PROBLEM 2: Assume that the information desk employee in Problem 1 earns $10 per

Question

PROBLEM 2: Assume that the information desk employee in Problem 1 earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.

(Stated in Problem 2) PROBLEM 1: A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.

NEED PROBLEM 2 ANSWERED. Provided 1 because of background.

Explanation / Answer

arrival rate, lamda = 20/ hr

Service rate, mu = 60/2 = 30/hr

Utilization, rho = lamda/ mu = 2/3 =.667

Length of queue, Lq = (rho)2 / (1-rho) = 0.6672 / (1-0.667) = 1.35

Average waiting time in queue, Wq = Lq/ lamda = 1.35/ 20 = 0.0675 hours

Average arrival in one hour = 20

Total arrival in 8 hours = 160

Total cost of waiting = $12* (160)*(0.0675) = $129.6

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.