## 1. INTRODUCTION

Service industries have realized the need for an extreme increase in efficiency and productivity in competitive markets in order to enhance and improve their service levels. In this regard, customer satisfaction is one of the most important parameters of competitive advantage in service industries. Many people use the services of gas stations throughout their lives. Therefore, gas stations and oil companies can increase their profit by keeping customers satisfied (Saeidi *et al*., 2015;Barzamini and Ghassemian, 2019). In this industry, competitive advantage is defined by visions such as fuel quality, service speed, price, service method and provision of by-products. Given the similarity of most fuel stations in Iran in terms of fuel cost and quality, service speed and queue length are considered as some of the most effective factors in customer satisfaction and sales rate. The present study aims to analyze and optimize a fuel station performance by using the design of experiments (DOEs) (Yang *et al*., 2021). Given the lack of ability of the approach to stop the system or change the general map due to constraints such as cost, time and workforce constraints, it needs to be integrated with the simulation approach to make the analysis possible (Gopi *et al*., 2021;Akhmetova *et al*., 2021;Qazani *et al*., 2019). In the current research, queue length and sales rate are the performance evaluation criteria. Despite the broad use of simulation in many service industries, its integration with experiment design is challenging and no combination of these techniques has been used to assess queue system performance of fuel stations in Iran. In today’s world, queue systems play an important role in modeling and interpreting different issues such as transportation, information technology, supply chain and urban service sector.

In a study, Kazemzadeh *et al*. (2013) presented one robust approach to optimize queuing networks. The proposed model was solved as a numerical example of a restaurant. Yalçınkaya and Bayhan (2009) presented another study on queue system simulation, in which response surface methodology (RSM) and simulation were used for modeling and optimizing average travel time in metro lines. In the foregoing study, some of the objectives of discrete research and simulation included improving the efficiency of the transportation system and wagon fullness and enhancing the performance of the metro and customer satisfaction. Van Weyenberge *et al*. (2017) conducted response surface modeling in quantitative risk analysis for life safety in case of fire. Simulation occurred in various sections, including service, production, health care, defense and general services. This method is one of the commonly used approaches in management operations. Some of the most important issues for use of simulation techniques in real examples are appropriateness, sustainability and relevance. In general, the majority of studies attempt to eliminate corporates’ problems since managers of service organizations are concerned with the number of customers and their own profit (Tan *et al*., 2013). The most important constructs of a standard queue system include the structure of the queue, entry, service processes and queue order. Most studies in service industries have emphasized increased customer satisfaction. In a study, Mende *et al*. (2014) pointed out the effect of customer satisfaction on competitive advantage in service industries (Mende *et al*., 2014). In fact, the service level has a direct effect on customer satisfaction (Saeidi *et al*., 2015). Therefore, service level optimization will increase corporate efficiency in competitive markets (Hurst, 2014;Mazilov and Sakhanevich, 2020; Movchan *et al*., 2020).

The type and quality of demand or number of customers, service priority, appropriate queue length and acceptable waiting time are among the most important factors that affect customer satisfaction, among which queue length and waiting time are important issues that play a considerable role in customers’ perspective toward service quality. Notably, both customer satisfaction and corporate revenues can be considered simultaneously to establish optimal service provision. As a result, multiple decisions must be made to attain the best scenario that is acceptable to both customers and service providers. Several techniques have been proposed to improve service quality and customer satisfaction in the fuel service industry. For instance, Cornillier *et al*. (2008) used an accurate algorithm for a refill at the gas station. In another study, Moazzami *et al*. (2013) focused on simulation and analyzed and modeled a fuel station. The behavior of a fuel station was simulated as one of the most effective parts of a service industry. DOE is a statistical, mathematical and systematic method used to determine the relationship between effective operating factors and process output. In other words, this method is used to find the cause-and-effect relationship between the parameters. The DOE results must be evaluated for managing process inputs, which means that the outputs must be optimized.

