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Office Equipment, Inc.
Office Equipment, Inc. (OEI), leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of
providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of three hours from the time that the customer notifies OEI of an equipment problem.
Current Business Model
One service technician
contracts with 10 customers
1 call per 50 hours of operation
1 hr travel time to reach customer
1.5 hrs. to complete repair
cost of service technician is $80/hr
dowtime costs for customer is $100/ hr
Within one year, OEI plans on having 20 customers, and within two years, 30 customers. Management is concerned about the ability of one technician to meet the average 3 hour service call guarantee when it's customer base expands.
the arrival rate for each customer per hour
Service rate in terms of the number of customers per hour
1/50 = 0.02 Calls per hour
1/2.5 = 0.4 Customers per hour
How should the travel time and the waiting time predicted by the waiting line model be combined to determine the total customer waiting time?
The travel time is 1 hour. While this is considered part of the service time, it actually means that the customer will be waiting during the first hours of the service time. Travel time must be added to the time spent in line as the predicted model in order to determine the total customer waiting time.
Probability that no customers are in the system 0.5380
Average number of customers waiting 0.2972
Average number of customers in the system 0.7593
Average time a customer spends in the waiting line 1.6082 hrs
Average time until the machine is back in operation 4.1082 hrs
Probability of a wait more than an hour 0.4620
Hours a week the technician is not on service calls 21.5 hrs
(0.5380) x 40 hrs=21.5 hrs
Total cost per hour for the service operation $155.93
Can one technician meet the average 3 hour service call guarantee?
The average time a customer spends waiting in line is 1.6082 hrs. That is the time for a technician to complete all previous service calls and be ready for a new customer. Total customer waiting time is 1.6082 + 1 = 2.6082, which means that they will meet the 3 hour service guideline.
Recommendation for 20 customers
Probability that no customers are in the system 0.3525
Average number of customers in the waiting line 0.2104
Average number of customers in the system 1.1527
Average time a customer spends in the waiting line 0.5581 hrs
Average time until the machine is back in operation 3.0581 hrs
Probability of a wait more than an hour 0.2949
Hours a week technician is not on service calls
= 0.3525 (0.35250) x 2 technicians x 40hrs = 28.2 hrs
= 0.3525 (0.3525) x 1 technician x 40hrs = 14.1 hrs
Total Cost per hour of service operation $275.27
Recommendation for 30 customers
Probability that no customers are in the system 0.1760
Average number of customers in the waiting line 0.9353
Average number of customers in the system 2.3194
Average time a customer spends in the waiting line 1.6895 hrs
Average time until the machine is back in operation 4.1895 hrs
Probability of a wait more than an hour 0.5600
Hours a week that the technician is not on service calls
P = 0.1760 (0.1760)x 2 technicians x 40 hrs = 14.08 hrs
P = 0.2640 (0.2646) x 1 technician x 40 hrs = 10.56 hrs
Total = 24.64 hrs
Total cost per hour of service operation $391.94
Annual Savings of Recommendation
The recommendation is to stay with two technicians because it has an annual savings of
($397.08-$391.94)x8hrs/day x 250 days/yr = $10,280