In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-andbound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branchprice-and-cut. We introduce the common concepts ...

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

Column generation has been very useful in solving single objective vehicle routing problems (VRPs). Its role in a branch-and-price algorithm is to compute a lower bound which is then used in a branch-and-bound framework to guide the search for integer solutions. In spite of the success of the method, only a few papers treat its application to multi-objective problems and this paper seeks to con...

We are given a rectangle R in the plane and a nite set P of n points in the interior of R. A rectangular partition of R is a partition of the surface of R into smaller rectangles. A rectangular partition is said to be feasible with respect to P if no points in P lie in the strict interior of any rectangle of the partition. The length of a rectangular partition is computed as the sum of the leng...

We study an integrated charge batching and casting width selection problem arising in the continuous casting operation of the steelmaking process at Shanghai, China based Baosteel. This decision-making problem is not unique to Baosteel; it exists in every large iron and steel company in the world. We collaborated with Baosteel on this problem from 2006 to 2008 by developing and implementing a d...

There appear to be two versions of the Dual Bin Packing problem in the literature. In addition, one of the versions has a counterpart in the cutting stock literature, known as the Skiving Stock Problem. This paper outlines branch-andprice algorithms for both. We introduce combinatorial upper bounds and well-performing heuristics from the literature in the branch-and-price framework. Extensive c...

We study a multi-criteria variant of the problem of routing hazardous material on a geographical area subdivided in regions. The two objective functions are given by a generally defined routing cost and a risk equity equal to the maximum, over each region, of the risk perceived within a region. This is a multicommodity flow problem where integer variables are used to define the number of trucks...