# Generate a spreadsheet with 100 trials (replications) that reflect the following empirical

2
Problem #1 7 of 32 points
Genetrounce a spreadsheet with 100 trials (replications) that animadvert the coercionthcoming experimental distribution
(undivided month = 30 days):
Middle # holders transshipped / hour Observed # days/month
100 – 199 6
200 – 299 12
300 – 399 9
400 – 499 3
1. Mathematically, how divers holders would you await to be transshipped each hour, on
average?
2. Delight interpretation the average and measure failure athwart your 100 trials to indicate how divers
containers the harbor can await to transship per hour, on middle, and how proud the variability
of that compute faculty be. Delight contribute a culm file of the values you observed (e.g., “5
to 10”). Interpretation the midpoints of the categories (e.g., 150 coercion the file 100-199) coercion these
calculations.
3. Construct a histogram. When you re-run your trials (by urgent-compulsory F9), what happens to your
mean, measure failure and the model of the distribution as shown in the diagram?
happens to the middle, measure failure and histogram? What does that average really?
Problem #2 12 of 32 points
A coal barge arrives at the generating station’s harbor sum half hour, on middle. It takes abquenched 3 hours
and 18 microscopics to unimpeach a barge, a compute that varies with the bulk of the impeach. There is very little
space in the canal coercion pursuit arriving ships. The harbor currently has 8 lodgings, and the compute of ships in
the harbor is poor to the compute of lodgings.
The harbor antecedent is regarding re-sizing the harbor by changing the compute of lodgings conducive (fewer
or over than currently), to a climax of 10. It has enumerated on you, as a Master of Supply Chain
Management, to succor indicate how divers lodgings to reconfigure to.
1. Using queueing anatomy, estimate whole manageable utilization trounces, amid the file of lodgings
considered. What is the stint compute of lodgings needed?
2. (Delight smooth up your answers to these questions to the direct integer.) How fur period would
barges consume in sum? In sum (indetermination plus lodging)? How divers barges would be indetermination in front
of the harbor, and how divers would be in the harbor, on middle?
3. What would you applaud?
3
Formulas: Wq = Lq / l
W = Wq + 1/µ = Lq/ + 1/. = Wq + Ws
L = Lq + l/µ = Lq + Ls
r = l / Mµ
Do Referable Copy or Post
This muniment is identified coercion interpretation barely by MARKUS BIEHL until October 2010. Copying or posting is an
infringement of copyright. Permissions@hbsp.harvard.edu or 617.783.7860.
Note on the Management of Queues 680-053
13
Exhibit 3 Awaited Compute of People Indetermination in Line (Lq) coercion Values of M and !/µ.
Compute Of Labor Channels, M
!/µ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.10 0.0111
0.15 0.0264 0.0008
0.20 0.0500 0.0020
0.25 0.0833 0.0039
0.30 0.1285 0.0069
0.35 0.1884 0.0110
0.40 0.2666 0.0166
0.45 0.3681 0.0239 0.0019
0.50 0.5000 0.0333 0.0030
0.55 0.6722 0.0149 0.0043
0.60 0.9000 0.0593 0.0061
0.65 1.2071 0.0767 0.0084
0.70 1.6333 0.0976 0.0112
0.75 2.2500 0.1227 0.0147
0.80 3.2000 0.1523 0.0189
0.85 4.8166 0.1873 0.0239 0.0031
0.90 8.1000 0.2285 0.0300 0.0041
0.95 18.0500 0.2767 0.0371 0.0053
1.0 0.3333 0.0454 0.0067
1.2 0.6748 0.9040 0.0158
1.4 1.3449 0.1778 0.0324 0.0059
1.6 2.8444 0.3128 0.0604 0.0121
1.8 7.6731 0.5320 0.1051 0.0227 0.0047
2.0 0.8888 0.1739 0.0398 0.0090
2.2 1.4907 0.2770 0.0659 0.0158
2.4 2.1261 0.4305 0.1047 0.0266 0.0065
2.6 4.9322 0.6581 0.1609 0.0426 0.0110
2.8 12.2724 1.0000 0.2411 0.0659 0.0180
3.0 1.5282 0.3541 0.0991 0.0282 0.0077
3.2 2.3856 0.5128 0.1452 0.0427 0.0122
3.4 3.9060 0.7365 0.2085 0.0631 0.0189
3.6 7.0893 0.0550 0.2947 0.0912 0.0283 0.0084
3.8 16.9366 1.5184 0.4114 0.1292 0.0412 0.0127
4.0 2.2164 0.5694 0.1801 0.0590 0.0189
4.2 3.3269 0.7837 0.2475 0.0827 0.0273 0.0087
4.4 5.2675 1.0777 0.3364 0.1142 0.0389 0.0128
4.6 9.2885 1.4867 0.4532 0.1555 0.0541 0.0184
4.8 21.6384 2.0708 0.6071 0.2092 0.0742 0.0260
5.0 2.9375 0.8102 0.2786 1.1006 0.0361 0.0125
5.2 4.3004 1.0804 0.3680 1.1745 0.0492 0.0175
5.4 6.6609 1.4441 0.5871 1.1779 0.0663 0.0243 0.0085
5.6 11.5178 1.9436 0.6313 0.2330 0.0883 0.0330 0.0119
5.8 26.3726 2.6481 0.8225 0.3032 0.1164 0.0443 0.0164
6.0 3.6828 1.0707 0.3918 0.1513 0.0590 0.0224
6.2 5.2979 1.3967 0.5037 0.1964 0.0775 0.0300 0.0113
6.4 8.0768 1.8040 0.6454 0.2524 0.1008 0.0398 0.0153
6.6 13.7692 2.4198 0.8247 0.3222 0.1302 0.0523 0.0205
6.8 31.1270 3.2441 1.0533 0.4090 0.1666 0.0679 0.0271 0.0105
7.0 4.4471 1.3471 0.5172 0.2119 0.0876 0.0357 0.0141
7.2 6.3135 1.7288 0.6521 0.2677 0.1119 0.0463 0.0187
7.4 9.5102 2.2324 0.8202 0.3364 0.1420 0.0595 0.0245 0.0097
7.6 16.0379 2.9113 1.0310 0.4211 0.1739 0.0761 0.0318 0.0129
7.8 35.8956 3.8558 1.2972 0.5250 0.2243 0.0966 0.0410 0.0168
8.0 5.2264 1.6364 0.6530 0.2796 0.1214 0.0522 0.0220
8.2 7.3441 2.0736 0.8109 0.3469 0.1520 0.0663 0.0283
8.4 10.9592 2.6470 1.0060 0.4288 0.1891 0.0834 0.0361
8.6 18.3223 3.4160 1.2484 0.5236 0.2341 0.1043 0.0459
8.8 40.6824 4.4806 1.5524 0.6501 0.2885 0.1298 0.0577
9.0 6.0183 1.9368 0.7980 0.3543 0.1603 0.0723
9.2 8.3869 2.4298 0.9788 0.4333 0.1974 0.0899
9.4 12.4189 3.0732 1.2010 0.5287 0.2419 0.1111
9.6 20.6160 3.9318 1.4752 0.6437 0.2952 0.1367
9.8 45.4769 5.1156 1.8165 0.7827 0.3588 0.1673
10.0 6.8210 2.2465 0.9506 0.4352 0.2040
4
Problem # 3 13 of 32 points
The board beneath shows pallets of packets arriving at an unloading curtail, concurrently with their look periods.
Some pallets hold smwhole packets (S), others average (M), thus-far others vast packets (L). Using an RFID
reader, it takes 1.8 microscopics to “check in” whole smwhole packets on a pallet, 1.5 microscopics to list whole
average packets on a pallet and 1:00 microscopic to list whole vast packets on a pallet.
Look period
[hh:mm]
Pallet with
packet bulk …
0:00 S
0:02 M
0:03 L
0:05 L
0:06 S
0:09 M
0:10 M
0:11 L
0:16 S
0:18 M
0:19 S
0:20 S
In judgment the answers to the coercionthcoming questions, delight affect loose to interpretation Excel or referable – whatever works
best coercion you.
1. What is the overwhole look trounce, l?
2. What are the look trounces of pallets with smwhole packets, lS, with average packets, lM, and with
vast packets, lL?
3. What are the labor trounces coercion a pallet with smwhole (µS), average (µM) and vast packets (µL)?
What is the overwhole labor trounce, µ?
4. Assuming that the incoming pallets are treated First in-First quenched (FIFO), how divers pallets obtain
enjoy been alunitedly inventoried behind 14 microscopics?
Coercion the coercionthcoming questions, delight pretend that whole of the pallets that are shown in the board above
enjoy already arrived and are conducive coercion processing. I.e., delight overlook the look periods.
5. If you everyot the Shortest Processing Period (SPT) government, how divers pallets obtain enjoy been
alunitedly inventoried behind 14 microscopics?
6. Let’s rehearse that whole pallets with smwhole packets enjoy been staged unitedly in area S, pallets with
average packets in area M and pallets with vast packets in area L. Amid each area, you everyot
the FCFS government. Then picking from the areas is prioritized via the Longest Processing Period government
from the three areas. How divers pallets obtain enjoy been alunitedly processed behind 14 microscopics?

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