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LGT3105 Operations Management - Tutorial 5: Service Processes
1. The wheat harvesting season is short. Most farmers deliver their truckloads of wheat to a central storage bin and return back to the fields. The central storage bin is owned cooperatively by the farmers and they have assigned a waiting cost of $18 per hour for each truck and driver. The storage bin operates 16 hours per day and 7 days a week. It is capable of unloading an average of 35 trucks per hour. Full truckloads arrive at an average interval of 2 minutes. The unloading time is distributed exponentially and the arrival rate follows a Poisson distribution.
a. What is the average number of trucks and the average time per truck in the system?
b. What is the probability that more than 3 trucks are in the system?
c. The farmers use the storage bin only for 2 weeks per year. They estimate that enlarging the storage bin would speed up the unloading process. The estimated unloading time is 80 seconds on average, distributed exponentially. It will cost $9,000 for the expansion. Is it worthwhile to do so? Explain.
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2. Snack Times supplies vended food to a large university. Because students often kick the machines out of anger and frustration, management has a constant repair problem.
The machines break down on an average of three per hour and the breakdowns are distributed in a Poisson manner. Downtime costs the company $25 per hour per machine, and each maintenance worker gets $4 per hour. One worker can service machines at an average rate of five per hour; two workers working as a team can service seven per hour; and a team of three workers can do eight per hour. All service times are distributed exponentially. What is the optimal maintenance crew size for servicing the machines?
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3. Wonderful Car Wash is studying the service performance of its car wash centre in
Hung Hom. A wash station is installed inside the centre. During weekdays, five cars
1. The wheat harvesting season is short. Most farmers deliver their truckloads of wheat to a central storage bin and return back to the fields. The central storage bin is owned cooperatively by the farmers and they have assigned a waiting cost of $18 per hour for each truck and driver. The storage bin operates 16 hours per day and 7 days a week. It is capable of unloading an average of 35 trucks per hour. Full truckloads arrive at an average interval of 2 minutes. The unloading time is distributed exponentially and the arrival rate follows a Poisson distribution.
a. What is the average number of trucks and the average time per truck in the system?
b. What is the probability that more than 3 trucks are in the system?
c. The farmers use the storage bin only for 2 weeks per year. They estimate that enlarging the storage bin would speed up the unloading process. The estimated unloading time is 80 seconds on average, distributed exponentially. It will cost $9,000 for the expansion. Is it worthwhile to do so? Explain.
Page 1 of 3
2. Snack Times supplies vended food to a large university. Because students often kick the machines out of anger and frustration, management has a constant repair problem.
The machines break down on an average of three per hour and the breakdowns are distributed in a Poisson manner. Downtime costs the company $25 per hour per machine, and each maintenance worker gets $4 per hour. One worker can service machines at an average rate of five per hour; two workers working as a team can service seven per hour; and a team of three workers can do eight per hour. All service times are distributed exponentially. What is the optimal maintenance crew size for servicing the machines?
Page 2 of 3
3. Wonderful Car Wash is studying the service performance of its car wash centre in
Hung Hom. A wash station is installed inside the centre. During weekdays, five cars