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In this paper, we present a network-based optimization model describing a closed-loop supply chain for the provision of 5G network slices on demand to users and devices on the ground. The three-tier supply chain network consists of a fleet of pre-existing UAVs, to which others can be added, managed by a fleet of UAV controllers, whose purpose is to perform services requested by users and devices on the ground. The aim of this paper is to provide a constrained optimization problem through which the providers’ profits are maximized, determining the global optimal distributions of request flows, the global optimal distributions of executed services and the optimal reliability level of pre-existing UAVs of the fleet. We also derive the associated Variational inequality formulation of the problem and, finally, a numerical simulation is performed to validate the effectiveness of the model.

We introduce Ricerca Operativa Applicazioni Reali (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools. Its main aim is to improve students’ interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. ROAR offers examples and problems closely connected with students’ everyday life or with the industrial reality, balancing mathematical modeling and algorithmics. The project is composed of three teaching units, addressed to grades 10, 11, and 12. The implementation of the first teaching unit took place in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy). In particular, in this paper, we provide a full description of this first teaching unit in terms of objectives, prerequisites, topics and methods, organization of the lectures, and digital technologies used. Moreover, we analyze the feedback received from students and teachers involved in the experimentation, and we discuss advantages and disadvantages related to distance learning that we had to adopt because of the COVID-19 pandemic. Funding: E. Taranto and G. Colajanni were partially supported by the research projects “Programma Ricerca di Ateneo UNICT 2020-22 linea 2,” “EEEP&DLaD,” and “OMNIA” of the University of Catania. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ited.2022.0271 .

In this paper, we present a multi-tiered network-based optimization model describing the provision of services by network slices of 5G-Service providers (e.g. through Unmanned Aerial Vehicles (UAVs) organized as Flying Ad hoc Networks (FANET)), taking into account the security levels of each provider. The three levels of the network consist of the infrastructure layers, which contain resources needed to execute a service, the slices layer, where services are served for the services layer, which represents the upper layer of the network and consists of services or applications required by users or devices. The objective of the proposed model is to establish the optimal flows between network layers and the optimal security levels in order to maximize the providers’ profits, given by the difference between the revenues obtained by the sale of services and the rental of their resources and the costs. Numerical experiments are performed and solved with a new nature-inspired genetic algorithm adapted to the optimization 5G network problem.

Thanks to advances in modern medicine and the presence of an increasingly efficient organizational network, nowadays transplantation can save thousands of lives every year. In our paper we present a supply chain model with transplant centers and donor hospitals, where we assume that the medical teams move to the hospitals, take the organs, and go back to the transplant centers, using the most suitable transport mode. Since the availability of organs in each donor hospital is unknown a priori, we introduce a random variable which gives us an expected value of such an availability. The aim of the model is to obtain a social optimum in which we intend to minimize the total costs, given by transport costs of both teams and organs, as well as those of transplant patients, the costs of removal, of transplantation and of post-transplantation, the costs of disposal of diseased or non-functioning organs and of the damaged ones, and the penalties. We deduce the associated variational inequality formulation and an existing result for the solution. Finally, we present some numerical examples.

Cloud Computing is a type of Internet-based computing, much used in recent years, that relies on sharing computer processing resources and data to computers and other devices on demand, from any location and at any time rather than having local servers or personal devices to handle applications. This shared IT infrastructure contains large pools of systems that are linked together. Often, virtualization techniques are used to maximize the power of cloud computing. In this paper we describe the global network of a cloud computing environment with five different layers, represented by hardware/datacenter, infrastructure, platform, application and end-users. Then, we present the mathematical model of the network and study the behavior of the typical IaaS provider in order to find the optimization problem. A computational procedure for the calculus of the optimal solutions is proposed, is applied to two numerical examples and is compared with a linearization.

In this paper we present a financial mathematical model, based on networks, aiming at maximizing the profits while simultaneously minimizing the risk. In addition, our model is characterized by short selling, which consists in the sale of non-owned financial instruments with subsequent repurchase, and transfer of securities. We propose an Integer Nonlinear Programming (INLP) Problem, whose solution provides us with the optimal distribution of securities to be purchased and sold.

In this chapter we first present some theoretic concepts related to the strong duality in the infinite-dimensional setting. Then, we apply such results to the general financial equilibrium economy, studying also the dual formulation of the problem, analyzing both the sector’s and the system’s viewpoints and deriving the contagion phenomenon. Further, we provide an evolutionary Markowitz-type measure of the risk with a memory term. Finally, we apply Assumption S to the elastic-plastic torsion problem for linear operators and investigate the existence of Lagrange multipliers to the elastic-plastic torsion problem for nonlinear monotone operators, providing an example of the so-called Von Mises functions and searching for radial solutions.

Cloud Computing is a type of Internet-based computing, much used in recent years, that relies on sharing computer processing resources and data to computers and other devices on demand, from any location and at any time rather than having local servers or personal devices to handle applications. This shared IT infrastructure contains large pools of systems that are linked together. Often, virtualization techniques are used to maximize the power of cloud computing. In this paper we describe the network of a cloud computing environment with five different layers, represented by hardware/datacenter, infrastructure, platform, application and end-users. Then, we present the mathematical model of the network and study the behavior of the typical IaaS provider in order to find the optimization problem. A computational procedure for the calculus of the optimal solutions is proposed and is applied to a numerical example.