This is a repository copy of Jostle heuristics for the 2D-irregular shapes bin packing problems with free rotation.

Prediction of sewing thread consumption requires an accurate method of calculation since it relates to the cost of manufacturing and distribution of apparel products. Previous researchers highlighted problems in existing thread consumption calculation methods; i.e. limitations in existing formulae which cause inaccurate predictions of thread amount needed for sewing operations. The existing methods of consumption calculations exhibit significant error percentages due to the ignorance of important parameters which affect on thread consumption. This paper investigates on correlation of thread tension to thread consumption of lock-stitch 301 and chain-stitch 401. The existing thread consumption formulae are optimized by considering a new parameter; thread tension, using regression analysis and geometrical modeling techniques. For the chain-stitch 401, results indicate that the thread tension significantly affects in determination of the thread consumption. The error analysis of proposed formulae was performed to indicate that the proposed formulae more accurate compared to the available methods of predicting sewing thread consumption. In addition, there are combined effects of thread tensions together with parameters such as fabric thickness and stitch density which determines accurate consumption values considering the properties of the stitch. In comparison, inclusion of the proposed thread tension variable depicts reduction in error percentages, so that the proposed formulae are expected to be a better approach to calculate thread consumption of lock-stitch 301 and chain-stitch 401.

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In this paper we proposed a local search heuristic and a genetic algorithm to solve the two-dimensional irregular multiple bin-size bin packing problem. The problem consists of placing a set of pieces represented as 2D polygons in rectangular bins with different dimensions such that the total area of bins used is minimized. Most packing algorithms available in the literature for 2D irregular bin packing consider single size bins only. However, for many industries the material can be supplied in a number of standard size sheets, for example, metal, foam, plastic and timber sheets. For this problem, the cut plans must decide the set of standard size stock sheets as well as which pieces to cut from each bin and how to arrange them in order to minimise waste material. Moreover, the literature constrains the orientation of pieces to a single or finite set of angles. This is often an artificial constraint that makes the solution space easier to navigate. In this paper we do not restrict the orientation of the pieces. We show that the local search heuristic and the genetic algorithm can address all of these decisions and obtain good solutions, with the local search performing better. We also discuss the affect of different groups of stock sheet sizes.