Cutting patterns for efficient production of irregular-shaped pieces

Abstract

The research presented in this thesis belongs to the subject area of operations research. The study investigates and utilises the solution methodologies known as heuristics and local search for three practical problems related to cutting and packing using irregular shapes and multiple bins. From an application point of view, the problems domains remain in manufacturing, specifically where minimising the resources is required to meet a particular outcome. Many manufacturing processes begin with cutting desired items from a stock sheet of material, hence this study focuses on generating efficient cutting patterns, which is applicable in the manufacture of furniture, shoes, tools, ships, and garments.

First, we consider designing an efficient solution procedure for solving two-dimensional irregular shape single bin size bin packing problem and two-dimensional irregular shape multiple bin size bin packing problem. Our intention is to consider alternative strategies such as placement policies, hole-filling and handling rotation of pieces; particularly with unrestricted rotations. Despite the fact that both problems are widely applicable in sheet cutting, their consideration in the literature is limited. To our knowledge, only a few authors have attempted to incorporate the first problem with the unrestricted rotation of pieces while the second problem with unrestricted rotation has not been considered at all. Being applicable in the real world, both the problems require powerful algorithms to determine the arrangement of irregular pieces on stock sheets in order to minimise the material waste. In this thesis, our focus is on developing algorithms to solve each problem efficiently. These algorithms draw on concepts in computational geometry, computer science as well as operations research.

We investigate a set of newly proposed single-pass constructive algorithms that builds a feasible solution by adding pieces sequentially to a packing area defined by a set of bins which can either be homogeneous or heterogeneous. Each problem has a large solution space due to the different combinations of bins and arrangements of irregular pieces. We adopt the optimisation power of local search methods and metaheuristics to find good solutions. As one of the useful heuristic procedures, we use the Jostle heuristic (JS) to solve irregular shape single bin size bin packing problem and irregular shape multiple bin size bin packing problem due to its promising performances in handling both allocation and placement decisions of the pieces together. The Jostle was used in earlier studies for solving irregular strip packing problems and in this study we adopt it first time to solve irregular bin packing problems. Also, our implementation of Jostle handles identifying promising orientation angles of the pieces using the newly proposed angled tuning mechanism when placing pieces. Experimental results reveal that the proposed algorithms can manage different variants of the problem and find solutions with good utilisation of material.

For the third problem of this study, we consider multi-period irregular bin packing problem with use of residuals. This allows using leftovers of a certain period which are usable as input stock material for the next periods. Here, we expand the previous work on irregular bin packing algorithms for heterogeneous stock sheets to consider the inventory and production process of sheet cutting. We propose two models to test the impact of a variety of operational policies around the retention and reuse of residual materials in the sheet cutting process. It also examines the cost sensitivity of using residuals with respect to nine practical scenarios within those operational policies. The computational results demonstrate that the proposed multi-period approach with residuals derives better results than solving each order individually for a selected set of operational scenarios and disclose which policy would be more advantageous to operate in each scenario. The results facilitate developing a tool to guide the manufacturers to take effective decisions based on the scenarios applicable to their sheet cutting process.

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