1. l = 1 llamada/50 hours = 0.02 calls per hour
2. Mean service time = travel time + repair time = 1 + 1.5 = 2.5 hours m = 1 / 2.5 hours = 0.4 customers per hour
3. 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 hour of the service time. Thus, travel time must be added to the time spent in line as predicted model in order to determine the total customer waiting time.
4. Using output from The Management Scientist, we have the following:
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 hours* Average time until the machine is back in operation 4.1082 hours Probability of a wait more than one hour 0.4620 Hours a week the technician is not on service calls (0.5380) x 40 hours = 21.5 hours Total cost per hour for the service operation $155.93
*The average time a customer spends in the waiting line is 1.6082 hours. This is the average time for the service technician to complete all previous service call commitments and be ready to travel to the new customer. Since the average travel time is 1 hour for the service technician to reach the new customer's office, the total customer waiting time is 1.6082 + 1 = 2.6082 hours. Thus, the one technician is able to meet the company's 3-hour service guideline. The total cost is $155.93 per hour.
Note that the waiting line model indicates...