Abstract
Solving nesting problems or irregular strip packing problems is to position polygons on a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we use separation lines, i.e., straight lines that separate polygons. We present a nonlinear programming model that considers free rotations of the polygons and of the separation lines. This model uses a considerable smaller number of variables than the few other approaches proposed in the literature. We use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotations. © 2018 Brazilian Operations Research Society.

Abstract
Optimization problems that are motivated by real-world settings are often complex to solve. Bridging the gap between theory and practice in this field starts by understanding the causes of complexity of each problem and measuring its impact in order to make better decisions on approaches and methods. The Job-Shop Scheduling Problem (JSSP) is a well-known complex combinatorial problem with several industrial applications. This problem is used to analyse what makes some instances difficult to solve for a commonly used solution approach - Mathematical Integer Programming (MIP) - and to compare the power of an alternative approach: Constraint Programming (CP). The causes of complexity are analysed and compared for both approaches and a measure of MIP complexity is proposed, based on the concept of load per machine. Also, the impact of problem-specific global constraints in CP modelling is analysed, making proof of the industrial practical interest of commercially available CP models for the JSSP.

Abstract
Phasor Measurement Units (PMUs) are measuring devices that, when placed in electrical networks, observe their state by providing information on the currents in their branches (transmission lines) and voltages in their buses. Compared to other devices, PMUs have the capability of observing other nodes besides the ones they are placed on. Due to a set of observability rules, depending on the placement decisions, the same number of PMUs can monitor a higher or smaller percentage of a network. This leads to the optimization problem hereby addressed, the PMU Placement Problem (PPP) which aims at determining the minimum number and location of PMUs that guarantee full observability of a network at minimum cost. In this paper we propose two general mathematical programming models for the PPP: a single-level and a bilevel integer programming model. To strengthen both formulations, we derive new valid inequalities and promote variable fixing. Furthermore, to tackle the bilevel model, we devise a cutting plane algorithm amended with particular features that improve its efficiency. The efficiency of the algorithm is validated through computational experiments. Results show that this new approach is more efficient than state-of-the-art proposals.

Abstract

Abstract
For the predicted growth of e-commerce, supply chains need to adapt to new conditions, so that delivery can be fast, cheap and reliable. The key to success is the last-mile product delivery (LMD) - the last stage of the supply chain, where the ordered product is delivered to the final consumer's location. One innovative proposal puts foundations in a new delivery model where a professional delivery fleet (PF) is supplemented partially or fully with crowdshipping. The main idea of crowdshipping is to involve ordinary people - in our case in-store shoppers - in the delivery of packages to other customers. In return, occasional couriers (OC) are offered a small compensation. In hitherto formulated problems it was assumed that OCs always accept delivery tasks assigned to them. In this paper we consider OCs as independent agents, which are free to reject assignments. The main contribution of the paper is an original bi-level methodology for matching and routing problem in LMD with OCs and the PF. The goal is to use crowdshipping to reduce the total delivery cost in a same-day last-mile delivery system with respect to occasional couriers' freedom to accept or reject the assigned delivery. We introduce probability to represent each OC's willingness to perform the delivery to a given final customer. We study the OCs' willingness to accept or reject delivery tasks assigned to them and the influence of their decision on the total delivery cost associated to both the OCs' compensation fees and the delivery cost generated by the PF used for the delivery of remaining parcels. © 2018 The Author(s).

Abstract