Abstract: Electoral systems are modified by individuals who have incentives to bias the rules for their political advantage (i.e., gerrymandering). To prevent gerrymandering, legislative institutions can rely on mathematical tools to guarantee democratic fairness and territorial contiguity. These tools have been successfully used in the past; however, there is a need to accommodate additional meanings of the term fairness within the electoral systems of modern democracies. In this paper, we present an optimization framework that considers multiple criteria for drawing districts and assigning the number of representatives. Besides some typical districting criteria (malapportionment and contiguity), we introduce novel criteria for ensuring territorial equilibrium and incentives for candidates to deploy their representation efforts fairly during their campaign and period in office. We test the method, which we denote as Multi-criteria Pen, in a recent and a forthcoming reform of the Chilean electoral system. The results show the potential of our tool to improve the current territorial design and offers insights on the motivations, objectives, and deficiencies of both reform plans.

Abstract: The assembly line balancing problem is a classical optimisation problem whose objective is to assign each production task to one of the stations on the assembly line so that the total efficiency of the line is maximized. This study proposes a novel hybrid method to solve the simple version of the problem in which the number of stations is fixed, a problem known as SALBP-2. The hybrid differs from previous approaches by encoding individuals of a genetic algorithm as instances of a modified problem that contains only a subset of the solutions to the original formulation. These individuals are decoded to feasible solutions of the original problem during fitness evaluation in which the resolution of the modified problem is conducted using a dynamic programming based approach that uses new bounds to reduce its state space. Computational experiments show the efficiency of the method as it is able to obtain several new best-known solutions for some of the benchmark instances used in the literature for comparison purposes.

Abstract: E-commerce sales have led to a considerable increase in the demand for last-mile delivery companies, revealing several problems in their logistics processes. Among these problems, are not meeting delivery deadlines. For example, in Chile, the national consumer service (SERNAC) indicated that in 2018, late deliveries represented 23% of complaints in retail online sales and were the second most common reason for complaints. Some of the causes are incorrectly designed delivery zones because in many cases, these delivery zones do not account for the demographic growth of cities. The result is an imbalanced workload between different zones, which leads to some resources being idle while others fail to meet their workload in satisfactory conditions. The present work proposes a hybrid method for designing delivery zones with an objective based on improving the quality of express delivery services. The proposed method combines a preprocess based on the grouping of demand in areas according to the structure of the territory, a heuristic that generates multiple candidates for the distribution zones, and a mathematical model that combines the different distribution zones generated to obtain a final territorial design. To verify the applicability of the proposed method, a case study is considered based on the real situation of a Chilean courier company with low service fulfillment in its express deliveries. The results obtained from the computational experiments show the applicability of the method, highlighting the validity of the aggregation procedure and improvements in the results obtained using the hybrid method compared to the initial heuristic. The final solution improves the ability to meet the conditions associated with express deliveries, compared with the current situation, by 12 percentage points. The results also allow an indicative sample of the critical service factors of a company to be obtained, identifying the effects of possible changes in demand or service conditions.

Abstract: Small-medium enterprises (SMEs) represent 90% of business globally. Digital Transformation (DT) affects SMEs differently from larger companies because although SMEs have more flexibility and agility for adapting to new circumstances, they also have more limited resources and specialization capabilities. Thus, it is fundamental to measure SMEs' performance considering different perspectives. Here, we describe and analyze the state-of-the-art of DT in SMEs, focusing on performance measurement. We center on whether the tools used by SMEs encompass the triple bottom line of sustainability (i.e., environmental, social, and economic aspects). To do so, in December 2021, we performed a comprehensive systematic literature review (SLR) on the Web of Science and Scopus. In addition, we also explored a novel approach for SLR: topic modeling with a machine learning technique (Latent Dirichlet Allocation). The differences and interchangeability of both methods are discussed. The findings show that sustainability is treated as a separate topic in the literature. The social and environmental aspects are the most neglected. This paper contributes to sustainable development goals (SDGs) 1, 5, 8, 9, 10, and 12. A conceptual framework and future research directions are proposed. Thus, this paper is also valuable for policymakers and SMEs switching their production paradigm toward sustainability and DT.

