Problem 2

Cutting a Steel Coil

Brief description of the challenge:

A complex problem that arises in the flat steel industry is the cutting of coils to produce narrower strips. Companies stock coils of different widths and each customer orders a quantity (in kilos) of strips of a certain width. These strips are obtained by slitting the coils lengthwise.

It is often the case that the weight of the strips obtained by slitting the coil is much greater than the quantity ordered by the customers. To solve this problem, coils can be crosscut so that 1) shorter and lighter strips are obtained. 2) The crosscut coil is rewound and stored for future use.

However, deciding where to make this cut is not easy: the cut affects all customers supplied with the coil, but not all of them require the same weight (and, in addition, since the strips are of different widths, the effect of moving the cutting point is different for each customer). These customers demand a penalty if what they receive is different from what they ordered. On the other hand, the company does not want to produce a lot of leftovers, because if they are reusable, they complicate their management, and if they are not reusable, they generate very costly scrap.

The aim of this challenge is to obtain an expression of the cost function associated with the point at which a guillotine-type cut is applied, to study its convexity and, finally, to design an algorithm that allows us to obtain the optimal point.

Mathematical background:

Students need to have basic knowledge of convex functions and some programming language.

Coordinator:

Antonio Alonso Ayuso, DSLAB-CETINIA, Universidad Rey Juan Carlos, Madrid, España