I hope this site is the right place with many researchers to help me study stochastic programming and other courses by myself. I hope your help will help me and other ones to understand this hard courses. I search the internet but I do not find any "stochastic programming courses" that is useful. So if you know any sites, please give me link.

I am currently reading "Introduction to Stochastic Programming" and having many questions regarding the theory and practice section.

Specifically, I am doing the following exercise (exercise 1 - page 77/512)

Northam Airlines is trying to decide how to partition a new plane for its Chicago–Detroit route. The plane can seat 200 economy class passengers. A section can be partitioned off for first class seats but each of these seats takes the space of 2 economy class seats. A business class section can also be included, but each of these seats takes as much space as 1.5 economy class seats. The profit on a first class ticket is, however, three times the profit of an economy ticket. A business class ticket has a profit of two times an economy ticket’s profit. Once the plane is partitioned into these seating classes, it cannot be changed. Northam knows, however, that the plane will not always be full in each section. They have decided that three scenarios will occur with about the same frequency: (1) weekday morning and evening traffic, (2) weekend traffic, and (3) weekday midday traffic. Under Scenario 1, they think they can sell as many as 20 first class tickets, 50 business class tickets, and 200 economy tickets. Under Scenario 2, these figures are 10 , 25 , and 175 . Under Scenario 3, they are 5 , 10 , and 150 . You can assume they cannot sell more tickets than seats in each of the sections. (In reality, the company may allow overbooking, but then it faces the problem of passengers with reservations who do not appear for the flight (no-shows). The problem of determining how many passengers to accept is part of the field called yield management or revenue management. For one approach to this problem, see Brumelle and McGill [1993]. This subject is explored further in Exercise 1 of Section 2.7.)

My solution:

Let x1, x2, x3 be the number of 1st class, business and economy seats respectively. We have the constraints:

2x1+1.5x2+x3<=200 (1).

The number of events: 3 x 7 = 21 because each day we have weekday morning, midday, and evening traffic.

So the probability of the Scenario 1/2/3 is respectively 10/21, 6/21 and 5/21.

Let yij (j=1..3) be the number of 1st class, business and economy seats sold in Scenario i. We have the following formulation:

maximize 10/21(3y11+2y12+y13) + 6/21(3y21+2y22+y23)+5/21(3y31+2y32+y33)

s.t.:

2x1+1.5x2+x3<=200

y11<=min(x1,20); y12<=min(x2,50);y13<=min(x3,200); y21<=min(x1,10); y22<=min(x2,25);y23<=min(x3,175); y31<=min(x1,5); y32<=min(x2,10);y32<=min(x3,100);

So if you have any suggestions or comments, please explain them to me.

Many thanks in advance.

asked 01 Jun '15, 09:45

Duc%20Minh%20Vu's gravatar image

Duc Minh Vu
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edited 01 Jun '15, 09:59

1

We tend not to answer homework questions here. Even if you are doing it as part of a self-study, a solution posted here would be accessible by any enrolled student who could use a search engine.

(01 Jun '15, 22:59) Paul Rubin ♦♦

I understand. I would like to know if I want to ask for some suggestions ,it is ok or not?

(03 Jun '15, 05:35) Duc Minh Vu
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Asked: 01 Jun '15, 09:45

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