Nova Southeastern University

Wayne Huizenga Graduate School

Of Business & Entrepreneurship

Assignment for Course: MGT 5160 Data Driven Decision Making

Title of Assignment: Make the most cost efficient, revenue generating

business decision by manipulating data and using various of analytical

software.

Software used: Analytic Problem Solver (Simulation function)

Instructor’s Grade on Assignment: A

Executive Summary

Bling Max Car Wash offers three levels of car wash service: Economy, Custom, and Deluxe.

Bling Max Car Wash prices are relatively higher than its competitors; Therefore, The owner Bernard

West believes that extended wait times could result in loss of customers and profits. In an effort to

increase revenue, the car wash owner Barnard is considering investing in a blow-off equipment for

$11,500 that will reduce all wash cycles by one minute. In addition to the blow-off equipment, Barnard

is also considering adding a higher-end car wash service that would cost him $8,000. In order to justify

these investments, a case study was conducted that included: Statistical analysis, simulations models,

forecast, and histogram.

After conducting a series of simulations, the case study shows that the best possible choice is to

invest in the blow-off, and not the higher-end car wash service. Four different washing simulation

scenarios were presented during this case study: (1) Current Situation, (2) New Blow-off (3) New Blow-

off with fourth washing service at $10.00 (4) New Blow-off with fourth washing service at $11.00. The

simulations revealed that annual profit will increase by $4,855.00 when all service time is reduced by

one minute.

Background

Bernard West took a loan against his house and used his life savings to invest in an eight year

old car wash. Bling Max Car Wash, the car wash Bernard invested in has exceeded every expectation.

The car wash currently offers three washing service. Due to the relatively high prices of Bling Max

washing services, Bernard is concern that long lines and wait times will drive customers away (Rokicki,

2016). Bernard gathered data on service time and inter-arrival time, and is considering investing $11,500

on a Blow-off equipment that will reduce service time by one minute. In addition, Bernard is also

considering adding a fourth washing service (Elite) which would add one minute to the deluxe time. The

cost of adding the elite service is $8,000. Although Barnard has acquired data on the higher-end washing

service from his brother, he is unsure of his return on investment.

In order to gain clarity of the current situation, Bernard will conduct a series of simulations

using different scenarios to determine the best option. The current situation will stay the same in the first

scenario. The blow-off equipment will be added to the second scenario. The third scenario will include

the blow-off and the fourth washing service at $11.00. And finally the fourth scenario will include the

blow-off and the fourth washing service at $10.00. Bernard plans to make a decision based on the

scenario that has the most reasonable return on investment.

Problem

Determine if extended wait time affect revenue generation of Bling Max Car wash by conducting

a simulation modeling on four different scenarios.

Analysis

This report was conducted to show the statistical correlations between service times/

inter-arrival time and revenue by using a simulation model on four different operation scenarios.

This report includes the following analysis:

1) A brief one- variable summary of the revenue for the four

operation scenarios

2) Histogram of service time and inter arrival time

3) Simulation results of the four operation Scenarios

4) Future value of investment

One- Variable Summary

One variable summary is a descriptive statistic table that summarizes a set of data. This table

provides overviews of multiple data and is easy identify and analyze a given set of data. The table

includes but not limited to mean, medium, mode standard deviation, range, skewness, and the kurtosis. A

one- variable summary of the four simulated scenarios is list below in table 1.

Table 1: One- Variable Summary

The mean is the average daily revenue of the four operation scenarios. The mean is

calculated by adding the revenue of all four scenarios and dividing the sum by four. The average

daily revenue for all four scenarios is $ 694.01.

Histogram

Histograms are graphical displays of data using bars of different heights. It is similar to a bar

chart; however, histograms consolidate numbers into ranges (mathsisfun.com). A histogram may

measure the probability of an occurrence or simply the amount of an occurrence. Histograms are

constructed with variables which are split into intervals known as bins.

