Safe and secure vehicle routing problems refer to the transportation of dangerous (e.g., flammable liquids) or valuable goods (e.g., cash), the surveillance of streets (e.g., police patrols) or other areas (e.g., those within a factory or building), and the response to sudden incidents (e.g., robberies or street disruptions). It thus covers a multitude of models and methods with each having its own objective and constraints, such as unpredictability or risk. We review and classify literature in this field and thereby identify a starting point for researchers in this evolving and practically relevant field. Our study reveals that there are 82 articles that cover aspects related to safe and secure routing, a majority of which were published in the last five years. We classify the articles into five main categories: (i) transportation of hazardous materials, (ii) patrol routing, (iii) cash-in-transit, (iv) dissimilar routing problems, and (v) modeling of multi-graphs. Categories (i)-(iv) elaborate on the problem studied, while (v) provides a general concept based on road network characteristics most commonly found in safe and secure routing problems. Relevant methods and instances, along with their similarities and dissimilarities, have also been discussed in the paper. Furthermore, specific problem characteristics and future research directions are identified.

We study a feasibility-seeking problem with percentage violation constraints (PVCs). These are additional constraints that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a specified fraction of the number of constraints in each subset is allowed to be violated by up to a specified percentage of the existing bounds. Our motivation to investigate problems with PVCs comes from the field of radiation therapy treatment planning (RTTP) wherein the fully discretized inverse planning problem is formulated as a split feasibility problem and the PVCs give rise to nonconvex constraints. Following the CQ algorithm of Byrne (2002, , Vol. , pp. 441-53), we develop a string-averaging CQ-method that uses only projections onto the individual sets that are half-spaces represented by linear inequalities. The question of extending our theoretical results to the nonconvex sets case is still open. We describe how our results apply to RTTP and provide a numerical example.

We consider the problem of maximizing the number of people that a dining room can accommodate provided that the chairs belonging to different tables are socially distant. We introduce an optimization model that incorporates several characteristics of the problem, namely: the type and size of surface of the dining room, the shapes and sizes of the tables, the positions of the chairs, the sitting sense of the customers, and the possibility of adding space separators to increase the capacity. We propose a simple, yet general, set-packing formulation for the problem. We investigate the efficiency of space separators and the impact of considering the sitting sense of customers in the room capacity. We also perform an algorithmic analysis of the model, and assess its scalability to the problem size, the presence of (or lack thereof) room separators, and the consideration of the sitting sense of customers. We also propose two constructive heuristics capable of coping with large problem instances otherwise intractable for the optimization model.

In Chile, due to the explosive increase of new Coronavirus disease 2019 (COVID-19) cases during the first part of 2021, the ability of health services to accommodate new incoming cases was jeopardized. It has become necessary to be able to manage intensive care unit (ICU) capacity, and for this purpose, monitoring both the evolution of new cases and the demand for ICU beds has become urgent. This paper presents short-term forecast models for the number of new cases and the number of COVID-19 patients admitted to ICUs in the Metropolitan Region in Chile.

The evolution of the COVID-19 pandemic is highly unpredictable; however, its impacts are limited to neither a single sector nor a single country. This study evaluates the performance and efficiency of 49 Islamic banks across 10 countries during 2019-2020 to assess how those banks can preserve their performance and remain resilient in the aftermath of the COVID-19 pandemic. Using the conventional inverse data envelopment analysis (InvDEA) approach, we show that because of reductions in their outputs, 31 out of the 49 banks studied would need to reduce their inputs so that their efficiency can remain unchanged. However, we show that only 10 banks need to make such adjustments to maintain their efficiency levels using our proposed InvDEA efficiency model. The adjustment for those 10 banks would help in reducing more inputs, suggesting more cost savings, and improving the overall efficiency of the examined banks, compared with the other 31 banks.

In this paper, we develop a unified variational inequality framework in the context of spatial price network equilibrium problems that handles multiple products with multiple demand and supply markets in multiple countries as well as multiple transportation routes. The model incorporates a plethora of distinct trade measures, which is particularly important in the pandemic, as PPEs and other essential products are in high demand, but short in supply globally. In the model, product flows as well as prices at the supply markets and the demand markets in different countries are variables that allows us to seamlessly introduce various trade measures, including tariffs, quotas, as well as price floors and ceilings. Qualitative properties are analyzed. Numerical examples are provided to illustrate the impacts of the trade measures on equilibrium product path and link flows, and on prices, and demand and supply quantities. Given the relevance of the trade measures in the world today and discussions concerning the impacts, the framework constructed in this paper is especially timely.

Planning vaccine distribution in rural and urban poor communities is challenging, due in part to inadequate vehicles, limited cold storage, road availability, and weather conditions. The University of Washington and VillageReach jointly developed and tested a user-friendly, Excel spreadsheet based optimization tool for routing and scheduling to efficiently distribute vaccines and other medical commodities to health centers across Mozambique. This paper describes the tool and the process used to define the problem and obtain feedback from users during the development. The distribution and routing tool, named route optimization tool (RoOT), uses an indexing algorithm to optimize the routes under constrained resources. Numerical results are presented using five datasets, three realistic and two artificial datasets. RoOT can be used in routine or emergency situations, and may be easily adapted to include other products, regions, or logistic problems.

A block-iterative projection algorithm for solving the consistent convex feasibility problem in a finite-dimensional Euclidean space that is resilient to bounded and summable perturbations (in the sense that convergence to a feasible point is retained even if such perturbations are introduced in each iterative step of the algorithm) is proposed. This resilience can be used to steer the iterative process towards a feasible point that is superior in the sense of some functional on the points in the Euclidean space having a small value. The potential usefulness of this is illustrated in image reconstruction from projections, using both total variation and negative entropy as the functional.

We study the common fixed point problem for the class of directed operators. This class is important because many commonly used nonlinear operators in convex optimization belong to it. We propose a definition of sparseness of a family of operators and investigate a string-averaging algorithmic scheme that favorably handles the common fixed points problem when the family of operators is sparse. The convex feasibility problem is treated as a special case and a new subgradient projections algorithmic scheme is obtained.

This paper presents an applied study of scheduling buses and drivers for the Beijing Bus Group (BJBUS), the largest bus company in China. This is pioneering research in China for bus transit scheduling using computers based on a unified mode of operation. It is anticipated that the research fruits and experiences obtained would be of benefit to other bus operators in China. The bus transit scheduling problem in BJBUS is first presented in the paper. The particular characteristics are pointed out, which are different from those in developed countries, while many are common in China. After a brief review and analysis of the appropriateness of some currently successful approaches, the paper focuses on reporting the solution ideas and methods for BJBUS, especially those developed to solve the specific problems of BJBUS, such as scheduling buses with built-in meal periods, multi-type bus scheduling, restricting drivers to one or two particular buses, etc. Finally, the implementation and computational results are reported before the concluding remarks.