• Support PF! Buy your school textbooks, materials and every day products Here!

"Assortment of Structural Steel Beams"&amp

[SOLVED] "Assortment of Structural Steel Beams"&amp

Hi,
Dose anybody know the solution for this problem? Please, help.
Thanks,

A Japanese industrial firm, Itsa Steel Company, manufactures structural beams of a standard length. The strength of a beam depends on its weight, and Itsa Steel indexes the various strengths it can make as j = 1, 2, ...,N, where j = 1 is the heaviest beam and j = N is the lightest. Assume that if a customer requests Strength k, then Itsa Steel may, if it chooses, supply the demand by a beam of possibly greater Strength j, where j < k. Itsa Steel must solve the following assortment problem: The demand requirement for Strength j is D(j) beams; all demand must be satisfied. If Itsa Steel decides to manufacture Strength j, then it incurs and expensive setup cost, s(j). If the company meets the demand requirement D(j) by shipping beams of Strength k, where k <= j, then the company incurs a loss of h*[w(k)-w(j)]*D(j), where w(k) and w(j) are therespective weights of the beams and h is the cost per unit of weight.Formulate a model that will enable Itsa Steel to decide an optimalassortment of strengths to manufacture and the corresponding amounts of each.
 

Answers and Replies

29
0
Hi,
Dose anybody know the solution for this problem? Please, help.
Thanks,

A Japanese industrial firm, Itsa Steel Company, manufactures structural beams of a standard length. The strength of a beam depends on its weight, and Itsa Steel indexes the various strengths it can make as j = 1, 2, ...,N, where j = 1 is the heaviest beam and j = N is the lightest. Assume that if a customer requests Strength k, then Itsa Steel may, if it chooses, supply the demand by a beam of possibly greater Strength j, where j < k. Itsa Steel must solve the following assortment problem: The demand requirement for Strength j is D(j) beams; all demand must be satisfied. If Itsa Steel decides to manufacture Strength j, then it incurs and expensive setup cost, s(j). If the company meets the demand requirement D(j) by shipping beams of Strength k, where k <= j, then the company incurs a loss of h*[w(k)-w(j)]*D(j), where w(k) and w(j) are the respective weights of the beams and h is the cost per unit of weight.Formulate a model that will enable Itsa Steel to decide an optimal assortment of strengths to manufacture and the corresponding amounts of each.
For starters the wording of this problem is somewhat confusing.

"Assume that if a customer requests Strength k, then Itsa Steel may, if it chooses, supply the demand by a beam of possibly greater Strength j, where j < k."

Does this mean that the weight of the j beam is less than the k beam or that the greater Strength j beam preceeds alphabetically the lesser strength k beam?

"If the company meets the demand requirement D(j) by shipping beams of Strength k, where k <= j,".

Again are k, j weight grades or strength grades?

Chris
 
Chris,
Thanks,
I don't have any more information about it, but I think j and k are strength grades; also there is a relationship between strength, and weight. This is what I think. I hope it may help.
 

Related Threads for: &amp;amp;quot;Assortment of Structural Steel Beams&amp;amp;quot;&amp;amp;amp

  • Last Post
Replies
13
Views
917
  • Last Post
Replies
1
Views
387
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
6
Views
8K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
10
Views
920
  • Last Post
Replies
4
Views
1K
Top