In this paper we continue the investigations in GMW92a] for the Stei-ner tree packing polyhedron. We present several new classes of valid inequalities and give suucient (and necessary) conditions for these inequalities to be facet-deening. It is intended to incorporate these inequalities into an existing cutting plane algorithm that is applicable to practical problems arising in the design of e...

We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). propose an integer linear programming model for the ICP-HPBMPP, as well lower bound its optimal objective function value, which is empirically shown to be closer solution value than obtained from relaxation model. als...

Given a set of irregular shapes, the strip nesting problem is the problem of packing the shapes within a rectangular strip of material such that the strip length is minimized, or equivalently the utilization of material is maximized. If the packing found is to be repeated, e.g., on a roll of fabric or a coil of metal, then the separation between repeats is going to be a straight line. This cons...

We review the most important mathematical models and algorithms developed for the exact solution of the one dimensional bin packing and cutting stock problems, and experimentally evaluate, on state-of-the art computers, the performance of the main available software tools.

In this paper we examine a consolidation and dispatching problem motivated by a multinational chemical company which has to decide routinely the best way of delivering a set of orders to its customers over a multi-day planning horizon. Every day the decision to be made includes order consolidation, vehicle dispatching as well as load packing into the vehicles. We develop a heuristic based on a ...

Packing problems (sometimes also called cutting problems) are combinatorial optimization problems concerned with placement of objects (items) in one or several containers. Some packing problems are special cases of several other problems such as resource-constrained scheduling, capacitated vehicle routing, etc. In this paper we consider a bounding technique for oneand higher-dimensional orthogo...

Nesting (Cutting and Packing) problems are optimization problem encountered in many areas of business that look for good arrangement of multiple items in larger containing regions. The objective of this problem is to maximize the utilization of resource material. There is a large range of the applicability of these problems as there are many diverse instances of it that are encountered in the i...

This paper investigates a technique of building up discrete relaxations of combi natorial optimization problems. To establish such a relaxation we introduce a transformation technique —aggregation— that allows one to relax an integer program by means of another integer program. We show that knapsack and set packing relaxations give rise to combinatorial cutting planes in a simple and straightfo...

The d-dimensional bin packing problem (OBPP-d) is the problem of finding the minimum number of containers needed to contain a set of orthogonally packed d-dimensional rectangular boxes. In OBPP-d solvers two subproblems are crucial: Calculating lower bounds and solving the decision problem (OPP-d) of determining if a set of boxes can be orthogonally packed into a single container. This thesis f...