Explore BrainMass
Share

Explore BrainMass

    T.J.'s small local grocery store

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    T.J.'s market is a small local grocery store with only one checkout counter. Assume that the shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag.

    a) If T.J. does not want the average time waiting for service to exceed 5 minutes, what would you tell T.J. about the current system? Is the current system working well?

    b) One of the ways to meet this requirement is to improve the current service rate. But he does not know how much to do it. What would be the new service rate to meet his 5 minutes or less waiting time?

    c) Another option is to hire a full-time person to assist in the checkout operation. T.J. believes that if the new employee assists the checkout cashier, average service time could be reduced to 2 minutes. Will this satisfy his goal of 5 minutes or less waiting time?

    © BrainMass Inc. brainmass.com October 10, 2019, 2:04 am ad1c9bdddf
    https://brainmass.com/math/probability/tjs-small-local-grocery-store-361378

    Solution Preview

    Please see the attached files.

    In this problem we are dealing with an M/M/1 queuing model with:
    Arrival rate λ = 15/hour = 1/4 per minute
    Service rate µ = 1/3 per minute

    a) As per the theory of M/M/1 queuing model average waiting ...

    Solution Summary

    M/M/1 queuing model is integrated in this solution.

    $2.19