Packing items from a triangular distribution

We consider the problem of packing n items which are drawn according to a probability distribution whose density function is triangular in shape. For triangles which represent density functions whose expectation is 1/p for p = 3, 4, 5, ..., we give a packing strategy for which the ratio of the number of bins used in the packing to the expected total size of the items asymptotically approaches 1

A two-stage packing procedure for a Portuguese trading company

This case study deals with a two-stage packing problem that has to be solved in the daily distribution process of a Portuguese trading company. At the first stage boxes including goods are to be packed on pallets while at the second stage these pallets are loaded into one or more trucks. The boxes have to be transported to different customers and the actual goal is to guarantee a sufficient utilization of the truck loading spaces. A two-stage packing procedure is proposed to cover both problem stages. First boxes are loaded onto pallets using a well-known container loading algorithm. Then trucks are filled with loaded pallets by means of a new tree search algorithm. The applicability and performance of the two-stage approach was evaluated with a set of instances that are based on actual company data

Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms

In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536 ... lower bound for the 1-dimensional bin packing problem. Following their ideas, we present a general technique that can be used to derive lower bounds for other bin packing problems as well. We apply this technique to prove new lower bounds for the 2-dimensional (1.802...) and 3-dimensional (1.974...) bin packing problem

Heuristics for the score-constrained strip-packing problem

This paper investigates the Score-Constrained Strip-Packing Problem (SCSPP), a combinatorial optimisation problem that generalises the one-dimensional bin-packing problem. In the construction of cardboard boxes, rectangular items are packed onto strips to be scored by knives prior to being folded. The order and orientation of the items on the strips determine whether the knives are able to score the items correctly. Initially, we detail an exact polynomial-time algorithm for finding a feasible alignment of items on a single strip. We then integrate this algorithm with a packing heuristic to address the multi-strip problem and compare with two other greedy heuristics, discussing the circumstances in which each method is superior