow of objects through a network of processes. This chain of events contains more than one location and some time and frequency restrictions for the passage of items [4]. These conditions generate the waiting times between the processing of these objects.

The aim of Queue Theory is to generate mechanisms for predicting how a queue system will behave [4]. Based on this prognosis, assertive actions can be taken to optimize processes and prevent possible bottlenecks.

Industry applications

To meet the needs of industry in general, Kot Engenharia these and other concepts of statistics and mathematics, with the aid of CAE methods, to develop Discrete Event Simulations.

In short, discrete event simulations virtually emulate queuing scenarios. In these queues, the arrivals, processing or services and exits of the objects in question are evaluated [5].

Advantages and Limitations of Discrete Event Simulation

Firstly, it should be noted that most real systems are highly complex, making analytical evaluation impossible. In these cases, simulations can be used.

In addition, the virtual context of simulation brings other advantages such as the possibility of evaluating and comparing systems under specific conditions.

However, the main barrier to discrete event simulations is the high cost of the software available to run them.

Steps for carrying out Discrete Event Simulation [6]

• Model design: at this stage, the system must be studied in order to understand its particularities, the objectives of the simulation and the level of detail required. It is also at this stage that the necessary data is collected;

• Implementing the model: the second stage of development involves computer modeling of the system;

• Analysis of the model's results: the final stage in which the model is ready and used to reach more assertive conclusions and decisions.

Analysis of a Coal Port

In order to make the application of the method clearer, below is a case in which Kot carried out a discrete event analysis of a coal export port. The study covered everything from receipt of the material by the railroad logistics, through transportation and stacking in the storage yards, and then retrieval of the material, transportation to the port and loading onto ships.

From the model created, it became possible to establish and quantify the occupancy rate of equipment in each phase of the port's operation. The models in question can be seen in Figures 2 and 3.

Figure 2: Model for studying a coal export port. [3]

Figure 3: Modeling the ship queue - Gaussian distribution of ship arrivals, based on a known fleet provided by the shipowner[3].

The results of one year of operation, prior to the Kot study, can be seen in Figure 4.

Figure 4: Plant results after 1 year of operation - see reduction in stock (green) and increase in demurrage costs (red). [3]

Based on the simulation results, problems were detected in maintaining the port's stocks. As a result, Kot suggested some changes to the analyzed plant.

Once these changes had been implemented in the plant, a new simulation was carried out, proving the effectiveness of the modifications and the port's suitability in relation to the handling capacity envisaged in the project. In this case, no additional investment was needed in the plant, just adjustments to the processes. The new simulation with the suggested changes applied can be seen in Figure 5.

Figure 5: Maintaining stocks and reducing demurrage costs. [3]

Conclusion

With its knowledge of mathematics and statistics combined with CAE methods, Kot Engenharia able to conduct a comprehensive study of process systems, identifying potential bottlenecks and suggesting modifications to optimize these processes. Kot can evaluate different processes and operations to help optimize results. Consult our team for more information!

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References:

[1] B. Raphael and I.F.C Smith - Fundamentals of Computer Aided Engineering

[2] Miller, J. (1988). Discrete and continuous models of human information processing: Theoretical distinctions and empirical results.

[3] Kot Engenharia Collection

[4] Newell, G.F.N - Applications of Queueing Theory

[5] Fishman, George S. - Discrete-Event Simulation: Modeling, Programming, and Analysis

[6] Chwif, L. and Medina, A. C. (2006). Modeling and simulation of discrete events. Afonso C. Medina.