Case: Dupit Corp. •The Dupit Corporation is a longtime leader in the office photocopier marketplace. •Dupit’sservice division is responsible for providing support to the customers by promptly repairing the machines when needed. This is done by the company’s service technical representatives, or tech reps. Currently, 10,000 tech reps. •Current policy:Each tech rep’s territory is assigned enough machines so that the tech rep will be active repairing machines (or traveling to the site) 75% of the time. –A repair call averages 2 hours, so this corresponds to 3 repair calls per day. –Machines average 50 workdays between repairs, so assign 150 machines per rep. •Proposed New Service Standard:The average waiting time before a tech rep begins the trip to the customer site should not exceed two hours.
Alternative Approaches to the Problem •Approach Suggested by John Phixitt:Modify the current policy by decreasing the percentage of time that tech reps are expected to be repairing machines.-> We need to change arrival rate!•Approach Suggested by the Vice President for Engineering:Provide new equipment to tech reps that would reduce the time required for repairs. •Approach Suggested by the Chief Financial Officer:Replace the current one-person tech rep territories by larger territories served by multiple tech reps. •Approach Suggested by the Vice President for Marketing:Give owners of the new printer-copier priority for receiving repairs over the company’s other customers.
The Queueing System for Each Tech Rep •The customers:The machines needing repair •. •Customer arrivals:The calls to the tech rep requesting repairs. •The queue:The machines waiting for repair to begin at their sites. •The server:The tech rep. •Service time:The total time the tech rep is tied up with a machine, either traveling to the machine site or repairing the machine. (Thus, a machine is viewed as leaving the queue and entering service when the tech rep begins the trip to the machine site.)
Single-Server Queueing Models •O= Mean arrival ratefor customers = Expected number of arrivals per unit time 1/O= expected interarrival time •P= Mean service rate(for a continuously busy server) = Expected number of service completions per unit time 1/P= expected service time •r= the utilizationfactor = the average fraction of time that a server is busy serving customers = O/ P
Utilization factor •r= O/P•the average fraction of time that a server is busy serving customers •Dupit service division –O= 3 calls / day –P= 4 calls / day (if fully working) –r= O/P= ¾= 75% = active repairing machines (or traveling to the site) 75% of the time.
M/M/1 •Assumptions –Interarrival timeshave an exponential distribution with a mean of 1/O. –Service timeshave an exponential distribution with a mean of 1/P.
You've reached the end of your free preview.
Want to read all 49 pages?
Dr. A. Kader Mazouz
Probability theory, Exponential distribution, Queueing theory, John Phixitt