After careful mathematical research, Industrial Engineering student Loe Schlicher (University of Technology, Eindhoven) chooses simulation and specifically the simulation tool Enterprise Dynamics for his analysis. The delivered report of the project was chosen as the best thesis of 2011 for the bachelor study in Industrial Engineering and Operational Management. This article tells the story of a successful ED-Student.

In my research, average waiting time was the central topic. The company expected that the demand for their products would increase enormously. As a result, the average waiting time would increase too. They asked me how many machines are needed to reach an acceptable waiting time of their products in the future. The company had no specific idea of what an acceptable waiting time would be and therefore I decided to do a so-called performance analysis. For this, I proposed the company a few scenarios. "If you buy k new machines, the average waiting time of product i will decrease with q percent." As the purchase of one or more machines involves high costs, I tried to search for an optimal balance between the number of machines and an acceptable waiting time of their products.



Before the performance analysis actually took place, Schlicher did some literature research in the field of Queuing Theory to look for mathematical expressions that could describe the situation as best as possible. "Most scientific papers in the field of queuing theory are highly abstracted", Schlicher says. In almost all cases they assume a Poisson arrival process and processing times that are negative exponentially distributed.

Analysis of the given data showed that this was not really the case. Arrival processes are not stable and some product types have nearly deterministic processing time. "Seeing these results, my supervisor said: It is mission impossible to translate all these important details into a mathematical model!" However, this was not the end for Schlicher's project as he switched to simulation.
 
After some research Schlicher found the simulation tool Enterprise Dynamics (ED), an easy to learn simulation tool for beginners that also allows expert users with programming skills complete control over their simulation model. "With this tool, I was able to model even the most complex situations. For example, many products would repeatedly be sent back to the same machine. Also, after producing one specific product type, requests for exactly 5 products of another type would arrive. There were even more complicated issues like this, but I was able to deliver the first simulation model in less than two weeks."

"Another advantage of ED is the ease of use for employees who are not mathematically inclined. They can follow the process very easily because of the use of well-chosen symbols and colors. For example, it is possible to see some products waiting in a queue or being processed at a machine."
 
Together with some employees of the company I tried to exercise the performance analysis in combination with the simulation. "It is easy to show what the average waiting time will be with one, two or even 10 machines. Once programmed it is simply one, two or three mouse clicks and the simulation can be run again. "Soon it became clear that the current number of machines was already insufficient.

Increasing the number of machines is not the only solution for decreasing the average waiting time, Schlicher says. "I tried to explain this to the employees of the company. I decided to also take the priority rules into account. The company used the standard FCFS (First Come First Serve) priority rule, but there exist many other interesting priority rules. One priority rule that can reduce the average waiting time is the SPT rule. Products with a small processing time are put in front of the queue. Products with a large processing time will therefore get a longer waiting time on average. A drawback to this priority rule is that products with a large processing time sometimes have to wait for an unacceptable long time. Therefore, Schlicher came up with a new priority rule, the SPT ** rule. This rule indicates a maximum waiting time on each individual product. Products that have a longer waiting time than s time units are put in the front of the queue and get the highest process priority."

This priority rule was relatively simple to implement in ED. The simulation allowed me to show the employees that adopting such a priority rule can lead to an enormous reduction of the waiting period without purchasing a new machine. Together, the priority rule is a third element in the optimization of the average waiting time.

The difference in waiting time (about 40%) was the main reason for the company to switch to SPT** instead of FCFS. This way you reduce the average waiting time by 40% without spending money on new machines, Schlicher says. With the new priority rule, Schlicher did a performance analysis to investigate the appropriate number of machine needed for an acceptable waiting time. It turns out that the combination of the SPT** priority rule and 3 machines is sufficient to reach an acceptable waiting time.

Schlicher also mentioned that nowadays (three months later) the company still uses the simulation tool he created. They can easily vary the arrival intensity. This allows them to simulate and investigate what happens to the average waiting time. Basically they are now able to exercise a performance analysis at every moment. "An ideal situation, right?" Schlicher ends.