Calculate note if minutes some customers might be

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.
Image of page 22
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
Image of page 23
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).
Image of page 24
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).
Image of page 25
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.
Image of page 26
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.
Image of page 27
Image of page 28

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

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors