Nesting Problems : Exact and Heuristic Algorithms

Nesting problems are two-dimensional cutting and packing problems involving irregular shapes. This thesis is focused on real applications on Nesting problems such as the garment industry or the glass cutting. The aim is to study different mathematical methodologies to obtain good lower bounds by exact procedures and upper bounds by heuristic algorithms. The core of the thesis is a mathematical model, a Mixed Integer Programming model, which is adapted in each one of the parts of the thesis. This study has three main parts: first, an exact algorithm for Nesting problems when rotation for the pieces is not allowed; second, an Iterated Greedy algorithm to deal with more complex Nesting problems when pieces can rotate at several angles; third, a constructive algorithm to solve the two-dimensional irregular bin packing problem with guillotine cuts. This thesis is organized as follows. The first part is focused on developing exact algorithms. In Chapter 2 we present two Mixed Integer Programming (MIP) models, based on the Fischetti and Luzzi MIP model. We consider horizontal lines in order to define the horizontal slices which are used to separate each pair of pieces. The second model, presented in Section 2.3, uses the structure of the horizontal slices in order to lift the bound constraints. Section 2.5 shows that if we solve these formulations with CPLEX, we obtain better results than the formulation proposed by Gomes and Oliveira. The main objective is to design a Branch and Cut algorithm based on the MIP, but first a Branch and Bound algorithm is developed in Chapter 3. Therefore, we study different branching strategies and design an algorithm which updates the bounds on the coordinates of the reference point of the pieces in order to find incompatible variables which are fixed to 0 in the current branch of the tree. The resulting Branch and Bound produces an important improvement with respect to previous algorithms and is able to solve to optimality problems with up to 16 pieces in a reasonable time. In order to develop the Branch and Cut algorithm we have found several classes of valid inequalities. Chapter 4 presents the different inequalities and in Chapter 5 we propose separation algorithms for some of these inequalities. However, our computational experience shows that although the number of nodes is reduced, the computational time increases considerably and the Branch and Cut algorithm becomes slower. The second part is focused on building an Iterated Greedy algorithm for Nesting problems. In Chapter 6 a constructive algorithm based on the MIP model is proposed. We study different versions depending on the objective function and the number of pieces which are going to be considered in the initial MIP. A new 11 idea for the insertion is presented, trunk insertion, which allows certain movements of the pieces already placed. Chapter 7 contains different movements for the local search based on the reinsertion of a given number of pieces and compaction. In Chapter 8 we present a math-heuristic algorithm, which is an Iterated Greedy algorithm because we iterate over the constructive algorithm using a destructive algorithm. We have developed a local search based on the reinsertion of one and two pieces. In the constructive algorithm, for the reinsertion of the pieces after the destruction of the solution and the local search movements, we use several parameters that change along the algorithm, depending on the time required to prove optimality in the corresponding MIP models. That is, somehow we adjust the parameters, depending on the difficulty of the current MIP model. The computational results show that this algorithm is competitive with other algorithms and provides the best known results on several known instances. The third part is included in Chapter 9. We present an efficient constructive algorithm for the two dimensional irregular bin packing problem with guillotine cuts. This problem arises in the glass cutting industry. We have used a similar MIP model with a new strategy to ensure a guillotine cut structure. The results obtained improve on the best known results. Furthermore, the algorithm is competitive with state of the art procedures for rectangular bin packing problems

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

Exploring fairness in food delivery routing and scheduling problems

Demand for delivery of take-away meals to customers has been growing worldwide, with deliveries often performed by non-specialised gig economy couriers working for online platform operators such as Deliveroo or Just Eat. This has led to the introduction of the ‘meal delivery problem’, characterised by a series of individual pickup and delivery tasks to be assigned to available couriers. While there is a vast set of algorithms proposed in the literature that aim to minimise total workload, very little attention has been given to equitably distributing work between couriers. We propose a new multi-objective problem that is aiming at distributing orders equitably between couriers as well as minimising total workload, where all information is known upfront. We propose an integer linear programming (ILP) model with a weighted objective function that is used to derive the Pareto front in small-scale problems by exploiting the ϵ − constraint approach. This formulation has been proven to solve in a reasonable time for problems with up to 60 orders, however, the optimal Pareto front can only be computed within a reasonable time for problems up to 30 orders. For problems with more orders, we propose a Variable Neighbourhood Search (VNS) algorithm, for which the fitness evaluation evolves in order to explore a wider set of the solution space. The VNS is compared against the ILP and also tested on more realistic size instances with up to 3123 orders, improving the performance over the business as usual and shows that equitable distribution of work can be achieved alongside reducing the total travelled distance

Solving the Hydration Structure of the Heaviest Actinide Aqua Ion Known: The Californium(III) Case

Wish they all could be californium: X-ray absorption spectroscopy (black points) and Monte Carlo simulations (blue line) of CfIII in aqueous solutions have been combined to determine the ligand distance and coordination number (CN) of the CfIII aqua ion (see picture), the heaviest cation measured and simulated to date. The results confirm that a contraction takes place in the actinide series as in the lanthanide series

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