Lone Star Insurance Co (LSI) specializes in automobile insurance business. The management of its claims department is preparing operating plans for the next year, particularly the ideal staffing level for claims representatives (who are called "claims reps" for short).
Based on the past and the planned future sales of insurance policies, LSI forecasts the new claims arrival rate to be about 10,000 claims per quarter during the next four quarters (i.e. one year). The claims department has determined that a claims rep reeds to perform four hours of claims handling work per claim to close a claim.
The average age of a claim at closing is estimated to be months (i.e. two quarters). Studies also indicate that a claims rep can effectively perform (after adjusting for lunch and other breaks, administrative meetings, etc.) about 400 hours of claims handling work per quarter. The company desires to achieve a claims' closing rate that is equal to the new claims arrival rate (i.e., 10,000 claims per quarter).
a) What average level of pending claims (i.e. number of open claims) may LSI expect at any point in time during the coming year? Explain. (Please note that this is an ongoing, not a startup, operation.)
b) How many claims reps should LSI employ next year? Explain. What caseload (average number of pending claims per claims rep) will the claims reps experience?