求助一道运筹学的解法，谢谢

xuezhongcao 发表于 2008-3-20 23:06

某航空公司在 A 市到 B 市的航线上用波音 737 客机执行飞行任务。已知该机有效载客量为 138 人。按民用航空有关条例，旅客因有事或误机，机票可免费改签一次，此次也有在飞机起飞前退票的。为避免由此发生的空座损失，该航空公司决定每个航班超量售票（即每班售出票数为 138+S 张）。但由此会发生持票登机旅客多于座位数情况，这种情况下，航空公司规定，对超员旅客愿改乘本公司后续航班的，机票免费（即退回原机票款）；若换乘其他航空公司航班的，按机票价的 150% 退款。据统计前一类旅客占超员中的 80% ，后一类占 20% 。又据该公司长期统计，每个航班旅客退票和改签发生的人数的概率如下表 5-4 所示。<table class="MsoNormalTable" cellspacing="0" cellpadding="0" border="1" style="BORDER-RIGHT: medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid black .5pt; mso-yfti-tbllook: 1184; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insideh: .5pt solid black; mso-border-insidev: .5pt solid black;"><tbody><tr style="mso-yfti-irow: 0; mso-yfti-firstrow: yes;"><td valign="top" width="58" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: black 1pt solid; WIDTH: 43.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt;">i</td><td valign="top" width="59" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 44.4pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">0</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">1</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">2 
</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">3</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">4</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">5</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">6</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">7</td><td valign="top" width="55" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 41.55pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt;">8</td></tr><tr style="mso-yfti-irow: 1; mso-yfti-lastrow: yes;"><td valign="top" width="58" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: black 1pt solid; WIDTH: 43.7pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">P(i)</td><td valign="top" width="59" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 44.4pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.18</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.25</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.25</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.16</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.06</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.04</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.03</td><td valign="top" width="56" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 42.35pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.02</td><td valign="top" width="55" style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ffffff; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ffffff; WIDTH: 41.55pt; PADDING-TOP: 0cm; BORDER-BOTTOM: black 1pt solid; BACKGROUND-COLOR: transparent; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt;">0.01</td></tr></tbody></table>试确定该航空公司从 A 市到 B 市的航班每班应多售出的机票张数 S ，使预期的获利最大。<a href="mailto:yanzhaoernv@126.com">yanzhaoernv@126.com</a>谢谢 
 

[此贴子已经被作者于2008-3-20 23:07:04编辑过]

clwca 发表于 2011-1-8 13:56

顶一个。。。

panther_qd 发表于 2011-3-1 23:27

设最优超售量为S，它应该在满足下面条件中找最大值：
顾客出现的期望成本〈＝多售出一张票的收益。
出现一名超订顾客的成本：1.5r*0.2+r*0.8=1.1r
故1.1r*p(不到的人数《＝s)<=r
p(不到的人数《＝s)<=0.91
根据题中的概率，可知s=5

hbdkfk2 发表于 2012-8-24 13:25

谢谢分享！！！！！！！！！！！！！

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求助一道运筹学的解法，谢谢