Simulation of Sortation SystemRituparna Sarkar

Illustrative Model

Component of the problem• System State

– LPA(t) : No of packages that were sorted successfully at time t– LPR(t) : No of packages that were rejected at time t– Qi(t) : No of package in lane at time t

• Where i is the lane (1,2,3….,12)

– TW(t) : 0 or 1, Takeaway conveyor is free or busy• Entity

– In-feed conveyor (Length:60feet; Speed:240feet/minute; Accumulating)

– Sortation Lane (Length:15feet; Speed:90feet/minute; Accumulating)– Takeaway conveyor (Length:50feet; Speed: <To be determined>; Non-

Accumulating)– Exit conveyor (Length:30feet; Speed:<Same as Takeaway

Conveyor> ;Accumulating)

• Event– Arrival of package– Package rejected/accepted– Lane ready with slug of 8– Lane chute cleared– Takeaway conveyor completes

service

• Activities– Inter-arrival time of package– Travel time on In-feed conveyor– Travel time on lane conveyor– Travel time on takeaway conveyor

• Delay– Lane accumulating waiting time– Lane release waiting time

Constraints• While feeding the packages into the system. The leading edge of 2 packages has to

be minimum 2 feet apart.• Sortation Lane can release only when

• It has a slug of 8 packages• Takeaway conveyor is empty

• Sortation lane will not accept any package after the 8th package has been collected, and resume accepting only after the 8th package clears the chute of the lane when released.

Problem StatementsA) The speed of takeaway conveyor is to be determined in such a way so that the number of rejection are minimum.Constrained to :

Minimum Conveyors speed 60 feet/min Conveyor speed can increment only in steps of 30Conveyor with higher speed is costly

B) Change the destination allocation of the lane to find the optimal allocation pattern.

Simulation model

• Designed in MS Excel.• Uses probability table and random number

function to simulate

Microsoft Excel Worksheet

Model Run & Analysis

0 1 2 3 4 5 6 7 8Avg 223.65 157.75 112.1 90.79 80.34 75.29 68.88 68.14 66.21CI 95% 204.9 137.9 96.95 76 65.475 58.95 52.475 54.475 54.475

241.1 177.2 136.1 107.1 93.55 89 85 81.1 78Imp 65.9 45.65 21.31 10.45 5.05 6.41 0.74 1.93

StatsModel No

𝑆𝑝𝑒𝑒𝑑=𝐵𝑎𝑠𝑒𝑆𝑝𝑒𝑒𝑑+(𝑆𝑡𝑒𝑝𝐼𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 ∗𝑀𝑜𝑑𝑒𝑙 𝑁𝑜)

Destination Assignment Model0 – As given1 – Destination with highest probability 1st

2 – Destination with least probability 1st 3 – Destination aligned with highest in the middle

Stats 0 1 2 3Avg 80.34 81.43 77.45 78.54CI 95% 65.475 66.475 60 63

93.55 99.1 96.65 94.55Imp -1.09 2.89 1.8

Destination assignment model

What else can be tested?

• The modeling has been done in such way that change in any parameter can be tested until the system remains the same.

• What can be tested– Change in• Speeds & Length of conveyor• Change in destination assignment• Change in feed rate• Change in constraint

Conclusion

• So we see that Takeaway Conveyor speed of 180feet/min give us the optimal results.

• Also, the change in destination assignment does effect the performance of the system but further statistical test are required to check its significance.