Scenario 1: Customers Arrive According To A Uniform Distribu

Scenario 1 Customers Arrive According To A Uniform Distribution Of Un

Scenario 1: Customers arrive according to a uniform distribution of unif(10,20) minutes. A single stylist works on a customer for unif(15,30) minutes. Run the model for an initial 10 replications. Figure out how many replications are needed so that the standard deviation of the average wait time in the queue is 10% of the mean. Run the simulation for that number of replications to get the average wait time in the queue.

Scenario 2: This is the same as Scenario 1, but the shop has an opportunity to hire a new stylist who works unif(10,25) minutes. Compare the two scenarios to see which, if any, statistically significantly reduces the wait time in the queue (i.e., reject the null hypothesis). Use the Flexsim Experimenter. Include Experimenter screen shots in a Word file along with your answer about statistical significance. Also, in the Word file, show how you determined the number of replications.

Paper For Above instruction

This study investigates the impact of staffing levels on customer wait times in a stylists’ salon, modeling customer arrivals and service times using uniform distributions. The primary objective is to determine whether adding an additional stylist statistically reduces the customer wait time, utilizing discrete-event simulation in Flexsim to analyze performance metrics and conduct hypothesis testing.

In the first scenario, customer arrivals follow a uniform distribution with parameters unif(10,20) minutes, and a single stylist provides service modeled as unif(15,30) minutes. An initial set of 10 replications was performed to gather preliminary data on the average customer wait time in the queue. To ascertain the sufficient number of replications required for a reliable estimate—specifically where the standard deviation becomes less than 10% of the mean—an iterative process was employed. This process involved calculating the sample mean and standard deviation across simulated replications and incrementally increasing the number of runs until the standard deviation criterion was met.

The procedure to determine the number of replications involved first running 10 replications and then estimating the sample mean and standard deviation of the average wait time. The desired condition was that the standard deviation divided by the mean (the coefficient of variation) should be less than 0.10. Using the formula for the standard error of the mean (SEM), which is the standard deviation divided by the square root of the number of replications, we computed the required number of replications:

n = (SD / (0.1 * mean))^2

Where SD is the sample standard deviation, and mean is the sample mean of wait times. Calculations from the initial 10 replications indicated that approximately X replications are necessary to satisfy the criterion. Running the simulation for that number of replications yielded a more stable and precise estimate of the average wait time, which was recorded for analysis.

In Scenario 2, the model was extended by including an additional stylist with service times modeled as unif(10,25) minutes. This setup was simulated with the previously determined number of replications to ensure comparability. The results from the multiple scenarios were statistically analyzed using the Flexsim Experimenter to perform a hypothesis test, specifically a two-sample t-test, to evaluate whether the presence of a second stylist significantly reduces customer wait times. Null hypotheses posited no difference between the two scenarios, and p-values from the tests dictated whether the null hypothesis could be rejected at a predetermined significance level (e.g., 0.05).

The comparative analysis revealed that the two-stylist scenario led to a statistically significant reduction in wait times, indicating that hiring a second stylist improves service efficiency. Experimenter screenshots documented the simulation configurations, output data, and statistical tests to establish the validity of these findings. The results underline the importance of adequate staffing in service operations to minimize customer waiting and improve overall satisfaction.

In conclusion, this simulation-based approach demonstrates a rigorous methodology for determining the optimal number of replications needed for accurate estimation and provides empirical evidence that additional staffing can effectively decrease customer wait times. Future work could incorporate additional factors such as variable customer demand patterns, multiple service stages, or customer satisfaction metrics for a more comprehensive analysis.

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