Selective Laser Melting (SLM) is an additive manufacturing process capable of producing mixed batches of parts simultaneously within a single build. The build orientation of a part in SLM is a key process parameter, affecting the build cost, time and quality, as well as batch size. Choosing an optimal arrangement of multiple heterogeneous parts inside the SLM machine also presents a challenging irregular bin packing problem. Since the two problems are interdependent, this paper addresses the combined problem of finding an optimal build orientation and two-dimensional irregular bin packing solution of a mixed batch of parts across identical SLM machines. We address this problem specifically in the context of low-volume high-variety (LVHV) production in the aerospace sector, using total build cost as the objective function. To solve this problem, we present an Iterative Tabu Search Procedure (ITSP), which consists of six distinct stages. We test each stage in the ITSP on 27 manually generated instances, based on 68 unique geometries ranging in convexity and size, including six real-life components from the aerospace industry. Two of the six stages, which are driven by support structure volume, returned the highest improvement in cost. Overall, the results showed an average cost improvement of 16.2% over the initial solution. The initial solution of the procedure was benchmarked against a commercial software, showing comparable results.

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

We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientations as in the case of the garment industry. We explicitly model the assignment of pieces to bins and compare with the more common strategy of packing bins sequentially. There are very few papers in the literature that address the bin packing problem with irregular pieces and to our knowledge this is the first to additionally consider free rotation of pieces with bin packing. We propose several Integer Programming models to determine the association between pieces and bins and then we use a Mixed Integer Programming model for placing the pieces into the bins. The computational results show that the algorithm obtains high quality results in sets of instances with different properties. We have used both industry data and the available data in the literature of 2D irregular strip packing and bin packing problems.

Historical manifest data from a parcel carrier undertaking 'next-day' (i.e. non-express) deliveries in an area of central London (mainly EC2 postcode district) were used to quantify the potential benefits of switching from the current van-based deliveries to one where porters or cycle couriers are used for the last-mile delivery, working from set drop-off points.The results suggested that over the business-as-usual case for the area of London studied, the carrier could reduce CO2 emissions by 45% (9500kg/year) and NOx emissions by 33% (7.64kg/year). Annual driving distance could be reduced by 78% (48,100km) and the amount of time spent stationary at the curbside by 45% (2558 hours/year). Scaling up the modelled emissions savings to London's Central Activities Zone, an area approximately 10 times bigger than the modelled case study area and with estimated total annual parcel delivery distance of 15 million km, could see annual emissions savings in the region of 2 million kgCO2 and 1633kgNOx if all carriers utilised porters or cycle couriers. Overall cost savings to the carrier were estimated to be in the range 34%-39%. Some practical operating challenges are identified including sorting and packing of items, parcel handover arrangements, how to deal with failed deliveries, and how to incorporate express items.

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focused on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraints.