We consider the feasibility problem in d-dimensional orthogonal packing (d ≥ 2), called Orthogonal Packing Problem (OPP): given a set of ddimensional rectangular items, decide whether all of them can be orthogonally packed in the given rectangular container without item rotation. We review two kinds of 1D relaxations of OPP. The first kind is non-preemptive cumulative-resource scheduling, equiv...

The cutting and packing problem belongs to the combinatorial optimization problems; it covers a wide range of practical cases in industries. present paper investigates new real world needs be solved through daily operations foam blocks an industrial company. is considered as one non-classical problems area. It represents variant three dimensional Cutting Stock Problem. originality studied indic...

In this paper, we study how well one can approximate arbitrary polytopes using sparse inequalities. Our motivation comes from the use of sparse cutting-planes in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cutting-planes? In ord...

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switch-box routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we deve...

The problem of packing many small boxes into a single larger box underlies a number of cutting, packing, scheduling, and transportation applications. There are a number of heuristic solvers, but the progress in exact solvers, in general, and integer programming solvers, in particular, has been limited. Padberg [Math. Methods Oper. Res., 52(1):1–21, 2000] estimated the integer linear programming...

We present a new algebraic algorithmic scheme to solve convex integer maximization problems of the following form, where c is a convex function on R and w1x, . . . , wdx are linear forms on R, max {c(w1x, . . . , wdx) : Ax = b, x ∈ N} . This method works for arbitrary input data A, b, d, w1, . . . , wd, c. Moreover, for fixed d and several important classes of programs in variable dimension, we...

Entanglement in marine debris is a contributing factor in Steller sea lion (SSL; Eumetopias jubatus) injury and mortality. We quantified SSL entanglement by debris type, sex and age class, entanglement incidence, and estimated population level effects. Surveys of SSL haul-outs were conducted from 2000-2007 in Southeast Alaska and northern British Columbia. We recorded 386 individuals of all age...

In this paper, we present an analysis of the strength of sparse cutting-planes for mixed integer linear programs (MILP) with sparse formulations. We examine three kinds of problems: packing problems, covering problems, and more general MILPs with the only assumption that the objective function is non-negative. Given a MILP instance of one of these three types, assume that we decide on the suppo...

the date of receipt and acceptance should be inserted later Abstract. When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-G...

Rectangle-packing problem involves many industrial applications, such as shipping, timber cutting, very large scale integration (VLSI) floor planning, and so on. This problem has shown to be NP hard, and many algorithms such as genetic algorithm, simulated annealing and other heuristic algorithms are presented to solve it. Based on the wisdom and experience of human being, an efficient heuristi...