# Calculate note if minutes some customers might be

• No School
• AA 1
• 31

This preview shows page 22 - 28 out of 31 pages.

Calculate . Note: if minutes, some customers might be waiting more than 5 minutes. It is more appropriate to ask what percentage of customers wait less than 5 minutes, but this is more difficult to calculate. Capacity What is the average number of customers in the system or in the queue? Calculate or . Note: if customers, it is possible that at some point the number of waiting customers might exceed 5. What is the probability that the number of customers in the system exceeds 5? e.g., What is the probability that the number of customers in M/M/2 queuing system exceeds 5? With 2 servers, 5 customers are waiting when 2 + 5 = 7 customers are in the system.
A Case Study Tech reps repair machines at customers’ sites. Current policy: Each rep’s territory is assigned machines so that s/he will be active (repairing machines or travelling to site) 75% of time. A repair call averages 2 hours (3 repair calls per day). Machines average 50 workdays between repairs. Hence, 150 machines per rep. Proposed New Service Standard: average waiting time before a rep begins trip to customer site should not exceed two hours. In Queuing terms: Customers: machines needing repair. Arrivals: calls to tech rep requesting repairs. Queue: machines waiting for repair to begin at sites. Server: tech rep. Service time: total time rep is tied up (traveling to site or repairing). Thus, a machine leaves queue and enters service when rep begins trip to site.) Assuming M/M/1: = 3 =0.75 (from M/M/1) Proposed New Service Standard: day
Dupit Corp. Problem Suggested Approaches Approach 1 : Decrease % of time reps are expected to be repairing machines. Approach 2: Provide new equipment to reduce time required for repairs. Approach 3: Adopt larger several-rep territories, rather than 1-person territories. Approach 4: Give owners of printer- copier priority for receiving repairs over others (Will not be analysed).
Approach 1 : Decrease % of time reps are expected to be repairing machines Effectively, lower rep’s utilization factor sufficiently: i.e., Lower r = l / m , until W q 1 / 4 day , Recall , is given = 4 Modify l = (# of machines assigned to rep)/50, until you get required W q. Use Queuing calculator M/M/1 (Justify?) to find that l = 2 gives = 0.25 . Hence, assign to each rep a territory with 100 machines (rather 150).
Approach 2: Provide new equipment to reduce time required for repairs New equipment would have following effect on service-time distribution: Decrease mean ( from 1 / 4 day to 1 / 5 day . Decrease standard deviation () from 1 / 4 day to 1 / 10 day . Memoryless service time assumption not justified ( ). Hence use M/G/1 calculator, with = 3 = 0.1 to find = 0.118.
Approach 3: Adopt several-rep territories, rather than 1-person territories Experiment (M/M/s) with territories with 2 reps, then 3, then ….. Until you get desired result.

#### You've reached the end of your free preview.

Want to read all 31 pages?

• Fall '19
• Normal Distribution, Probability theory, Exponential distribution, Poisson process, Queueing theory

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern