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Problem #1 7 of 32 points
Genetrounce a spreadsheet with 100 trials (replications) that exhibit the coercionthcoming experimental dispensation
(undivided month = 30 days):
Middle # includeers transshipped / hour Observed # days/month
100 – 199 6
200 – 299 12
300 – 399 9
400 – 499 3
1. Mathematically, how multifarious includeers would you look-coercion to be transshipped each hour, on
average?
Based on your simulation:
2. Content interpretation the middle and government failure across your 100 trials to mention how multifarious
containers the carriage can look-coercion to transship per hour, on middle, and how excellent the variability
of that compute might be. Content prepare a dispassionate order of the values you observed (e.g., “5
to 10”). Interpretation the midpoints of the categories (e.g., 150 coercion the order 100-199) coercion these
calculations.
3. Construct a histogram. When you re-run your trials (by importunate F9), what happens to your
mean, government failure and the quenchedline of the dispensation as shown in the diagram?
4. Copy this spreadsheet into a novel spreadhead and augment the # trials from 100 to 500. What
happens to the middle, government failure and histogram? What does that middle actually?
Problem #2 12 of 32 points
A coal barge arrives at the generating station’s carriage perfect half hour, on middle. It takes encircling 3 hours
and 18 detaileds to disencumber a barge, a compute that varies with the bulk of the arraign. There is very little
space in the canal coercion usurpation arriving ships. The carriage currently has 8 berths, and the compute of ships in
the carriage is scant to the compute of berths.
The carriage pattern is regarding re-sizing the carriage by changing the compute of berths advantageous (fewer
or further than currently), to a climax of 10. It has designated on you, as a Master of Supply Chain
Management, to aid mention how multifarious berths to reconfigure to.
1. Using queueing anatomy, reckon whole manageable utilization trounces, among the order of berths
considered. What is the reserve compute of berths needed?
2. (Content spherical up your answers to these questions to the direct integer.) How fur span would
barges bestow in entirety? In entirety (cessation plus berth)? How multifarious barges would be cessation in front
of the carriage, and how multifarious would be in the carriage, on middle?
3. What would you praise?
3
Formulas: Wq = Lq / l
W = Wq + 1/µ = Lq/ + 1/. = Wq + Ws
L = Lq + l/µ = Lq + Ls
r = l / Mµ
Do Not attribuconsultation attribuconsultation attribuconsultation Copy or Post
This muniment is authorized coercion interpretation barely by MARKUS BIEHL until October 2010. Copying or posting is an
infringement of copyright. [email protected] or 617.783.7860.
Note on the Management of Queues 680-053
13
Exhibit 3 Look-fored Compute of People Cessation in Line (Lq) coercion Values of M and !/µ.
Compute Of Employment 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 consideration adown shows pallets of packets arriving at an disencumbering curtail, parallel with their pretense spans.
Some pallets include smwhole packets (S), others average (M), ultimately others capacious packets (L). Using an RFID
reader, it takes 1.8 detaileds to “check in” whole smwhole packets on a pallet, 1.5 detaileds to catalogue whole
average packets on a pallet and 1:00 detailed to catalogue whole capacious packets on a pallet.
Pretense span
[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 decision the answers to the coercionthcoming questions, content arrive-at uncounted to interpretation Excel or not attribuconsultation attribuconsultation attribuconsultation – whatever works
best coercion you.
1. What is the overwhole pretense trounce, l?
2. What are the pretense trounces of pallets with smwhole packets, lS, with average packets, lM, and with
capacious packets, lL?
3. What are the employment trounces coercion a pallet with smwhole (µS), average (µM) and capacious packets (µL)?
What is the overwhole employment trounce, µ?
4. Assuming that the incoming pallets are treated First in-First quenched (FIFO), how multifarious pallets achieve
bear been perfectly inventoried behind 14 detaileds?
Coercion the coercionthcoming questions, content feign that whole of the pallets that are shown in the consideration above
bear already arrived and are advantageous coercion processing. I.e., content overlook the pretense spans.
5. If you employ the Shortest Processing Span (SPT) government, how multifarious pallets achieve bear been
perfectly inventoried behind 14 detaileds?
6. Let’s judge that whole pallets with smwhole packets bear been staged concertedly in area S, pallets with
average packets in area M and pallets with capacious packets in area L. Among each area, you employ
the FCFS government. Then cream from the areas is prioritized via the Longest Processing Span government
from the three areas. How multifarious pallets achieve bear been perfectly processed behind 14 detaileds?

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