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Capacity of the system to process checks

Suppose a bank clears checks drawn on customers’ checking accounts by using the following process:
Receive checks to Short checks by banks to Ship checks to check clearing house
a) If the capacity for receiving checks is 1000 checks per hour, for sorting checks is 800 checks per hour, and for shipping checks is 1200 per hour, what is the capacity of the system to process checks?
b) If the flow rate is an average of 600 checks per hour and there are an average of 200 checks in the system, what is the average throughput time of checks?
c) What could be done to decrease the throughput time

a) Capacity of the system to process checks

The capacity of the system to process checks is the minimum of the three capacities: 1000 checks/hour, 800 checks/hour, and 1200 checks/hour. Therefore, the capacity of the system is 800 checks/hour.

b) Average throughput time of checks

The average throughput time of checks is the total time spent in the system divided by the number of checks processed. If the flow rate is an average of 600 checks per hour and there are an average of 200 checks in the system, then the total time spent in the system is 200/600 = 0.33 hours. Therefore, the average throughput time of checks is 0.33 hours or 20 minutes.

c) Decreasing the throughput time

There are a few things that could be done to decrease the throughput time of checks:

Increase the capacity of the system. This could be done by adding more resources to the system, such as more employees or more machines.
Reduce the number of checks in the system. This could be done by processing checks more quickly or by reducing the number of checks that are received.
Improve the efficiency of the system. This could be done by streamlining the process or by using better technology.

Additional thoughts The throughput time is important because it is a measure of how long it takes to process a check. A shorter throughput time means that customers will have to wait less time for their checks to be processed. Additionally, a shorter throughput time can save the bank money, as it will reduce the amount of time that checks are sitting in the system. The capacity of the system is also important. A larger capacity means that the bank can process more checks per hour. This can be beneficial if the bank is experiencing a high volume of checks. Additionally, a larger capacity can help the bank to avoid bottlenecks, which can slow down the processing of checks.

Sample Solution

The capacity of the system to process checks is the minimum of the three capacities: