SIMULATION AS A TOOL FOR SERVICE LEVEL ANALYSIS AND SERVICE CAPACITY AT A NATURAL GAS STATION

The main objective of this paper is to study the formation of waiting lines on a Petroleum Natural Gas station (PNG station) by using simulation. Also, the expected number of customers in queuing system and waiting times are evaluated, as well as alternative solutions to improve the PNG station's current capacity to provide the service to taxi-drivers.

1. THE SUPPLY PROBLEM

As revealed by several surveys, Natural Petroleum Gas (GNP) is the lowest cost automotive fuel per kilometer driven. Its sale was regulated in 1991, thus meeting the wishes of a large number of fleet owners and taxi drivers, enabling the conversion of their vehicles to gas.

Over time, the few inaugurated stations proved to be insufficient to meet the growing demand, contributing to the deterioration of service levels (measured by taxi waiting time in line and queue length).

The main motivations of our work are: to evaluate the current service level of a GNP filling station: to determine methods to increase productivity and to quantify increments in sales volume. Thus, there are several factors that contribute to this scenario: (a) lack of service supply: only 5 stations distribute natural gas in Rio de Janeiro; (b) high investments required to set up a service station, mainly in compressors, other equipment and civil works, in the order of one million dollars; (c) methods used in fueling operations that have not yet been scientifically studied, as well as safety procedures that make service more time consuming, also forcing each taxi to contain only one gas tank, which reduces autonomy.

The factors mentioned above show a complex system, difficult to analyze analytically, justifying, therefore, the application of computational simulation to study the size of queues, as well as the characteristic behavior of the system in face of the demand.

2. PROBLEM MODELING

A characteristic of the source of arrival or potential population is its “size”, or the potential number of gas taxis that can fill up at the station. As there are few natural gas stations in the city of Rio de Janeiro and as vehicles powered by GNP have less autonomy, we can assume an infinite source of arrivals. On the other hand, the statistical pattern within which customers are generated over time was assumed to be Poisson.

We therefore measured how many taxis arrived at each two-hour interval on average and, applying the Chi-square adherence test, the Poisson distribution was accepted at 5% significance.

It should be noted that in order to assess arrival rates in time slots that were not surveyed, such as at dawn, we resorted to the experience of the station operator, who estimated it at 1 taxis every 10 minutes.

In order to calculate the supply times, we have broken this process down into several main activities, from the moment the taxi enters the system until the moment it leaves. Four main activities were identified, as shown in the table below:

Several samples of the duration of these activities were collected, over different time slots, establishing an average time and their respective standard deviations.

It was shown, using ANOVA for three samples of different sizes and a classification (10:00 – 11:00 am, 11:40 – 12:40 pm and 14:50 pm – 16:50 pm), that the average supply times significantly differ, at the 5% level, with the gas station team. changing work shifts at 7:00 am, 15:00 pm and 23:00 pm.

Finally, it was statistically verified that issuing invoices to taxi drivers' cooperatives increases the taxi's permanence at the station.

3. COMPUTATIONAL MODELING

Digital simulation was adopted as a working tool. The simulation aims to make it feasible to carry out tests on the station configuration, without requiring any real change in its structure. Basically, the simulation comprises two stages: the modeling of the problem and the computational simulation.

For system modeling, the Simul simulation package was used, which is basically a set of subroutines that organize and manage a set of activities that must start under certain conditions and end after a certain period of time. In the process of modeling the problem, the concept of the Activity Cycle Diagram (DCA) was used, which brings general information about the simulated system and is recommended to users of the simulation package in question. The DCA is a schematic representation of the simulation model and has three basic concepts: entity, activity and queue, as shown in the table below:

The figure below represents the DCA of the station's current system and table 4 presents the related activities, the entities that participate in them and their attributes, as well as the queues through which the entities pass.

Based on operating times and arrival rates, events were programmed that would simulate the station's activities, using, for this purpose, the concept of generating random variables (normal and exponential), with means and standard deviations calculated from the data. real.

The number of nozzles can be chosen by the system user and varies between 3 and 5. The number of gas station attendants was established as n, where n is half the number of nozzles. In fact, a gas station attendant operates two nozzles simultaneously, with no work overload. That is, when a gas station attendant is participating in an activity, he can also participate in another at the same time, without his performance being impaired. Furthermore, the system is capable of carrying out simulations for several consecutive days, without re-initializing variables, and of collecting statistical data by time bands, thus facilitating future analyses.

