Question

Students are going through a three-step process to obtain their ID cards. Each student will spend 2 minutes at registration desk before going to one of three cashiers to pay a fee for the ID card. After that, he/she will visit one of four ID processing stations to have his/her picture taken and ID card printed. Visits to the cashier and ID processing station take 10 and 20 minutes respectively. If the demand rate is 0.125 student per minute, how long does it take to process 20 students assuming the system is full

Answer 1

To be calculated:

Time taken to process 20 students

Given values:

A 3-step process

Process 1 - Registration desk, Number of servers = 1, Time taken = 2 minutes

Process 2 - Cashier, Number of servers = 3, Time taken = 10 minutes

Process 3 - ID processing station, Number of servers = 4, Time taken = 20 minutes

Demand rate = 0.125 student per minute

Solution:

Capacity of each of the server at three-processes is calculated as;

Capacity = Number of students served per minute

Registration desk

Time taken to serve 1 student = 2 minutes

Capacity = 0.5 students per minute

Cashier

Time taken to serve 1 student = 10 minutes

Number of servers = 3

Capacity = 0.3 students per minute

ID processing station

Time taken to serve 1 student = 20 minutes

Number of servers = 4

Capacity = 0.2 students per minute

Of the given three processes, the bottleneck process is the ID processing station as it takes the highest time to serve 1 student. Therefore, the process capacity is equal to the capacity of the bottleneck process.

Process capacity = 0.2 students per minute

Given, Demand rate = 0.125 student per minute

Since, the demand rate is less than the process capacity, the number of students served per minute will be equal to the demand rate.

Number of students served per minute = 0.125

Time taken to serve 1 student = 1 / 0.125 = 8 minutes

Time taken to serve 20 students = 8 x 20 = 160 minutes

Time taken to process 20 students is 160 minutes.