Optimal steel beam manufacturing assortment problem for Itsa Steel

[sahar_soltani]

[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.

 

[ctjen]

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

 

[sahar_soltani]

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.