This paper introduces an analytical approach for solving the Benney equation using the q-homotopy analysis transform method. The Benney equation is a nonlinear partial differential equation that has applications in diverse areas of physics and engineering. The q-homotopy analysis transform method is a numerical technique that has been successfully employed to solve a broad range of nonlinear problems. By utilizing this method, we derive approximate analytical solutions for the Benney equation. The results demonstrate that this method is a powerful and effective tool for obtaining accurate solutions for the equation. The proposed method offers a valuable contribution to the existing literature on the behavior of the Benney equation and provides researchers with a useful tool for solving this equation in various applications.

Preventive Maintenance (PM) is a periodic maintenance strategy that has great results for devices in extending their lives, increasing productivity, and, most importantly, helping to avoid unexpected breakdowns and their costly consequences. Preventive maintenance scheduling (PMS) is determining the time for carrying out PM, and it represents a sensitive issue in terms of impact on production if the time for the PM process is not optimally distributed. This study employs hybrid heuristic methods, integrating Genetic Algorithm (GA) and Tabu Search (TS), to address the PMS problem. Notably, the search for an optimal solution remained elusive with GA alone until the inclusion of TS. The resultant optimal solution is achieved swiftly, surpassing the time benchmarks set by conventional methods like integer programming and nonlinear integer programming. A comparison with a published article that used metaheuristics was also applied in order to evaluate the effectiveness of the proposed hybrid approach in terms of solution quality and convergence speed. Moreover, sensitivity analysis underscores the robustness and efficacy of the hybrid approach, consistently yielding optimal solutions across diverse scenarios. The schedule created exceeds standards set by waterworks experts, yielding significant water and electricity surpluses—16.6% and 12.1%, respectively—while simultaneously matching or surpassing total production levels. This method can be used for power plants in private or public sectors to generate an optimal PMS, save money, and avoid water or electricity cuts. In summary, this hybrid approach offers an efficient and effective solution for optimizing PMS, presenting opportunities for enhancement across various industries.

Preventive maintenance (PM) is a maintenance program with activities created at a determined interval or according to certain principles, designed to reduce the likelihood of failure or deterioration of item performance. This aims to improve overall reliability and system availability. In this research, a preventive maintenance schedule (PMS) was designed for electricity and desalination of water in power plants, subject to meeting relevant constraints. The proposed methodology is used to generate a PMS for the boilers, turbines, and distillers. A nonlinear integer programming (NLIP) model was employed to address this problem. The results of the proposed method were compared with the PMS for a power station in Kuwait. The results were better in terms of the volume of production and in terms of the gap between the available production and demand in order to continue providing consumers with electricity and water without a shortage in the event of a breakdown in equipment. It produces an improvement of 12.12% and 16.58% respectively, for water and electricity. Furthermore, the sensitivity and robustness of the proposed method were analysed by increasing the maintenance duration for some equipment, increasing the demand, and adding various additional conditions. In addition, a comparison of additional conditions with a binary problem method in terms of computer time for the search for an optimal solution was carried out, where the model provided an optimal solution in a reasonable time. Among the most important benefits that the user can obtain for this technique are extending the life of the equipment, increasing efficiency, and reducing expenses.

Preventive Maintenance (PM) is a periodic maintenance strategy, which has great results for devices in extending their life, increasing productivity, and most importantly, help avoid unexpected breakdowns and their costly consequence. A preventive maintenance scheduling (PMS) is determining the time for carrying out PM, and it represents a sensitive issue in terms of impact on production if the time for the PM process is not optimally distributed. In this study, hybrid heuristic methods were used to solve the PMS problem, as genetic algorithm and Tabu research were adopted. The optimal solution was reached in a short time compared to previous studies in which optimal methods were used, integer programming and nonlinear integer programming. Also, sensitivity analysis was applied to measure the robustness and strength of the method used, where an optimal solution was obtained for all experiments and in record time. This method can be used for power plants in privet or public sectors, to generate an optimal PMS, to save money, and to avoid water or electricity cuts.

This paper describes a method developed to schedule the preventive maintenance tasks of the generation and desalination units in separate and linked cogeneration plants provided that all the necessary maintenance and production constraints are satisfied. The proposed methodology is used to generate two preventing maintenance schedules, one for electricity and the other for distiller. Two types of crossover operators were adopted, 2-point and 4-point. The objective function of the model is to maximize the available number of operational units in each plant. The results obtained were satisfying the problem parameters. However, 4-point slightly produce better solution than 2-point ones for both electricity and water distiller. The performance as well as the effectiveness of the genetic algorithm in solving preventive maintenance scheduling is applied and tested on a real system of 21 units for electricity and 21 units for water. The results presented here show a great potential for utility applications for effective energy management over a time horizon of 52 weeks. The model presented is an effective decision tool that optimizes the solution of the maintenance scheduling problem for cogeneration plants under maintenance and production constraints.

This paper considers the scheduling of preventive maintenance for the boilers, turbines, and distillers of power plants that produce electricity and desalinated water. It models the problem as a mathematical program (MP) that maximizes the sum of the minimal ratios of production to the demand of electricity and water during a planning time horizon. This objective encourages the plants’ production and enhances the chances of meeting consumers’ needs. It reduces the chance of power cuts and water shortages that may be caused by emergency disruptions of equipment on the network. To assess its performance and effectiveness, we test the MP on a real system consisting of 32 units and generate a preventive maintenance schedule for a time horizon of 52 weeks (one year). The generated schedule outperforms the schedule established by experts of the water plant; it induces, respectively, 16% and 12% increases in the surpluses while either matching or surpassing the total production. The sensitivity analysis further indicates that the generated schedule can handle unforeseen longer maintenance periods as well as a 120% increase in demand—a sizable realization in a country that heavily relies on electricity to acclimate to the harsh weather conditions. In addition, it suggests the robustness of the schedules with respect to increased demand. In summary, the MP model yields optimal systematic sustainable schedules.