Question

A bank receives load applications from 6 customers a day. The bank has promised customers that applications will be processed in the order they are received. The table below shows the applications in the order they were received, the processing time for each loan application, and the due date that customers need to hear about their application status: Customer Processing time (days) Due date (days) A 9 12 B 11 17 C 8 10 D 7 12 E 10 21 F 12 27

a. Determine the average processing time for applications, the average days tardy for each customer's application, and the average number of applications being processed if the bank processes the applications in the order they were received. (Round your answers to 2 decimal places.)

b. The bank decides to improve their application processing performance by giving priority to the loans that take a shorter time to be processed (SPT). If they do this, determine the average processing time, average tardiness, and the average number of applications processed. (Round your answers to 2 decimal places.)

c. Now assume the bank gives priority to the applications who have the earliest due dates (EDD). Determine the average processing time, average tardiness, and average number of applications in this scenario. (Round your answers to 2 decimal places.)

d. Now assume the bank announces that it will take into account both the processing time and the due dates in order to determine the order of the applications to be processed (CR). Calculate the average processing time, average tardiness, and average number of applications. (Round your answers to 2 decimal places.)

Answer 1

The average processing time and the other metrics can be calculated using simple arithmetic operations, with the applications being analyzed in different orders as specified by SPT, EDD, and CR methodologies.

Step-by-step explanation:

Loan Application Processing Times

The average processing time for applications can be calculated by adding all processing times together and dividing by the number of applications, which in this case, is 6. For example, (9+11+8+7+10+12)/6 would give the average processing time.

To find the average days tardy for each customer's application, we would first determine if any applications are late by subtracting the processing time from the due date. If a result is negative, that application is tardy. Summing these negative values (for just the tardy applications) and diving by the number of applications will give the average tardiness.

When calculating the average number of applications processed, we consider the total time span in days from the start of processing the first application to the completion of the last application, and then divide by the processing time for each application to find the average.

To answer parts b, c, and d involving the Shortest Processing Time (SPT), Earliest Due Date (EDD), and Critical Ratio (CR) respectively, we would run similar calculations with the applications reordered according to the relevant method, noting that reordering may alter processing start times and due dates with respect to the original order.

Answer 2

The question involves calculating average processing time, average tardiness, and average number of applications under different priority processing rules in a bank setting, which involves operations management concepts like queueing theory and scheduling.

Step-by-step explanation:

The question pertains to the calculation of average processing time, average tardiness, and average number of applications processed under different priority rules at a bank. These calculations involve concepts from operations management, specifically queueing theory and scheduling.

To calculate the average processing time, we would take the sum of all processing times and divide it by the number of customers. Average tardiness requires us to calculate the difference between the completion time of an application and its due date for each customer, considering the sequence the applications are processed. Average number of applications being processed involves understanding the workflow and determining how many applications are, on average, in the system at any given time.

For scenario a, where applications are processed in the order they are received, we would simply average the given processing times and due dates. In scenario b with Shortest Processing Time (SPT), we would reorder the processing times in ascending order before calculating averages. Scenario c with Earliest Due Date (EDD) would require us to reorder the applications based on due dates. Lastly, for scenario d, which combines both criteria (Critical Ratio, CR), we must consider a strategy that takes into account both processing time and due dates, such as prioritizing based on the ratio of time left to due date over processing time.

These calculations form part of scheduling and operational efficiency studies, which can lead to improved customer service and optimized bank operations.