Abstract
Additive Layer Manufacturing, particularly Fused Deposition Modelling, faces significant batch loss risks during production. The traditional Concurrent Printing Mode produces all parts simultaneously (layer-by-layer, bottom-to-top), efficiently using printing space but risking complete batch failure if problems occur. In contrast, Sequential Printing Mode produces one part at a time, reducing the risk of total batch loss but utilising printing space less efficiently. In this work, we propose an algorithm that, given a set of parts, performs the nesting of the parts for Concurrent Printing Mode, and for the first time, for the Sequential Printing Mode. A no-fit polygon based approach is used to handle geometry between pairs of parts by using multiple horizontal 2D layer projections of 3D parts, to ensure non-overlapping constraints and prevent machine-part collisions. A Greedy Randomized Adaptive Search Procedure is proposed, tested and benchmarked against a commercial software, using a new set of real-world instances. The approach shows the ability to find high-quality solutions. The approach significantly reduces the number of batches, minimises waste, reduces manufacturing time, and promotes parts quality.

Abstract
The efficient last-mile delivery of goods involves complex challenges in optimizing driver sectors and routes. This problem tends to be large-scale and involves several criteria to meet simultaneously, such as creating compact sectors, balancing the workload among drivers, minimizing the number of undelivered packages and reducing the dissimilarity of sectors on different days. This work proposes a Decision Support System (DSS) that allows decision-makers to select improved allocation strategies to define sectors. The main contribution is an interactive DSS tool that addresses a many-objective (more than 3 objectives) sectorization problem with integrated routing. It establishes a global allocation strategy and uses it as a benchmark for the created daily allocations and routes. A Preference-Inspired Co-Evolutionary Algorithm with Goal vectors using Mating Restriction (PICEA-g-mr) is employed to solve the many-objective optimization problem. The DSS also includes a visualization tool to aid decision-makers in selecting the most suitable allocation strategy. The approach was tested in a medium-sized Metropolitan Area and evaluated using resource evaluation metrics and visualization methods. The proposed DSS deals effectively and efficiently with the sectorization problem in the context of last-mile delivery by producing a set of viable and good-quality allocations, empowering decision-makers in selecting better allocation strategies. Focused on enhancing service efficiency and driver satisfaction, the DSS serves as a valuable tool to improve overall service quality.

Abstract
Sectorization problems refer to dividing a large set, area or network into smaller parts concerning one or more objectives. A decision support system (DSS) is a relevant tool for solving these problems, improving optimisation procedures, and finding feasible solutions more efficiently. This paper presents a new web-based Decision Support System for Sectorization (D3S). D3S is designed to solve sectorization problems in various areas, such as school and health districting,planning sales territories and maintenance operations zones, or political districting. Due to its generic design, D3S bridges the gap between sectorization problems and a state-of-the-art decision support tool. The paper aims to present the generic and technical attributes of D3S by providing detailed information regarding the problem-solution approach (based on Evolutionary Algorithms), objectives (most common in sectorization), constraints, structure and performance.

Abstract

Abstract
Sectorization problems, also known as districting or territory design, deal with grouping a set of previously defined basic units, such as points or small geographical areas, into a fixed number of sectors or responsibility areas. Usually, there are multiple criteria to be satisfied regarding the geographic characteristics of the territory or the planning purposes. This work addresses a case study of parcel delivery services in the region of Porto, Portugal. Using knowledge about the daily demand in each basic unit (7-digit postal code), the authors analysed data and used it to simulate dynamically new daily demands according to the relative frequency of service in each basic unit and the statistical distribution of the number of parcels to be delivered in each basic unit. The sectorization of the postal codes is solved independently considering two objectives (equilibrium and compactness) using Non-dominated Sorting Genetic Algorithm-II (NSGA-II) implemented in Python.