Question

To manage their rental counter, Too Late can add a computerized check-in option. Upon arrival, customers will first go to the check-in machine, enter their reference number, (electronically) sign a waiver, and make a payment. After this step is complete, the customer will go to the attendant on duty to receive the vehicle’s keys and directions to its parking location.

If a customer arrives at the check-in station and finds that it is being used by another customer, the incoming customer must wait in line until the machine is open. Similarly, if a customer arrives to the attendant’s station and finds that the attendant is working with another customer, the incoming customer must wait in line until the attendant is free.

The time spent at the check-in machine is assumed to be normally distributed with a mean of 210 seconds and a standard deviation of 50 seconds. The time spent with the attendant is distributed as follows:

Time (seconds)	180	240	300	360
Probability	.1	.15	.5	.25

The time between customer arrivals is distributed as follows:

Time between arrivals (seconds)	60	120	180	240
Probability	.4	.3	.2	.1

This computerized check-in option will be considered viable if the average time that a customer spends in the system (the difference between the time when the customer finishes with the attendant and the time when the customer arrived) is less than 6 minutes and if the average time a customer spends waiting in line (the total of the time waiting for the machine and the time waiting for the attendant) is less than 30 seconds.

Build a model that will simulate the next 100 customers that arrive. Does this option appear viable?

Answer 1

Ans. According to the question please look at the following image :-

Now in the above image customer arrive random times from {1,2,3,4} minutes and service time vary from {3,4,5,6} minutes. Consider the system for 100 customers.

Now look at the simulations run for 100 customers : Below is the attached image

Now this computerized check-in option will be considered viable if the average time that a customer spends in the system is less than 6 minutes & if the average time a customer spends waiting in line is less than 30 seconds.

Now,

Average time that a customer spends in the system

[From the table]

Again average time a customer spends wainting =

This is simulation model for the next 100 customers that arrive. Where a machine is viable if average time spends in the system is less than 6 minutes & we have got 4.56 minutes.

But , average time waiting in line should be less than 30 seconds. And we have found it is as 1.55 minutes.