To manage process inputs, one must examine. Cheng *et al*. (2000) evaluated a DOE optimization by queue simulation models. According to studies, the use of computer simulation and its results is more efficient for solving variable problems in production systems. However, a simulation model is applied only as a tool in performance evaluation. In a study, Tsai (2002) focused on the evaluation and optimization of integrated manufacturing system operations. This scholar attempted to carry out DOE with mathematical simulation. According to the results, this method could also evaluate and optimize operational situations in production systems. In another study, Can and Heavey (2011) compared DOEs for simulation-based symbolic regression of manufacturing systems. Their main objective was to identify a robust sampling method. In a recent study, Li *et al*. (2014) performed a simulation-based DOE and statistical modeling for lead time quotation. They proposed a statistical and simulation method and made a quality reactive prediction based on their results. Previous studies have shown that simulation findings could be used as DOE input. In fact, simulation and DOE are a system’s behavior analysis tools. In a study, Gopi *et al*. (2021) presented a multi-channel queue system, which can be used in production and distribution systems. Yang *et al*. (2021) used optimal control of arrivals in a G/G/c/K queue with general startup times and non-exponential service time. Moreover, the startup time of the queue system was predicted by a simulation-based technique.

In the present research, we use a simulated fuel station queue system’s behavior and model outputs as DOE raw data. With regard to the previous studies, we analyze a fuel station queue system using a combination of DOE and simulation modeling. In this regard, an integrated DOE-simulation model is used to assess and optimize a fuel station queue system. Different scenarios are considered to assist managers in efficient management. A comparison of simulation results and data obtained from the field study showed appropriate accordance.

## 2. MATERIALS AND METHODS

In the present research, we evaluate 224 Parvin Gas Station located in the fourth district of Tehran, Iran. The station comprises four fueling platforms, each having three fuel pumps. Each fuel station offers two ordinary and super gasoline types, meaning that each platform has two ordinary and super nozzles. Each platform is managed by a worker, meaning that the entire station has four workers. The desired fuel station is situated in a crowded main street. The fuel station queue station is simulated from the moment of entering the fuel station. Each car enters the station and chooses a queue based on its length and closeness to the platform. After joining the shortest queue, the driver waits for their turn to refuel. Then, the desired fuel is chosen and the nozzle related to ordinary or super gasoline is picked up and refuel is done. The fuel fee is paid to the worker and the car exits the queue at the end. In total, 12 fuel platforms are named with two ordinary and super nozzles. In platform 1, the first pump is entitled PN1_1 and PS1_1, the former showing ordinary gasoline and the latter showing super gasoline. As observed in Figure 1, each platform has a worker, meaning that there are four workers working in the fuel station. Different assumptions are considered in the simulation modeling process; for instance, all customers have 12 choices. There are two ordinary and super gasoline types. No customer leaves the queue after entering it. There is no movement in the system, meaning that it is not possible to change the queue lines. Process observations (data collection) are performed on weekdays and at different times of the day. In addition, changes in the selling price of gasoline are ignored, and each liter of gasoline is assumed to have a fixed price. In this regard, one liter of ordinary and super gasoline is 1000 and 1200 Tomans, respectively. Fuel consumption data are collected by the software. The sales amount of each type of gasoline is based on liters. Moreover, Arena software and Input Analyzer are used to analyze data and determine the appropriateness of probable distribution, respectively (16, 17).

In the simulation of 22 Parvin Fuel Station done in Arena software, there are four platforms, each having three pumps with two ordinary and super gasoline nozzles. There are four workers in the station, each managing a platform. The overall module of the process in Arena software explains the logic of choosing the type of gasoline and the decision to choose the desired platform and gas station for each car.