Abstract: A network is given whose edges need to be constructed (or restored after a disaster). The lengths of edges represent the required construction/restoration times given available resources, and one unit of length of the network can be constructed per unit of time. All points of the network are accessible for construction at any time. For each pair of vertices, a due date is given. It is required to find a construction schedule that minimizes the maximum lateness of all pairs of vertices, where the lateness of a pair is the difference between the time when the pair becomes connected by an already constructed path and the pair's due date. We introduce the problem and analyze its structural properties, present a mixed-integer linear programming formulation, develop a number of lower bounds that are integrated in a branch-and-bound algorithm, and discuss results of computational experiments both for instances based on randomly generated networks and for instances based on 2010 Chilean earthquake data.

Abstract: Supply chain network design aims at the integration of the different actors of a supply chain within a single framework in order to optimise the total profit of the system. In this paper, we consider the integration of line balancing issues within the tactical decisions of the supply chain, and we offer a novel model and a solution approach for the problem. The new approach decomposes the problem into multiple line balancing problems and a mixed integer linear model, which is easier to solve than the previously available non-linear mixed integer formulation. The results show that the new method is able to solve previously studied models within a fraction of the reported running times, and also allows us to solve larger instances than those reported in earlier works. Finally, we also provide some analysis on the influence of the cost structure, the demand and the structure of the assembly process on the final configuration of the assemblies and the distribution network.

Abstract: A line balancing problem considers the assignment of operations to workstations in an assembly line. While assembly lines are usually associated to mass production of standardised goods, their advantages have led to their widespread use whenever a product-oriented production system is applicable and the benefits of the labour division and specialisation are significant, even when some of its characteristics may deviate from classical assembly lines. In this work, we study a line balancing problem found in the textile industry in which the line must be balanced for multiple types of goods taking into account resource requirements. In order to solve the problem, a hybrid method that combines classical methods for line balancing with an Estimation of Distribution Algorithm is proposed. Computational experiments show that the new procedure improves upon the state of the art when compared using a benchmark set derived from the literature, as well as when compared using data from the manufacturer that originated this research work.

Abstract: Assembly lines are production flow systems wherein activities are organised around a line consisting of various workstations through which the product flows. At each station, the product is assembled through a subset of operations. The assembly line balancing problem (ALBP) consists of allocating operations between stations to maximise the system efficiency. In this study, a variable-depth local search algorithm is proposed for solving simple assembly line balancing problems (SALBPs), which are the most widely studied versions of the ALBP. Although the state-of-the-art techniques for solving the SALBP consist of exact enumeration-based methods or heuristics, this paper proposes a local search-based heuristic using variable-length sequences that allow the solution space to be efficiently explored. The proposed algorithm improves the best solution known for multiple instances reported in the literature, indicating that its efficiency is comparable to those of the state-of-the-art method for solving the SALBP. Moreover, the characteristics of the instances for which the proposed procedure provides a better solution than previously reported construction procedures are investigated.

Abstract: Battarra et al. recently proposed a novel assembly line balancing problem with applications to the apparel industry, where the tasks are performed in a fixed order. To solve the problem, one has to assign workers and tasks to the workstations with the objective of maximising the throughput of the assembly line. In this paper, we provide dynamic programming formulations for the general problem and some special cases. We then use these formulations to develop an exact solution approach that optimally solves the instances in Battarra et al. within seconds.

Abstract: This work studies an assembly line balancing problem with uncertainty on the task times. In order to deal with the uncertainty, a robust formulation to handle changes in the operation times is put forward. In order to solve the problem, several lower bounds, dominance rules and an enumeration procedure are proposed. These methods are tested in a computational experiment using different instances derived from the literature and then compared to similar previous approaches. The results of the experiment show that the method is able to solve larger instances in shorter running times. Furthermore, the cost of protecting a solution against uncertainty is also investigated. The results highlight that protecting an assembly line against moderate levels of uncertainty can be achieved at the expense of small quantities of additional resources (stations). (C) 2017 Elsevier Ltd. All rights reserved.