Question1,2

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Linear Program

Network Example
Total Revenue $ 20,600.00
SFO-DEN Full Fare SFO-DEN Discount DEN-STL Full Fare DEN-STL Discount SFO-STL Full Fare SFO-STL Discount
Fare 150 100 120 80 250 170
Allocated Capacity 30 30 20 40 30 0
Constraints: 1 1 0 0 1 1 90 90 Fligh 1 Capacity 100
0 0 1 1 1 1 90 90 100% Fligh 2 Capacity 120
1 0 0 0 0 0 30 30 100% Demand for ODF 1 50 150 30
0 1 0 0 0 0 30 60 50% Demand for ODF 2 0 100 60 0.5 6.00%
0 0 1 0 0 0 20 20 100% Demand for ODF 3 40 120 20
0 0 0 1 0 0 40 80 50% Demand for ODF 4 0 80 80 0.5 8.00%
0 0 0 0 1 0 30 30 100% Demand for ODF 5 70 250 30
0 0 0 0 0 1 0 40 0% Demand for ODF 6 0 170 0
Admit 30 60 20 80 30 0
mubar1 100 theta1 250
mubar2 80 theta2 170
Vbar 20600
R 26800
D1 120
D2 130
c1-D1 -30 100
c2-D2 -40 80 -6200
k Pr(D_1 >=k) Pr(D_2>=k) Emin(D_1,k) Emin(D_2,k)
E(D_1-c_1)^+ 30.0063006489 1 1 1 1 1
E(D_2-c_2)^+ 40.0002574329 2 1 1 2 2
Gamma_nu,nu $ 20,599.35 3 1 1 3 3
Gamma_theta,nu $ 6,298.38 4 1 1 4 4
5 1 1 5 5
6 1 1 6 6
7 1 1 7 7
8 1 1 8 8
9 1 1 9 9
10 1 1 10 10
11 1 1 11 11
12 1 1 12 12
13 1 1 13 13
14 1 1 14 14
15 1 1 15 15
16 1 1 16 16
17 1 1 17 17
18 1 1 18 18
19 1 1 19 19
20 1 1 20 20
21 1 1 21 21
22 1 1 22 22
23 1 1 23 23
24 1 1 24 24
25 1 1 25 25
26 1 1 26 26
27 1 1 27 27
28 1 1 28 28
29 1 1 29 29
30 1 1 30 30
31 1 1 31 31
32 1 1 32 32
33 1 1 33 33
34 1 1 34 34
35 1 1 35 35
36 1 1 36 36
37 1 1 37 37
38 1 1 38 38
39 1 1 39 39
40 1 1 40 40
41 1 1 41 41
42 1 1 42 42
43 1 1 43 43
44 1 1 44 44
45 1 1 45 45
46 1 1 46 46
47 1 1 47 47
48 1 1 48 48
49 1 1 49 49
50 1 1 50 50
51 1 1 51 51
52 1 1 52 52
53 1 1 53 53
54 1 1 54 54
55 1 1 55 55
56 1 1 56 56
57 0.9999999999 1 56.9999999999 57
58 0.9999999999 1 57.9999999998 58
59 0.9999999998 1 58.9999999995 59
60 0.9999999995 1 59.999999999 60
61 0.999999999 1 60.999999998 61
62 0.999999998 1 61.999999996 62
63 0.999999996 1 62.999999992 63
64 0.9999999922 0.9999999999 63.9999999842 63.9999999999
65 0.9999999852 0.9999999999 64.9999999693 64.9999999998
66 0.9999999721 0.9999999998 65.9999999414 65.9999999996
67 0.9999999484 0.9999999996 66.9999998899 66.9999999992
68 0.999999906 0.9999999992 67.9999997958 67.9999999983
69 0.9999998311 0.9999999984 68.9999996269 68.9999999967
70 0.9999997008 0.9999999969 69.9999993277 69.9999999936
71 0.9999994775 0.9999999941 70.9999988051 70.9999999878
72 0.9999991 0.9999999891 71.9999979051 71.9999999769
73 0.9999984709 0.99999998 72.999996376 72.9999999569
74 0.9999974368 0.9999999638 73.9999938128 73.9999999207
75 0.9999957598 0.9999999354 74.9999895726 74.9999998561
76 0.9999930767 0.9999998861 75.9999826493 75.9999997422
77 0.9999888401 0.9999998018 76.9999714894 76.9999995439
78 0.9999822377 0.9999996594 77.9999537271 77.9999992033
79 0.9999720802 0.9999994221 78.9999258073 78.9999986254
80 0.999956651 0.9999990316 79.9998824583 79.999997657
81 0.9999335072 0.9999983971 80.9998159656 80.9999960541
82 0.9998992202 0.9999973787 81.9997151857 81.9999934327
83 0.999849044 0.9999957641 82.9995642297 82.9999891969
84 0.9997765001 0.9999932354 83.9993407297 83.9999824322
85 0.9996728659 0.9999893218 84.9990135956 84.999971754
86 0.9995265589 0.9999833363 85.9985401545 85.9999550903
87 0.9993224095 0.9999742885 86.9978625641 86.9999293787
88 0.9990408242 0.9999607687 87.9969033883 87.9998901475
89 0.9986568443 0.9999407964 88.9955602326 88.9998309438
90 0.9981391185 0.9999116233 89.9936993511 89.9997425671
91 0.9974488175 0.9998694844 90.9911481686 90.9996120515
92 0.9965385304 0.9998092859 91.987686699 91.9994213374
93 0.9953511994 0.9997242229 92.9830378984 92.9991455603
94 0.9938191595 0.9996053176 93.9768570579 93.998750878
95 0.9918633637 0.9994408742 94.9687204216 94.9981917521
96 0.989392885 0.9992158462 95.9581133066 95.9974075984
97 0.9863047865 0.9989111209 96.9444180931 96.9963187193
98 0.9824844585 0.9985027262 97.9269025515 97.9948214455
99 0.9778065058 0.9979609781 98.9047090573 98.9927824236
100 0.9721362601 0.9972495916 99.8768453174 99.9900320152
101 0.9653319653 0.9963247893 100.8421772827 100.9863568045
102 0.9572476546 0.9951344496 101.7994249374 101.9814912541
103 0.9477367009 0.99361735 102.7471616383 102.9751086041
104 0.9366559782 0.9917025642 103.6838176165 103.9668111683
105 0.9238705288 0.9893090818 104.6076881453 104.9561202501
106 0.9092585867 0.9863457227 105.5169467319 105.9424659728
107 0.8927167654 0.9827114144 106.4096634974 106.9251773872
108 0.8741651902 0.9782958996 107.2838286875 107.9034732868
109 0.8535523288 0.9729809281 108.1373810163 108.8764542149
110 0.8308592703 0.9666419713 108.9682402866 109.8430961862
111 0.8061032066 0.9591504768 109.7743434932 110.802246663
112 0.7793398945 0.9503766545 110.5536833877 111.7526233175
113 0.7506649172 0.9401927536 111.3043483049 112.6928160712
114 0.7202136139 0.9284767614 112.0245619188 113.6212928326
115 0.6881596104 0.9151164195 112.7127215292 114.5364092521
116 0.6547119546 0.9000134242 113.3674334837 115.4364226762
117 0.6201109313 0.8830876536 113.987544415 116.3195103299
118 0.5846227023 0.8642812419 114.5721671174 117.1837915718
119 0.5485329779 0.8435623137 115.1207000953 118.0273538855
120 0.5121399785 0.8209281905 115.6328400738 118.848282076
121 0.4757469792 0.7964078903 116.108587053 119.6446899663
122 0.4396547484 0.7700637662 116.5482418014 120.4147537325
123 0.4041541935 0.7419921585 116.9523959949 121.156745891
124 0.3695195058 0.7123229797 117.3219155007 121.8690688707
125 0.3360020661 0.6812181954 117.6579175668 122.5502870661
126 0.303825324 0.6488692197 117.9617428908 123.1991562858
127 0.2731808077 0.6154932924 118.2349236985 123.8146495782
128 0.2442253592 0.5813289575 118.4791490577 124.3959785357
129 0.2170796263 0.5466308047 118.696228684 124.9426093404
130 0.1918277817 0.5116636741 118.8880564657 125.4542730145
131 0.1685183867 0.4766965434 119.0565748524 125.9309695579
132 0.1471662691 0.4419963374 119.2037411215 126.3729658953
133 0.1277552532 0.4078218921 119.3314963746 126.7807877874
134 0.1102415545 0.374418299 119.4417379292 127.1552060864
135 0.0945576453 0.342011828 119.5362955745 127.4972179144
136 0.0806163927 0.3108055967 119.6169119672 127.8080235111
137 0.0683152874 0.2809761109 119.6852272546 128.088999622
138 0.0575405967 0.2526707594 119.7427678513 128.3416703814
139 0.0481713004 0.2260062979 119.7909391517 128.5676766792
140 0.0400826993 0.2010683122 119.831021851 128.7687449915
141 0.0331496126 0.1779116113 119.8641714635 128.9466566028
142 0.0272491133 0.1565614615 119.8914205768 129.1032180643
143 0.0222627759 0.1370155497 119.9136833527 129.240233614
144 0.0180784368 0.119246539 119.9317617895 129.359480153
145 0.0145914875 0.103205071 119.946353277 129.462685224
146 0.0117057364 0.0888230652 119.9580590134 129.5515082892
147 0.0093338862 0.0760171696 119.9673928995 129.6275254588
148 0.0073976819 0.064692228 119.9747905814 129.6922176867
149 0.0058277866 0.0547446441 119.980618368 129.7469623308
150 0.0045634413 0.046065544 119.9851818093 129.7930278748
151 0.0035519651 0.0385436573 119.9887337744 129.8315715321
152 0.002748143 0.0320678608 119.9914819174 129.8636393929
153 0.0021135465 0.0265293506 119.9935954639 129.8901687436
154 0.0016158238 0.021823427 119.9952112877 129.9119921705
155 0.001227988 0.017850894 119.9964392757 129.9298430646
156 0.000927728 0.0145190922 119.9973670037 129.9443621567
157 0.0006967587 0.0117425906 119.9980637624 129.9561047474
158 0.0005202217 0.0094435766 119.9985839841 129.965548324
159 0.000386143 0.0075519828 119.998970127 129.9731003068
160 0.0002849515 0.0060053967 119.9992550785 129.9791057035
161 0.0002090578 0.0047487955 119.9994641363 129.9838544989
162 0.0001524912 0.0037341485 119.9996166275 129.9875886474
163 0.0001105899 0.0029199256 119.9997272174 129.9905085731
164 0.0000797424 0.0022705454 119.9998069598 129.9927791185
165 0.000057171 0.0017557928 119.9998641308 129.9945349113
166 0.0000407555 0.0013502302 119.9999048863 129.9958851415
167 0.0000288888 0.0010326209 119.9999337751 129.9969177624
168 0.0000203619 0.0007853801 119.9999541369 129.9977031425
169 0.0000142712 0.0005940628 119.9999684081 129.9982972053
170 0.0000099465 0.0004468957 119.9999783546 129.998744101
171 0.0000068937 0.0003343561 119.9999852483 129.9990784571
172 0.0000047514 0.0002487997 119.9999899997 129.9993272568
173 0.0000032568 0.000184135 119.9999932565 129.9995113918
174 0.0000022201 0.000135543 119.9999954766 129.9996469349
175 0.0000015051 0.0000992387 119.9999969817 129.9997461735

Booking Limits

OD 1 1 2 2 3 3
Fares 150 100 120 80 250 170
means 30 60 20 80 30 40
Ratios 0.67 0.67 0.68
0.00 0.04 0.05
Protection Levels 28 18 27
LP Solution 30 40 20 70 30 0
Booking Limits 42 72 3
Lp nested 30 70 20 90 30 30
EMSR_b 28 70 18 90 27 30

CB_DATA_

Sim Mixed Arrivals

Simulation of LP Based Policy
Revenue $ - 0
0.26 3.00% 6.00% 2.00% 8.00% 3.00% 4.00% 70 42 90 72 30 3 Nest LP Nest LP
Period 0 0 0 0 0 0 CD1 CD2 CD3 CD4 CD5 CD6 S1 S2 S3 S4 S5 S6 with EMSR_b BL deterministic BL
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Statistics Revenue Revenue
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Trials 1000 1000
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Mean $23,062.43 $22,946.80 0.5%
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Median $23,280.00 $23,080.00
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Mode $23,580.00 $24,000.00
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Standard Deviation $695.66 $913.62 -23.9%
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Variance $483,939.13 $834,701.26
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Skewness -1.36 -0.8990
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Kurtosis 5.14 3.74
10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Coeff. of Variability 0.0302 0.0398
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Minimum $19,540.00 $18,950.00
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Maximum $24,140.00 $24,370.00
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Range Width $4,600.00 $5,420.00
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Mean Std. Error $22.00 $28.89
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 remaing capacity cumulative revenue
21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
52 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
53 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
56 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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952 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
953 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
954 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
955 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
956 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
957 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
958 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
959 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
960 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
961 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
962 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
963 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
964 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
965 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
966 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
967 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
968 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
969 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
970 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
971 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
972 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
973 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
974 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
975 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
976 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
977 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
978 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
979 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
980 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
981 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
982 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
983 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
984 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
985 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
986 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
987 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
988 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
989 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
990 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
991 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
992 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
993 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
994 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
995 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
996 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
997 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
998 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
999 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Resolving

Network Example
Total Revenue $ - 0
SFO-DEN Full Fare SFO-DEN Discount DEN-STL Full Fare DEN-STL Discount SFO-STL Full Fare SFO-STL Discount
Fare 150 100 120 80 250 170
Allocated Capacity 12 0 10 20 15 0
Constraints: 1 1 0 0 1 1 27 0 Fligh 1 Capacity
0 0 1 1 1 1 45 0 Fligh 2 Capacity
1 0 0 0 0 0 12 15 Demand for ODF 1
0 1 0 0 0 0 0 30 Demand for ODF 2
0 0 1 0 0 0 10 10 Demand for ODF 3
0 0 0 1 0 0 20 40 Demand for ODF 4
0 0 0 0 1 0 15 15 Demand for ODF 5
0 0 0 0 0 1 0 20 Demand for ODF 6