Abstract Throughout its history, Operational Research has evolved to include methods,
models and algorithms that have been applied to a wide range of contexts. This …

In this chapter we further develop the main tool of our studies, phi-functions. We define new
functions, called quasi-phi-functions, that we use for analytic description of relations of …

This paper addresses a special case of irregular bin packing problem which the irregular
pieces with free rotation have to fill a large irregular stock sheet with defective regions while …

We consider two NP-hard open dimension nesting problems for which a set of items has to
be packed without overlapping into a two-dimensional bin in order to minimize one or both …

We study NP-hard placement optimisation problems, which cover a wide spectrum of
industrial applications, including space engineering. This chapter considers tools of …

This paper addresses a special knapsack packing problem in which identical pieces are
packed into an irregular board with unusable regions to maximize the number of pieces …

In the present paper, the platform layout optimization problem for the simultaneous
fabrication of different parts, which is addressed in the batch planning of Stereolithography …

This paper introduces a fully general, exact algorithm for nesting irregular shapes. Both the
shapes and material resource can be arbitrary nonconvex polygons. Moreover, the shapes …

The economy of the laser cutting process depends on two productivity issues:(i) nesting, a
classic problem of finding the most efficient layout for cutting parts with minimum material …

Nesting Problems, which are important subjects in the cutting and packing field, involve
convex and nonconvex polygons and are common in several industries. These irregular …