Table: 2 Histogram

Inter-Arrival Times (IAT) shows that while a large percentage (60.27%) of customers will be in

and out in seven minutes, there are still 2% of the customers who will wait for 35 minutes from arrival

to completion

Simulation results

Computer simulation imitates the operation of a stochastic system by using the corresponding

probability distributions to randomly generate the various events that occur in the system (F.S. Hillier

and M.S. Hillier, 2014). One of the few benefits of using simulation is that it enables experimentation

without risk to the actual system. The four simulations that was generated for Bernie’s Bling-Max

Carwash produced different results in regards to revenues and profits. In addition, the average wait time

for current situation (long cycle + 3 wash levels) and invest in exiting blow-off (3 wash levels)

decreased drastically to eleven minutes and forty-one seconds. On the other hand, simulation for blow-

off +4 wash levels at pricing “a”, and blow-off +4 wash levels at pricing “b” generated the same number

of average wait time of eight minutes and eight seconds.

Furthermore, estimating the probability distributions for service times and inter-arrival times is

very important for Bling-Max Carwash. The exponential distribution best represented the IAT (inter-

arrival times) because the arrival of customers is known as random events. Customer-selected service

time is represented by uniform integer distribution since there is a fixed minimum and maximum value,

and all integer values are equally likely. The simulation models can be used for a wide range of

decisions, since it is easy to use and understand. The simulations for the current situation (long cycle + 3

wash levels), investing in the new blow-off (3 wash levels), blow-off +4 wash levels at pricing “a”, and

blow-off +4 wash levels at pricing “b” enables Bling-Max Carwash to experiment with the system and

observe its behavior at the same time. The four simulations run can be represented as a statistical

experiment that is generating statistical observations of the performance of the simulated system.

One of the main purpose of running experiments on a simulation model is to answer “what-if”

questions (F.S. Hillier & M.S. Hillier, 2014). The output of Bling-Max Carwash from simulation run

delivered statistical estimates of the desired measures of the performance based on changes in minutes,

price and probability. Setting the initial seed to 1234 and running 10,000 iterations, will most likely

generate more accurate results when using the simulation due to the increase number of replications.

Since Bling-Max Carwash had surpassed the Bernie’s expectations as a small business among other

similar enterprises in Fort Lauderdale, conducting the simulation was the best approach for determining

the best option that would benefit Bernie’s Bling-Max Carwash. The results for running the simulation

can help in finding the cause of a past occurrence, or to forecast future effects or outcomes of assumed

conditions. Comparing the results from the four simulation run with analytical results available is very

important.

Table: 3 Simulation Result (Profit & Revenue)

Current Situation Blow-off

Blow-off + 4 wash ($ 11.00) Blow-off + 4 wash ($ 10.00)

The current situation simulation that was conducted had a ninety-five percent probability that

eighty-five cars washed will exceed the car count of eighty. According to the results for the current

situation simulation, Bling-Max Carwash annual revenue and profit was $234,491 and $153,719,

respectively. Simulation for the new Blow-off investment reflected the improved cycle times that

generated annual revenue and profit of $243,959 and $158,574, respectively. The average wait time for

the new Blow-off investment of six minutes and forty seconds is very impressive. By investing in the

existing blow-off, Bernie will have an increase in annual profit of $4,855.00, and a change in average

wait time of eleven minutes and forty-one seconds. The reduced minutes will enable Bling-Max

Carwash to generate additional revenue and profit. In addition, Bernie’s Bling-Max Carwash will have a

simple payback of about 2.37 years for investing in existing Blow-off.

The simulation for the new blow-off + 4-washes with pricing “a” generated annual revenue of

$249,451, and annual profit of $162,143. The annual revenue and profit is higher than all of the

simulation that was conducted. The simulation model reflected the improved cycle times from the new

blow-off including the impact of “a” pricing. The simulation for the new blow-off + 4-washes with

pricing “b” generated lower annual revenue and profit. The total annual revenue for this simulation was

$222,568, and $144,669 for annual profit. The simulation was updated to reflect the improved cycle

times from the new blow-off including the impact of “b” pricing. Changes in price and probability

lowered the annual revenue and profit for the new blow-off plus the 4-washes with “b” pricing. Based

on the simulation results, the new blow-off plus 4-washes with pricing “a” and “b” differs from the

current situation and new blow-off investment due to accommodation of elite car wash and changes in

costs and probabilities.

