SIMULATION EXAMPLE

Let's consider an industrial manufacturing example where we will build a model which has numerical, not graphical, output. Terms such as ``computer-integrated manufacturing" (CIM) and ``flexible manufacturing" guide the development of more productive plant configurations for building products from raw material. We introduce the following categories and definitions:

1. Material. Plants are built to process material---often called raw material stock---and shape the material into a product. As raw material goes through its changes, it turns into a part to be processed.

2. Machines. Plants are composed of machines of all kinds which process material and parts. Some examples are ovens, lubricators, flame cutters, lathes, and robots.

3. Transportation. Material flows through a network of machines. The method of transport is effected by devices such as conveyors and automated guide vehicles (AGVs). During this transit, it encounters storage areas and accumulators which buffer parts until the machines can operate upon them.

Figure 3 shows a sample manufacturing system containing nine parts. This type of drawing is essentially a schematic defining the overall structure of the system but lacking details on dynamics and geometry. The raw stock arrives from the left via a central conveyor. At this point, the material stock is a cylinder shape. The cylinder parts are loaded into a spiral accumulator (A) which holds parts for the pick-and-place robot (R) until both it and the lathe (L) are ready. Once both are ready to work with the part, the cylinder is turned into a barbell shape by the lathe and sent on toward a second spiral accumulator using a conveyor belt. A second robot also performs a pick-and-place operation and hands the barbell part to a drill machine (D) which punches a longitudinal hole through the part. That is the final product part, which proceeds to a small storage bin taken by the AGV which runs around a closed track while dropping the bin contents into longer-term storage. This type of application involves discrete parts flowing through a network of resources. The resource constraints and network flow suggests the use of a Petri net to model the system as in Fig. 4.

  
Figure 3: Manufacturing line with two robots and two machines..

  
Figure 4: Petri net model for manufacturing line.

Figure 4 is the mathematical model for the system and is categorized as a declarative model (i.e., the Petri net sub-states and events are visible and emphasized in the model structure). In a nutshell, a Petri net operates by having tokens (the black circles) flow through the network while encountering resources (lathe,drill press, robot arm, AGV). Each resource operates or ``processes" a token as it passes by. This is the specification that we need to encode in the form of a program and then execute on a computer. There are many Petri net simulators to be found. One such simulator is a tool within SimPack (See section SIMPACK SIMULATION TOOLKIT), which is a toolkit for exploring mathematical modeling and simulation. Once simulated, this Petri net can yield data which is subject to analysis (the third sub-field of computer simulation). The types of analysis methods for simulations are plentiful. For our manufacturing example, we may simply want to analyze the throughput of the system as a whole to determine how many parts can be processed in one hour. Actually, we pre-determined our use of a Petri net model because we knew ahead of time that we wanted throughput information. If we had wanted, say, information on the stability of the robot arm controller then a Petri net would not have served our purpose. Moreover, if our Petri net model has a stochastic element (i.e., it uses random variates) then it is vital to make many simulation runs of the same model but with different samples; otherwise, we will not know the accuracy (measured by a confidence interval) associated with the simulation output.