Question

An insurance agency wants to analyze its claims process. There are two steps in the

process: evaluation and payment processing. When a customer claim arrives at the

agency, it is first evaluated to see if it is a legitimate claim, where the customer would

receive a payment. If it is indeed legitimate, the claim goes to payment processing,

where additional checks are performed and the agency cuts a check to the customer.

The agency on average receives 30 claims per day. There are on average 15 cases under

evaluation and 24 cases in payment processing every day. Only 40% of the cases will

pass evaluation and enter payment processing; the other cases are denied payment and

terminated. What is the average total processing time per case in this agency?

Answer 1

Number of claims in evaluation process = lambda / mu -lambda = 30/mu-30 =15

which gives mu =32

waiting time = lambda / mu ( mu-lambda) = 30/32*2 =0.46875 day

service time = 1/32 day =0.03125 day

total time in system =0.5 day

cases passing evaluation and reaching next process each day= 30x0.4 =12 per day

number of claims in payment processing = 12 / mu-12 = 24

which gives mu =12.5

total time in system = 1/ mu-lambda = 1/12.5-12 = 2 days

total processing time in agency = 0.5+2 =2.5 days