Table: 4 Simulation Result (Profit & Revenue)

Current Situation Blow-off

Blow-off + 4 wash ($ 11.00) Blow-off + 4 wash ($ 10.00)

The simulation is especially useful for situations too complex to be analyzed using the analytical

models (F.S. Hillier & M.S. Hillier, 2014). In this case, increasing the number of trials increased the

accuracy of the simulation results. The average waiting time per minutes for the new blow-off plus 4-

washes with pricing “a” and “b” was the same at eight minutes and eight seconds. Investing in the new

blow-off seems like a great idea because it has less average waiting time per minute. During the

simulation process, the percentage chance that the average wait time is ten minutes or less, ten to twenty

minutes, changed a lot from the current situation to the new blow-off investment. In addition, there was

a big shift in percentage chance that the average wait time will be ten minutes or less, wait time is ten to

twenty minutes. For instance, the new blow-off plus 4-washes with pricing “a” has ten percent chance of

waiting less than ten minutes, and a twenty percent chance of waiting for ten to twenty minutes. The

incremental annual profit for the new blow-off plus 4-washed with pricing versus investing in existing

blow-off (3 wash levels) is an increase of $ 3,569. The new blow-off plus 4-washes with pricing “b” will

result in a loss of $ 13,905 when comparing the incremental annual profit by investing in new blow-off.

Based on the simulation model, the average wait time for the new blow-off plus 4-washes with pricing

“a” and “b” as compared to investing in the new blow-off is two minutes and four seconds.

Future Value of Investment

Future Value is the value of cash in a specific time period; this value is the amount of money

accumulated from an interest rate. Future value is calculated when the original data is multiplied by the

accumulation function. Below are sets of tables that show the future value of different investment

scenarios.

Table: 5

Figure 1 Figure 2

This table shows the loan payback amount when $11,500 is borrowed at a 6.5 % interest rate.

Figure 1 illustrate that $15,756.00 will be paid back when a loan of $11,500 is taking out at a five year

pay period. Figure 2 illustrate that $16,780.14 when the same loan is taking out, but the pay period is six

years. An access of $1,024.14 interest will be accrued if a six-year period is select instead of the five-

year period paid if option.

$ 15,756.00 $ 16,780.14

5 Years 6 Years

Conclusion and Recommendations

Bernard should invest in the blow-off equipment. Series of simulations model shows that

revenue will increase by 5 % when just the blow-off equipment is added to the three washing service.

Even though yearly revenue will increase by investing in the special dispenser, Bernard is expecting a

child and cannot afford to make further investment. The car wash will be more profitable with reduction

of service/ wait time.

End of Case Study Answers

What are the implications from the standpoint of business performance and from customer perception

and retention?

The biggest issue is wait time which is correlated to service time. When wait time is extended,

Customers are more likely to go to a nearby competitor since prices are not on the low end. The

Blow-off equipment will reduce service time thus allowing more cars to enter the wash service. In

addition, reduction of service time will create less wait time and increase of customer satisfaction.

Profit and customer satisfaction will increase when service time decrease.

“Efficiency is doing thing right and effectiveness is doing the right thing”

While efficiently increasing profits by gathering data, Bernie effectively increase customer

satisfaction

References

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Brigham, E. F., & Ehrhardt, M. C. (2014). Financial management: Theory and practice. Mason, OH:

South-Western.

Histograms. (2015). Mathisfun.com. Retrieved from https://www.mathsisfun.com/data/histograms.html

Rokicki, P. (2015).Bling Max Car Wash case study. Fort Lauderdale, FL: Nova Southeastern University.

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