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This paper deals with generating paths for cutting irregular parts nested on thin or thick metal sheets. The objective is to minimise the total time required to cut all parts from the metal sheet explicitly taking the cost of piercing and pre-cutting into account. The problem is modelled as a generalised travelling salesperson problem with special precedence constraints. A set of construction heuristics is presented that incorporates the constraints originating from inner-outer contours, common cuts, piercing points and pre-cuts. Computational tests on a set of real-life cutting problems show that our solution approach is able to generate tool paths that for thick plates spend on average 33.4% less time than those generated by a commercial package for air movements, pre-cuts and sharp angle macros with cutting and piercing times being equal.

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This paper presents a review of the literature on generating cutting paths for laser cutting machines. Firstly, the cutting path problem is defined including all relevant technical side constraints which exist plentifully in laser cutting. Secondly, a former classification method is updated to include all types of cutting path problems. Thirdly, a comprehensive review of solution methods and related applications is presented. Throughout the literature review, trends in research in cutting path generation and interesting areas for future research are identified.

a b s t r a c tThis paper shows how the maximum covering and patrol routing problem (MCPRP) can be modeled as a minimum cost network flow problem (MCNFP). Based on the MCNFP model, all available benchmark instances of the MCPRP can be solved to optimality in less than 0.4s per instance. It is furthermore shown that several practical additions to the MCPRP, such as different start and end locations of patrol cars and overlapping shift durations can be modeled by a multi-commodity minimum cost network flow model and solved to optimality in acceptable computational times given the sizes of practical instances.