Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

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 focuses 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 constraint

Optimised solutions to the last-mile delivery problem in London using a combination of walking and driving

Inspired by actual parcel delivery operations in London, this paper describes a two-echelon distribution system that combines the use of driving and walking as part of last-mile deliveries in urban areas for a single driver. The paper presents an optimisation model that explicitly treats and integrates the driving and walking elements, and describes a branch-and-cut algorithm that uses new valid inequalities specifically tailored for the problem at hand. Computational results based on real instances obtained from a courier operating in London are presented to show the performance of the algorithm

Jostle heuristics for the 2D-irregular shapes bin packing problems with free rotation

The paper investigates the two-dimensional irregular packing problem with multiple homogeneous bins (2DIBPP). The literature on irregular shaped packing problems is dominated by the single stock sheet strip packing problem. However, in reality manufacturers are cutting orders over multi-stock sheets. Despite its greater relevance, there are only a few papers that tackle this problem in the literature. A multi-stock sheet problem has two decision components; the allocation of pieces to stock sheets and the layout design for each stock sheet. In this paper, we propose a heuristic method that addresses both the allocation and placement problems together based on the Jostle algorithm. Jostle was first applied to strip packing. In order to apply Jostle to the bin packing problem we modify the placement heuristic. In addition we improve the search capability by introducing a diversification mechanism into the approach. Furthermore, the paper presents alternative strategies for handling rotation of pieces, which includes a restricted set of angles and unrestricted rotation. Very few authors permit unrestricted rotation of pieces, despite this being a feature of many problems where the material is homogeneous. Finally, we investigate alternative placement criteria and show that the most commonly applied bottom left criteria does not perform as well as other options. The paper evaluates performance of each algorithm using different sets of instances considering convex and non-convex shapes. Findings of this study reveal that the proposed algorithms can be applied to different variants of the problem and generate significantly better results

Including Limited Partners in the Diversity Jurisdiction Analysis

This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29–30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition

Voxel-Based Solution Approaches to the Three-Dimensional Irregular Packing Problem

Research on the three-dimensional (3D) packing problem has largely focused on packing boxes for the transportation of goods. As a result, there has been little focus on packing irregular shapes in the operational research literature. New technologies have raised the practical importance of 3D irregular packing problems and the need for efficient solutions. In this work, we address the variant of the problem where the aim is to place a set of 3D irregular items in a container, while minimizing the container height, analogous to the strip packing problem. In order to solve this problem, we need to address two critical components; efficient computation of the geometry and finding high-quality solutions. In this work, we explore the potential of voxels, the 3D equivalent of pixels, as the geometric representation of the irregular items. In this discretised space, we develop a geometric tool that extends the concept of the nofit polygon to the 3D case. This enables us to provide an integer linear programming formulation for this problem that can solve some small instances. For practical size problems, we design metaheuristic optimisation approaches. Because the literature is limited, we introduce new benchmark instances. Some are randomly generated and some represent realistic models from the additive manufacturing area. Our results on the literature benchmark data and on our new instances show that our metaheuristic techniques achieve the best known solutions for a wide variety of problems in practical computation times

Dynamic Pricing for Vehicle Ferries: using Packing and Simulation to Optimize Revenues

We propose an heuristic approach to the vehicle ferry revenue management problem, where the aim is to maximize the revenue obtained from the sale of vehicle tickets by varying the prices charged to different vehicle types, each occupying a different amount of deck space. Customers arrive and purchase tickets according to their vehicle type and their willingness-to-pay, which typically increases over time because customers purchasing tickets closer to departure tend to accept higher prices. The optimization problem can be solved using dynamic programming but the possible states in the selling season are the set of all feasible vehicle mixes that fit onto the ferry. This makes the problem intractable as the number of vehicle types and ferry size increases. We propose a state space reduction, which uses a vehicle ferry loading simulator to map each vehicle mix to a remaining-space state. This reduces the state space of the dynamic program. Our approach allows the value function to be approximated rapidly and accurately with a relatively coarse discretization of states. We present simulations of the selling season using this reduced state space to validate the method. The vehicle ferry loading simulator was developed in collaboration with a vehicle ferry company and addresses real-world constraints such as manoeuvrability, elevator access, strategic parking gaps, vehicle height constraints and ease of implementation of the packing solutions

Quantifying environmental and financial benefits of using porters and cycle couriers for last-mile parcel delivery

Parcel carriers face increasingly difficult operating conditions in busy metropolitan areas due to growing consumer demand for ever faster delivery services and having to cope with traffic congestion and city authority measures that may restrict or penalise access for certain types of vehicle. This paper evaluates the potential environmental and financial benefits of switching from traditional van-based deliveries to an alternative operating model, where porters or cycle couriers undertake deliveries supported by a substantially reduced van fleet. Results using a specially-developed algorithm to model operations of a real carrier in an area of central London, UK, suggested that the carrier could reduce CO2 emissions by 45%, NOx emissions by 33%, driving distance by 78% and curbside parking time by 45%. Overall cost savings to the carrier were estimated to be in the range 34–39%. Scaling up the modelled emissions savings to London’s Central Activities Zone, an area of approximately 30 km2 and with current total annual parcel delivery distance of around 15 million km, could see annual emissions savings in the region of 2 million kg CO2 and 1633 kg NOx if all carriers utilised porters or cycle couriers. The key operating challenges identified were related to sorting and consolidating items by weight and volume, parcel handover arrangements and how to deal with express items and failed deliveries

Homologous Helical Jets: Observations by IRIS, SDO and Hinode and Magnetic Modeling with Data-Driven Simulations

We report on observations of recurrent jets by instruments onboard the Interface Region Imaging Spectrograph (IRIS), Solar Dynamics Observatory (SDO) and Hinode spacecrafts. Over a 4-hour period on July 21st 2013, recurrent coronal jets were observed to emanate from NOAA Active Region 11793. FUV spectra probing plasma at transition region temperatures show evidence of oppositely directed flows with components reaching Doppler velocities of +/- 100 km/s. Raster Doppler maps using a Si IV transition region line show all four jets to have helical motion of the same sense. Simultaneous observations of the region by SDO and Hinode show that the jets emanate from a source region comprising a pore embedded in the interior of a supergranule. The parasitic pore has opposite polarity flux compared to the surrounding network field. This leads to a spine-fan magnetic topology in the coronal field that is amenable to jet formation. Time-dependent data-driven simulations are used to investigate the underlying drivers for the jets. These numerical experiments show that the emergence of current-carrying magnetic field in the vicinity of the pore supplies the magnetic twist needed for recurrent helical jet formation.Comment: 15 pages, 10 figures, accepted by Ap