IMPROVING THE UTILIZATION OF TELLERS USING SIMULATION AT XYZ BANK

Simulation is one of the techniques of operations research and management science that is most used widely. The goal of simulation is to estimate the performance measures of the evaluated system using computers. This paper provides the simulation of tellers to estimate and then improve its performance measure which is the utilization. The initial utilization of XYZ Bank is 24.13% on average. Two scenario are conducted to improve the utilization. Scenario 1 improves the utilization by 32.26% on average and scenario 2 improves the utilization by 47.84% on average. This paper suggests XYZ Bank to apply scenario 2 that can improve the utilization by 23.72%.


I. INTRODUCTION
According to Law and Kelton (1991), simulation is one of the techniques of operations research and management science that is most used widely. Simulation is used in complex systems which the models can not be evaluated analytically. The goal of simulation is to estimate the performance measures of the evaluated system using computers (Taha, 2007). This paper provides the simulation of tellers to estimate and then improve its performance measure which is the utilization. The simulation that is built in this paper adopts the methodology of Law and Kelton (1991).
There are four tellers that are available in the XYZ Bank. The conceptual model of XYZ Bank is given in Figure 1. Customers arrive at the bank and they queue to get the service. The customers are served based on FCFS (first come first served) rule and the availability of the tellers. After the customers are served by the tellers, they leave the bank.

II. METHODOLOGY
As it was mentioned previously, this paper adopts the methodology of Law and Kelton (1991) to build the simulation. The flow chart to build the simulation can be seen in Figure 2.

III. 1 Data
Based on Figure 1, it can be known data needed to build the simulation. They are interarrival time of the customers, service time of Teller 1, Teller 2, Teller 3, and Teller 4. The distribution of all the data is given in Table 1. In Figure 3, the result of goodness of fit test for interarrival time of the customers is given.

Figure 3. The result of goodness of fit test for interarrival time
The result of goodness of fit test for service time of Teller 1 is given in Figure 4. The result of goodness of fit test for service time of Teller 2 is given in Figure 5. The result of goodness of fit test for service time of Teller 3 is given in Figure 6.

III.2 Verification and Validation
Verification is performed to assess whether the model (computer model) operates correctly (Altiok and Melamed, 2007). After performing verification for simulation model in this paper, it concludes that the simulation model is verified.
The accuracy of the simulation model to represent the real system is known as validation (Law and Kelton, 1991). Hypothesis testing is used to validate the simulation model. The result of the simulation model in the terms of number of customers exiting is given in Table 2. Meanwhile, from collected data, the number of customers exiting for ten days of observation is given in Table 3. Hypothesis testing used is confidence interval on the difference in means where (Montgomery and Runger, 2003). The hypothesis is given as follow.

…[1] …[2]
Confidence interval on the difference in means is as follow.

…[3]
Degree of freedom is given as follow. For , the conclusion is do not reject and states that the model is valid.

III.3 Number of replications
The method used to determine the number of replications needed is relative error method that is given as follow.

…[5]
For the evaluated system, the data are given in Table 2. For and , the number of replications needed is 7 replications.

IV. DESIGN OF EXPERIMENTS
Result of the initial simulation in the terms of the utilization can be seen in Table 4. As it was mentioned before, this paper tries to estimate and then improve the utilization of the tellers. There are two scenarios developed to improve the utilization. Scenario 1 is removing Teller 4 and the result of scenario 1 is given in Table 5. Scenario 2 is removing Teller 3. The result of scenario 2 can be seen in Table 6.

V. ANALYSIS OF COMPARING SYSTEM
Number of customers exiting for initial, scenario 1, and scenario 2 is given in Table 7. Since there are 3 populations and single experiment, the hypothesis testing used is one-way Analysis of Variance or one-way ANOVA (Walpole et al., 2007).
The hypothesis is given as follow.

…[6]
for at least one …[7] For , the conclusion is do not reject and states that one population is not significantly different than the others.

VI. CONCLUSIONS
This paper estimates and improves the utilization of tellers at XYZ Bank using simulation. As it can be seen in Figure 8, initial utilization of XYZ Bank is 24.13% on average. Two scenario are conducted to improve the utilization. Scenario 1 improves the utilization by 32.26% on average and scenario 2 improves the utilization by 47.84% on average.

Figure 8. Improvement of the utilization
This paper suggests XYZ Bank to apply scenario 2 that can improve the utilization from 24.13% to 47.84%. There is an improvement by 23.72%. The number of tellers also decreases from 4 tellers to 2 tellers which means the cost also decreases.