Antonio Martinez-Sykora

Matheuristics for the irregular bin packing problem with free rotations

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 Programing models to determine the association between pieces and bins and then we use a Mixed Integer Programing 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.

A simheuristic approach to the vehicle ferry revenue management problem

We propose a Simheuristic approach to the vehicle ferry revenue management problem, where the aim is to maximize the revenue 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 varies over time. 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 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, enabling it to be solved rapidly. We present simulations of the selling season using this reduced state space to validate the method.

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.

Cost-driven build orientation and bin packing of parts in Selective Laser Melting (SLM)

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.

Dynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference

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.

Balanced vehicle routing: Polyhedral analysis and branch-and-cut algorithm

This paper studies a variant of the unit-demand Capacitated Vehicle Routing Problem, namely the Balanced Vehicle Routing Problem, where each route is required to visit a maximum and a minimum number of customers. A polyhedral analysis for the problem is presented, including the dimension of the associated polyhedron, description of several families of facet-inducing inequalities and the relationship between these inequalities. The inequalities are used in a branch-and-cut algorithm, which is shown to computationally outperform the best approach known in the literature for the solution of this problem.

A beam search approach to solve the convex irregular bin packing problem with guillotine cuts

This paper presents a two dimensional convex irregular bin packing problem with guillotine cuts. The problem combines the challenges of tackling the complexity of packing irregular pieces, guaranteeing guillotine cuts that are not always orthogonal to the edges of the bin, and allocating pieces to bins that are not necessarily of the same size. This problem is known as a two-dimensional multi bin size bin packing problem with convex irregular pieces and guillotine cuts. Since pieces are separated by means of guillotine cuts, our study is restricted to convex pieces.A beam search algorithm is described, which is successfully applied to both the multi and single bin size instances. The algorithm is competitive with the results reported in the literature for the single bin size problem and provides the first results for the multi bin size problem.

Efficient local search heuristics for packing irregular shapes in two-dimensional heterogeneous bins

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.