At the security station of Singapore Airport, all carry-on bags must first be X-rayed. Two resources are involved in X-raying. First, there is a conveyer belt that moves the bags through the X-ray machine. The conveyer belt can hold at most 5 bags and it takes 25 seconds for a bag to travel from the beginning to the end of the machine. You can assume that the conveyor belt is always moving and never stopped. The second resource is the X-ray inspector, who examines a picture of the bag while it is on the belt. Examining the picture takes an average of 4 seconds. The inspector is able to work while the belt is moving. After being X-rayed, most bags are given back to the passengers. However, 5% of the bags are selected for bomb testing. First, a security agent wipes a special disposable cloth on the luggage and puts the cloth into a ‘sniffer’ machine that detects chemicals that might be used to make bombs. This ‘wiping and placing’ takes 10 seconds and does not use up any time at the sniffer. Then the sniffer tests the cloth. Testing does not require the attention of the security agent. Testing requires, on average, 80 seconds. After testing, the sniffer cloth is thrown away and replaced.
a) Draw a process-flow diagram for this process. Make it as complete as possible. If you must make any assumptions, describe them below your diagram.
b) Calculate the capacity of each resource in the process.
c) Suppose that the arrival rate of bags is increasing dramatically. Identify the bottleneck resource and find the capacity of the process (in bags/minute).
d) New security rules implemented require that more than 5% of the bags must be passed through the sniffer. How high can the percentage rise without affecting the capacity of the system?