## 3. RESULTS AND DISCUSSION

The module of Cars Arrive to Gas Station indicates how cars enter the station. The module works based on a specified schedule, which is displayed in the schedule section of the data module, such that the number of cars entering the station per hour for 24 hours a day (i.e., an entire day) is considered. The Decide rejected module is the decision to stay or leave the queue. When the cars arrive according to the mentioned schedule, 3% of them leave the system for any reason (e.g., lack of money or lack of time) before entering the station. This number is obtained from objective observations. On the other hand, 97% of the cars enter the fuel station. The Record rejected cars module records the number of cars that have left the system for any reason and have not entered the station. Dispose rejected module shows the number of cars that are completely removed from the system, which is the same as 3% of output machines. In decide about the type of fuel model, the number of cars refueling with ordinary and super gasoline is determined. According to the data collected, 86% of cars are refilled with ordinary gasoline and the rest (14%) are refilled with super gasoline. In the assign amount of fuel module, a refueling capacity is considered for cars that are refueled by ordinary gasoline, which is, in fact, the amount of gasoline each car is refueled with and is based on the distribution function . This distribution function is obtained using the data collected for a typical gasoline nozzle 24 hours a day. In the assign amount of fuel for super module, a refueling capacity is considered for each car that is refueled with super gasoline. This is, in fact, the amount of gasoline each car is refueled with and is based on distribution function TRIA(-0.001, 26, 60). This distribution function is obtained from the data collected for a super gasoline nozzle 24 hours a day. In the decide about which queue for norm module, we determine which platform is chosen by the cars entering the fuel station. Platform selection is done based on the length of queue of each platform, meaning that the car entering the station chooses the shortest queue and waits in the queue to refuel. The decide about which queue for super module, the process is similar to that of the decide about which queue for norm module. However, cars wait in queues to refuel with super gasoline. The platform module is defined for entering the desired platform, which actually includes logic in platforms and final refueling with the desired gasoline. Different modules of fueling logic at each platform is described below. In Pump 1_1 normal gasoline module and seize module, the car enters the station and chooses the nozzle to carry out the refueling stages. In open the tank door in pump 1_1 and delay modules, a certain period is considered for opening the gas tank cap, which is based on the distribution function NORM (50,5), which is considered based on objective observations. In delay for pump 1_1 module, we consider the time taken to refuel a car, which is a function of the amount of gasoline used for refueling. Therefore, considering the assign amount of fuel module, we have the amount of gasoline used for refueling a car. In addition, considering objective observations, we consider three seconds to be sufficient for refueling with one liter of gasoline. In this module, the time taken to refuel a car is estimating by multiplying the amount of gasoline refueled by each car into three (capacity norm*3). In pay money to worker 1 for pump 1_1 and process module, we consider the time taken to pay the gasoline fee. Based on the objective observations, the mentioned time is considered a triangular distribution function with parameters (10, 30, 40). In close the tank door in pump 1_1 module and delay module, we consider the time taken to close the gas tank cap, which is based on the distribution function Norm (30,5). In release pump 1_1 module and release module, the nozzle is let go of at the end of the fueling stages so that the next car could use the nozzle, and the car moves to the exit. In record car need normal fuel module and record module, we record the number of cars that are fueled with ordinary gasoline. In the record car need super fuel module, we record the number of cars that are refueled with super gasoline and have left the system. In the assign normal fuel cost module, we record the income of fuel station from ordinary gasoline- i.e., the ordinary gasoline sales rate. In the assign super fuel cost, we record the income of fuel station from super gasoline- i.e., the super gasoline sales rate. In the record all leaved car module and record module, we record the total number of cars entering the fuel station and performing the fueling process. In the leaved car module and dispose module, we record the number of all cars that leave the system and completely exit the fuel station after finishing all fueling stages. Statistical analysis is carried out in Input Analyzer, for which raw data are entered into the software, and type and constants of the data are calculated following studying their goodness of fit. The probable distribution of the input values is shown in Table 1.

### 3.1 Model Confirmation and Validation

The generated model must be first confirmed to evaluate its accuracy. To this end, the model simulated in the Arena software is compared to a real operational system. After constructing the model, its behavior is compared to a real sample situation. In general, model validation is the overall process of comparing the model and its behavior with a real system and its behavior. The simulated model is implemented for 30 days with data based on December. Then, the model is iterated 100 times and the mean sales rate and queue length are compared with the real results of the mentioned month. As observed, the results obtained from 100 iterations of the model for December matches the actual sales rate of the fuel station with a slight difference. According to the results, the sales rate of December is 4218907800 Tomans and the sales rate of the simulation is 4288407140 Tomans. The relative error of the sales rate is -1.6%, which is a very small amount of error and is acceptable in simulation. To validate the simulated model, the output values (i.e., the sales rate of December) are compared to the sales rates of the past three months. Our input information for fuel station simulation is based on the data recorded in December. The error rate is very low and the output of the fuel station system simulated by the Arena software is completely similar to the output of the real operating system in the past months.

