We consider the problem of scheduling $n$ jobs with identical processing times and given release as well as delivery times on $m$ uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (``branch less and cut more''). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is $O(\gamma m^2 n\log n)$, where $\gamma$ can be either $n$ or the maximum job delivery time $q_{\max}$. This complexity can even be reduced further by using a smaller number $\kappa<n$ in the estimation describing the number of jobs of particular types. However, this number $\kappa$ becomes only known when the algorithm has terminated.

University course scheduling (UCS) is one of the most important and time-consuming issues that all educational institutions face yearly. Most of the existing techniques to model and solve UCS problems have applied approximate methods, which are different in terms of efficiency, performance, and optimization speed. Accordingly, this research aims to apply an exact optimization method to provide an optimal solution to the course scheduling problem. In other words, in this research, an integer programming model is presented to solve the USC problem. In this model, hard and soft constraints include the facilities of classrooms, courses of different levels and compression of students' curriculum, courses outside the faculty and planning for them, and the limited time allocated to the professors. The objective is to maximize the weighted sum of allocating available times to professors based on their preferences in all periods. To evaluate the presented model's feasibility, it is implemented using the GAMS software. Finally, the presented model is solved in a larger dimension using a real data set from a college in China and compared with the current program in the same college. The obtained results show that considering the mathematical model's constraints and objective function, the faculty courses' timetable is reduced from 4 days a week to 3 working days. Moreover, master courses are planned in two days, and the courses in the educational groups do not interfere with each other. Furthermore, by implementing the proposed model for the real case study, the maximum teaching hours of the professors are significantly reduced. The results demonstrate the efficiency of the proposed model and solution method in terms of optimization speed and solution accuracy.

Symbolic pole/zero analysis is an important step when designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. In this study, we present a mathematical model combined with a heuristic-metaheuristic solution method for the symbolic pole/zero simplification in operational transconductance amplifiers (OTA). At first, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is performed for the simplification of the derived symbolic pole/zero expressions. The developed method has been tested on three analog OTAs. The obtained results show the effectiveness of the proposed method to achieve accurate simplified symbolic pole/zero expressions with the least complexity.

In recent years, the management of health systems is a main concern of governments and decision makers. Home health care is one of the newest methods of providing services to patients in developed societies that can respond to the individual lifestyle of modern age and the increase of life expectancy. The home health care routing and scheduling problem is a generalized version of the vehicle routing problem, which is extended to a complex problem by adding special features and constraints of health care problems. In this problem, there are multiple stakeholders such as nurses for which an increase of their satisfaction level is very important. In this study, a mathematical model is developed to expand traditional home health care routing and scheduling models to downgrading cost aspects by adding the objective of minimizing the difference between the actual and potential skills of the nurses. Downgrading can lead to a dissatisfaction of the nurses. In addition, skillful nurses have higher salaries and high-level services increase equipment costs and need more expensive trainings and nursing certificates. Therefore, downgrading can enforce hidden huge costs to the managers of a company. To solve the bi-objective model, an -constraint based approach is suggested and the model applicability and its ability to solve the problem in various sizes are discussed. A sensitivity analysis on the Epsilon parameter is conducted to analyze the effect of this parameter on the problem. Finally, some managerial insights are presented to help the managers in this field, and some directions for future studies are mentioned as well.

Phosphorus (P) is the most important substance in inorganic fertilizers used in agriculture industry. In this study, a multi-product and multi-objective model is presented considering economic and environmental concerns to design a renewable and sustainable P-fertilizer supply chain management (PFSCM). To handle complexities of the proposed model, an ensemble knowledge-based three-stage heuristic-metaheuristic algorithm utilizing heuristic information available in the model, whale optimization algorithm, and variable neighborhood search (named H-WOA-VNS) is proposed. At first, a problem-dependent heuristic is designed to generate a set of near-optimal feasible solutions. These solutions are fed into a population-based whale optimization algorithm which benefits from both exploration and exploitation strategies. Finally, a single-solution metaheuristic based on variable neighborhood search is applied to further improve the quality of the solution using local search operators. The objective function of the algorithm is formulated as a weighted average function to minimize total economic cost, while increasing crop yield and P use efficiency. Experimental results over five synthetic datasets and a real case study of the P-fertilizer supply chain confirm the superiority of the proposed method against the state-of-the-art techniques. The results demonstrate that the proposed method performs well in optimizing both the economic cost and environmental issues.