Abstract
Many models have been proposed for the location-allocation problem. In this study, based on sectorization concept, we propose a new single-objective model of this problem, in which, there is a set of customers to be assigned to distribution centres (DCs). In sectorization problems there are two important criteria as compactness and equilibrium, which can be defined as constraints as well as objective functions. In this study, the objective function is defined based on the equilibrium of distances in sectors. The concept of compactness is closely related to the accessibility of customers from DCs. As a new approach, instead of compactness, we define the accessibility of customers from DCs based on the covering radius concept. The interpretation of this definition in real life is explained. As another contribution, in the model, a method is used for the selection of DCs, and a comparison is made with another method from the literature, then the advantages of each are discussed. We generate benchmarks for the problem and we solve it with a solver available in Python’s Pulp library. Implemented codes are presented in brief.

Abstract
One of the most widely used methods in multi-objective optimization problems is the weighted sum method. However, in this method, defining the weights of objectives is always a challenge. Various methods have been suggested to achieve the weights, one of which is Shannon’s entropy method. In this study, a bi-objective model is introduced to solve the sectorization problem. As a solution method, the model is transformed into two single-objective ones. Also, the bi-objective model is solved for the case where the weights are equal to one. The gained three results from a benchmark are supposed as alternatives in a decision matrix. After the limitation of this approach appears, solutions from different benchmarks are added to the matrix. With Shannon’s entropy method, the weights of the objective functions are got from the decision matrix. The limitations of the approach and possible causes are discussed.

Abstract
In sectorization problems (SPs), a large area is divided into smaller regions for administrative purposes. SPs have applications in many fields. Since real-life problems are often dynamic, in this study, a new model for dynamic SP is proposed. In the problem, points are assigned to service centres and in this way sectors are formed. The sectors must be balanced in terms of distance and demand, which is defined in the objective function and constraints of the model. In the problem, in a certain time period, the coordinates and demands of some points change according to certain statistical distributions. A two-stage solution method is suggested for this problem. In the first stage, the expected values of coordinates and demands of the points are estimated by a Monte Carlo simulation, and in the second stage, the problem is solved like a deterministic optimization problem. The model is nonlinear, but after linearization, it is solved in Python’s Pulp library for benchmarks of different sizes and the results are discussed.

Abstract
The retail shelf space planning problem has long been addressed by Marketing and Operations Research (OR) professionals and researchers, with the first empirical studies tracing back to the 1960s and the first modelling approaches back to the 1970s. Due to this long history, this field presents a wide range of different mathematical modelling approaches that deal with the decisions surrounding a set of products and not only define their space assignment and related quantity, but also their vertical and horizontal positioning within a retail shelf. These decisions affect customer demand, namely in the form of space- and position-dependent demand and replenishment requirements. Current literature provides either more comprehensive decision models with a wide range of demand effects but limited practical applicability, or more simplistic model formulations with greater practical application but limited consideration of the associated demand. Despite the recent progress seen in this research area, no work has yet systematised published research with a clear focus on shelf space planning. As a result, there is neither any up-to-date structured literature nor a unique model approach, and no benchmark sets are available. This paper provides a description and a state-of-the-art literature review of this problem, focusing on optimisation models. Based on this review, a classification framework is proposed to systematise the research into a set of sub-problems, followed by a unified approach with a univocal notation of model classes. Future lines of research point to the most promising open questions in this field.

Abstract
In this paper, we address the Constrained Three-dimensional Guillotine Cutting Problem (C3GCP), which consists of cutting a larger cuboid block (object) to produce a limited number of smaller cuboid pieces (items) using orthogonal guillotine cuts only. This way, all cuts must be parallel to the object's walls and generate two cuboid sub-blocks, and there is a maximum number of copies that can be manufactured for each item type. The C3GCP arises in industrial manufacturing settings, such as the cutting of steel and foam for mattresses. To model this problem, we propose a new compact mixed-integer non-linear programming (MINLP) formulation by extending its two-dimensional version, and develop a mixed-integer linear programming (MILP) version. We also propose a new model for a particular case of the problem which considers 3-staged patterns. As a solution method, we extend the algorithm of Wang (1983) to the three-dimensional case. We emphasise that the C3GCP is different from 3D packing problems, namely from the Container Loading Problem, because of the guillotine cut constraints. All proposed approaches are evaluated through computational experiments using benchmark instances. The results show that the approaches are effective on different types of instances, mainly when the maximum number of copies per item type is small, a situation typically encountered in practical settings with low demand for each item type. These approaches can be easily embedded into existing expert systems for supporting the decision-making process.

Abstract
Designing a viable carsharing system in a competitive environment is challenging and often dependent on a myriad of decisions. This paper establishes and presents an integrated conceptual decision-support framework for carsharing systems, encompassing critical decisions that should be made by carsharing organizations and users. To identify the main decisions in a carsharing system, and the inputs and interactions among them, it is crucial to obtain a comprehensive understanding of the current state of the literature as well as the business practices and context. To this aim, a holistic and in-depth literature review is conducted to structure distinct streams of literature and their main findings. Then, we describe some of the key decisions and business practices that are often oversimplified in the literature. Finally, we propose a conceptual decision-support framework that systematizes the interactions between the usually isolated problems in the academic literature and business practices, integrating the perspectives of carsharing organizations and of their users. From the proposed framework, we identify relevant research gaps and ways to bridge them in the future, toward more realistic and applicable research.