4. DOE and RLM: the results obtained from the simulation model are used for further analysis by the DOE technique. In this regard, DOE is used as a mathematical and statistical method for analysis, modeling and optimizing the performance of simulated fuel stations. Following the assessments, three main factors affecting fuel station performance include the number of gasoline pumps, the number of workers in the station and different time periods in the day. Three levels with a range of five pumps are considered for the pump factor. In this regard, the number of pumps includes three levels of 2, 7 and 12. The number of workers also has three levels with a range of two people, which includes three levels of one, three and five workers. To apply the effect of the reason for the arrival of cars at different hours of the day, evaluation is carried out based on three different scenarios. The busy hours of the fuel station during the day and night are divided into three periods of busy, average visit and solitude. This classification is based on objective observations. The first scenario is from midnight to seven a.m., which is the solitude hours of the station. The second scenario is from seven a.m. to two p.m., which is the average visit time. The third scenario is from two p.m. to midnight, which is busy hour. Each scenario has 3×3 different modes. The proposed method for investigating the impact of effective factors is using DOE and RSM. For each scenario, RSM is applied separately and is implemented by Minitab software. To perform DOE, responses are obtained from Arena simulation outputs since it is not possible to change the level of factors or increase and decrease them at the fuel station. Therefore, fuel station simulation allows us to virtually apply changes of factors in the system and achieve results that could ultimately be used as input in DOE. In RSM, the desired fuel station is analyzed by Central Composite Design (CCD). In this regard, two factors of the number of workers and number of pumps are considered as input factors. Moreover, sales rate and the number of cars in the queue are considered as the response variable. Table 2 shows the combination of two factors of the number of pumps and the number of workers.

The simulation and DOE results are obtained after analyzing different data based on various scenarios. In each scenario, output results for nine modes include sales rate in Tomans and number of cars in the queue. Moreover, the analysis of variance is separately performed for sales rate and the number of cars in the queue in each scenario. In each case, the acceptability of results is guaranteed after determining the ANOVA table results by calculating a P-value below 0.05. The important factors and the experimental model are determined and presented in the next section. In the end, the values related to the optimal number of workers and the number of pumps in each mode are obtained following the implementation of the optimization process. The desired experimental model is presented in Equation 1. For instance, regarding the busy hour or the third scenario, the ANOVA table is the sales rate as in Table 3 and the analysis of variance table is the third scenario for the queue length in Table 4. The experimental model of sales rate and queue length is shown in equations 2 and 3, respectively.

### 3.2 Optimization of Sales Rate and Queue Length Response Variables

Table 5 shows the optimization model of the third or busy scenario of the fuel station.

The third scenario optimization results are presented in Table 6 and Figure 2.

After optimization and observing the output of the process, it is observed that in order to achieve an optimal mode, Worker = 4.27273 and Pump = 10.2828. It is notable that the factor values of the model are integers, so the numbers obtained must be rounded according to the fuel station conditions. Given that the numbers obtained are related to the third scenario- i.e., busy hours of the station (2 p.m. to midnight), we round the number of pumps up and the number of workers down in consultation with the station supervisor. In other words, the optimal number of workers and pumps in busy-hour scenario are 4 and 11, respectively.

## 4 CONCLUSION

In this section, we briefly present the most important results of the present research. Our study was a combination of simulation modeling and DOE. In fact, a combination of computer simulation and different scenarios proposed as DOE input were used to evaluate the performance of the desired fuel station. In this study, fuel station performance was evaluated from two perspectives that are important to fuel station managers, namely the sales rate and customer satisfaction (i.e., queue length). Our findings properly responded to this need of the industry. The process was initiated with the simulation of the fuel station model and the outputs were used as input for DOE with RSM. After simulation and confirmation of the model, it was compared to the real situation for a month with 100 iterations. The relative error percentage was acceptable (1.6%). Moreover, the sales rate and queue length from one month of the model simulation were compared with the actual values of the last four months and the average relative error was estimated at 2.9%, which shows that the simulated system is reliable and its outputs can be used as input and response variables in DOE. Ultimately, DOE and RSM were used to optimize and evaluate the effects of critical factors such as the number of pumps, the number of workers and visit hours in a day. The hours of a day were divided into three scenarios, such that the first-third scenarios had the hours of midnight-seven a.m., seven a.m.-two p.m. and two p.m.-midnight, respectively (solitude, average visit and busy, respectively). Optimization was carried out for each station to minimize the queue length using Minitab software. The optimization results obtained from RSM showed that in the first scenario of sales rate maximization and solitude hours, a station with four workers and nine pumps had the maximum sales rate and minimum queue length. In the second scenario, the best performance was achieved with four workers and 10 pumps. In the last scenario (busy hours), a station with four workers and 11 pumps had the best performance. After accurate evaluation of optimization and RSM outputs, it seems that changes in the number of pumps had a greater effect on the performance of the fuel station, compared to changes in the number of workers, and the number of pumps was a more effective factor in this regard. Moreover, evaluation of optimization results of various scenarios with RSM demonstrated that one worker for each platform at different hours of the day was the optimal number of workers. On the other hand, optimal conditions could be achieved by adding a pump at busy hours. Ultimately, the present study was able to practically assist fuel station managers regarding decision-making and management in critical conditions.