1345 deals with assembling items in cartoons and then checking actval waechouse

Question

1345 deals with assembling items in cartoons and then checking actval waechouse optimization an 8-hour work day enters roller comveyor, these inputs are Service line coesists of an e-point that is wsed to record the information about the weight, number, haracteristics of cartooes Served one cartoon in e-point takes in average 5 minutes and ntation of the queving modet in the foms of (a wexiden & mark) b. Calculate the average number of items in the syste 3& marks) HintFind3 and c. What is the expected waiting time in the roller conveyor? Gmarks) the probability of having more than 3 items in the system. (2.marks) e Per new policy, the waiting time in the belt conveyor should not exced 10 min. How n servers should be added to meet the new requirements? (4 marks

Explanation / Answer

a) The characteristics of the model are: Single server, Infinite population, Poisson arrival, FCFS, Exponential service time, Unlimited queue length . So this is M/M/1 queue model

b) Arrival rate, = 80/8 = 10 per hour

Service rate, = 60/5 = 12 per hour

Average number of items in the system, L = /(-) = 10/(12-10) = 5

c) Expected time in the system, W = L/ = 5/10 = 0.5

Expected waiting time in the queue, Wq = /(*(-)) = 10/(12*(12-10) = 0.4167

f) Probability of n customers in system, Pn = (1-)*n , where = / = 10/12 = 0.833

Probability of having more than 3 items in the system = 1 - (P0 + P1 + P2 + P3) = 1 - ((1-0.833)*0.8330 + (1-0.833)*0.8331 + (1-0.833)*0.8332 + (1-0.833)*0.8333)

= 0.4823

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