Neutrosophic sets, expanded from the constructs of fuzzy and intuitionistic fuzzy sets, can accommodate degrees of truth, indeterminacy, and falsity for each element. This attribute equips them with an aptitude for a more refined interpretation of ambiguous or uncertain data. This study presents an innovative application of Neutrosophic Data Envelopment Analysis (Neu-DEA), incorporating pentagonal neutrosophic numbers in both input and output data. This novel methodology involves the transformation of traditional DEA models into a Pentagonal neutrosophic DEA model, subsequently converting it into a Crisp Linear Programming (CrLP) model. A unique ranking function is integral to this process. Performance evaluation of decision-making units (DMUs) is accomplished through the resolution of the CrLP model, with subsequent ranking of the DMUs based on their relative efficiency scores. The utility and effectiveness of this novel technique is validated through a numerical example.

Improper waste disposal by humans has created significant environmental issues in the marine ecosystem, including endangering aquatic life and accelerating the extinction of certain marine species. Due to the floating nature of the marine debris, the coordinates for collecting activities must be estimated in advance. In this article, GNOME software is used to estimate the coordinates of debris, and then a fleet of several ships is used to collect them. Also, a mixed integer linear programming model is presented for the routing optimization of debris collection fleets. The proposed optimization model formulates the objective function based on numerous factors, including labor cost, rent, and ship insurance, and considers constraints on fuel tank capacity, the time window, and the ship’s cargo capacity. A new hybrid algorithm combining the Puma algorithm and neighborhood search is proposed to address the problem. Metropolis acceptance is used in the simulated annealing algorithm to avoid the local optima and greedy selection. Numerical examples of the marine survey and the port of Rotterdam are used to test the proposed approach, which has been proven effective in several scenarios. Results achieved from the proposed hybrid method demonstrate considerable performance improvement in solving the problem. This approach has decreased total fuel and labor costs by 10–15% compared to conventional methods, with minimized time window violation reaching 25%. These results show a significant reduction in total operational costs with proper scheduling and route planning.

Traffic crashes and congestion generate high social and economic costs, yet traditional traffic monitoring methods, such as police patrols, fixed cameras, and helicopters, are costly, labor-intensive, and limited in spatial coverage. This paper presents a novel Drone Routing and Scheduling with Flexible Multiple Visits (DRSFMV) framework, an optimization model for planning drone-based highway monitoring under realistic operational constraints, including battery limits, variable monitoring durations, recharging at a depot, and target-specific inter-visit time limits. A mixed-integer nonlinear programming (MINLP) model and a linearized version (MILP) are presented to solve the problem. Due to the NP-hard nature of the underlying problem structure, a heuristic solver, Hexaly, is also used. A case study using real traffic census data from three Southern California counties tests the models across various network sizes and configurations. The MILP solves small and medium instances efficiently, and Hexaly produces high-quality solutions for large-scale networks. Results show clear trade-offs between drone availability and time-slot flexibility, and demonstrate that stricter revisit constraints raise operational cost.

This article presents a study on the job shop problem, a combinatorial optimization problem that models scheduling and resource allocation in industrial settings. The article aims to investigate the relationship between optimality gap and required computational resources, considering various optimality gap levels that are applicable in real-life situations. The study uses a Monte Carlo simulation to analyze the behavior of solvers in solving different sizes of random-generated scheduling problems. The findings of the study offer insights into the worthiness of reaching an optimal solution versus implementing a near-optimal solution and starting the work. The codes used in the study are accessible on the author's GitHub account.