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Operations Research Models and Methods
Models Section
Simulation with Extend
In this section we show the simulation of production models with the Extend Simulation application.

The LT (limited) version of the simulation application Extend+Manufacturing v 5 by Imagine That, Inc. of San Jose, CA, is included on the CD. The installation program for Extend places a folder called Examples within the Extend 5 LT directory. Among the many sample files in the Examples folder, the Models and Methods folder holds examples that are unique to this book. In the following pages, we describe these examples. Although we include screen shots of the Extend models, we will not try to explain in detail the processes of modeling with Extend or interpreting the Extend output. The package includes a full manual and tutorials that will help the student learn Extend Modeling.

The Manufacturing Station

Several identical machines have been gathered to perform some manufacturing operation. Parts enter the station from the left. Because of the variability in the interarrival times and the variability of the processing times, a queue of parts waiting processing forms in front of the machines. The length of the queue changes over time because of the randomness inherent in the process. One goal of an analysis is to measure the average number in the queue and the average time delay in the queue. The combination of queue and machines is called the station in the following discussion. Figure 1 shows a schematic of a single station production system.

Figure 1. Machine Station with Queue

The Arrival Process

Parts enter the station at a specified arrival rate. The inverse of the arrival rate is the mean time between arrivals. Variability in the arrival process means that the time between arrivals at the station is a random variable. A model of the process specifies a probability distribution for the time between arrivals. There are a number of well-known distributions that might be appropriate such as the Normal or exponential distributions. The one to use depends on the particular problem being studied and can be determined from analysis of historical data using statistical techniques.

Service Process

A station in the system performs some operation. Unless the station is highly automated, the actual time for the operation is probably not constant. When this time is a random variable, a model must specify the probability distribution for the time for replication of the operation. As for the time between arrivals there are many possible distributions that this random variable might take.

Extend Simulation

The Queueing Simulation model is an Extend simulation that allows parameters of the system to be easily changed. The model is shown in Figure 2.


Figure 2. Extend model of a single station manufacturing process

The simulation is constructed with various kinds of Extend blocks identified by their graphical icons. Most blocks have parameters that are set by double clicking on the block. In the example, the blocks have been labeled for discussion purposes.

The Generator block creates parts that pass through the simulation. The Rand block determines the probability distribution of the interarrival times. In this case the block is labeled Beta Dist. to indicate that the interarrival times have the Beta distribution.

Once created, parts pass from the Generator block into the FIFO Queue. The Activity-Mult block simulates the production activity. In this model the number of servers, or machines, is set in the field at the upper right to 3. The service time is governed by the Rand block connected to the Activity-Mult. The service distribution selected for the example is the exponential distribution with mean 0.5.

After service completion, the part passes to the Exit block. This particular simulation was setup to make 50 separate runs, each run consisting of 100 events. An event is either an arrival or a service. The number shown within the Exit block is the number of parts that left the system during the last simulation run – 48. Since the total number of events was 100, then 52 must have entered the system. When the simulation terminated, 4 parts remain in the service activity and queue.

Statistics on the simulation runs are discovered by opening the Notebook or by double clicking the Queue Stats or Activity Stats blocks. The results are presented for each run individually. Confidence limits on mean values can also be displayed.

The model provides access to some system parameters in the fields at the upper right. Other characteristics are set by the parameters within the blocks. Simulation characteristics are set with the Simulation Setup dialog in the Run menu.


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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved

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