4. EXPERIMENT PROJECT

We simulate three alternative basic configurations (experiments) to the current operation of the gas station. They are: (a) automatic issuance of invoice by electronic device, currently, twenty percent of the taxis that fill up at the station daily require invoice; (b) assumption that the average daily supply time reached the level of the best average time collected by sampling, through training of gas station attendants; (c) automatic issuance of invoices and a better team of attendants.

We will now describe the gains in the level of service to the taxi driver evaluated through simulations of these alternative configurations.

4.1. Automatic issuance of invoice

The simulation of this alternative for 50 consecutive days showed considerable reductions in the average queue size and in the average waiting time in the queue, especially in the peak time periods (15:17 to 17:19, 19:21 to XNUMX:XNUMX and XNUMX:XNUMX to XNUMX:XNUMX) as we can see in the graph below, compared to the station's current operating configuration.

Significant reductions in less busy time slots (0 am to 5 am, 5 am to 7 am, 7 am to 9 am and 21 pm to 24 am) must be analyzed with caution, since the average queue size per interval is not large enough to be established a significant difference. This caveat is implicit in all analyzes made from now on.

4.2. Best team of attendants without automatic invoice issuance

This configuration presents much more expressive service level improvements than the previous one for peak hours (15:17 to 17:19, 19:21 to 00:XNUMX and XNUMX:XNUMX to XNUMX:XNUMX).

For the time period between 17 pm and 19 pm, in particular, the simulation indicated a dramatic reduction of 00% in the average size of the queue, as shown in the graph below, which indicates a drop from 80 to 25 taxis on average.

4.3. Best team of attendants with automatic invoice issuance

This last configuration is the one that presents the greatest gains for peak hours; in particular, once again, for the hours from 17 pm to 19 pm, as shown in the graph below.

5. QUANTIFICATION OF INCREASE IN ANNUAL SALES VOLUME

We will present the gains arising from the implementation of the configurations described above. The basic assumptions for such sales potential to convert into revenue growth are: (a) demand will increase until the service level of the new configuration equals the level of the old configuration (in terms of waiting time), stabilizing it if from there; (b) population (potential number of taxis) infinite.

In this way, we can estimate the demand increase in number of taxis/day depending on the desired queue size (service level) for the most critical time slot.

5.1. Automatic issuance of invoice

It is easy to see that, for the average queue size to return to 25 taxis, an increase in demand of the order of 3% is necessary. This means just thirteen more cars in the system throughout the day and an increase in the annual sales volume of thirty thousand reais.

The paragraph above translates information of great relevance: the station was at its critical point of saturation, where the impact of the tested experiments translated into considerable increases in productivity. However, a small increase in the volume of cars serviced daily brought the system back to its saturation state.

5.2. Best team of attendants without automatic invoice issuance

This experiment showed greater productivity gains than the previous one. In other words, in an operating situation close to saturation, the post is more sensitive to the training of its human resources, in terms of productivity increases, than the implementation of the automatic issuance of invoices.

It is easy to see that, for the average queue size to return to 25 taxis, an increase in demand of the order of 16% is necessary. This means seventy-eight more cars in the system throughout the day and an increase in the annual sales volume of around one hundred and sixty thousand reais.

5.3. Best team of gas station attendants with automatic invoice issuance

As expected, this configuration presents as its main characteristic an increase in productivity that is not equivalent to the sum of the productivity increases of the other previous experiments.

If with the automatic issuance of invoices the average queue size for the worst time slot dropped from 25 to 15 cars, and with the best team the average size drops from 25 to 5 cars, running two experiments simultaneously does not necessarily mean that the queue will drop to zero car. There are interferences between the experiments, and a more detailed study is beyond the scope of our work.

It is easy to see that for the average queue size to return to 25 taxis, an increase in demand of around 18% is necessary. This means eighty-eight more cars in the system throughout the day and an increase in the annual sales volume of around one hundred and eighty thousand reais.

CONCLUSION

This work, through the use of computational simulation, evaluated alternative solutions to increase productivity in a saturated system, with no immediate prospects of increasing service capacity.

An attempt was made to evaluate the impact of these alternative configurations in terms of the level of service provided to the taxi driver (queue length and waiting time), as well as to estimate a probable increase in the annual sales volume.

BIBLIOGRAPHY

* Costa Neto, Pedro Luiz de Oliveira, “Statistics”, Editora Edgard Blücher, São Paulo, 1977.

* Hillier, Frederick S., “Operations Research”, Holden-Day, San Francisco, 1974

* Saliby, Eduardo; Pimentel, Milton, COPPEAD Report nº 255 – Simul: A Computational System for the Simulation of Discrete Events in Turbo Pascal, Rio de Janeiro, 1991.

Authors: Peter Wanke, Leonardo Barros and Milene Cauzin