Students are going through a three-step process to obtain their ID cards. Each s
ID: 353573 • Letter: S
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 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 fullExplanation / Answer
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.