In this paper, we consider a simplified real-life identical parallel machine scheduling problem with sequence-dependent setup times and job splitting to minimize makespan. We propose a heuristic to solve this problem. Our method is composed of two parts. The problem is first reduced into a single machine scheduling problem with sequence-dependent setup times. This reduced problem can be transformed into a Traveling Salesman Problem (TSP), which can be efficiently solved using Little's method. In the second part, a feasible initial solution to the original problem is obtained by exploiting the results of the first part. This initial solution is then improved in a step by step manner, taking into account the setup times and job splitting. We develop a lower bound and evaluate the performances of our heuristic on a large number of randomly generated instances. The solution given by our heuristic is less than 4.88% from the lower bound.

By 2050, the European Union plans to make Europe the first carbon-neutral continent and a global leader in climate-green industries. Recently, many decisions have been taken in the world to ensure the energy transition from fossil fuel to renewable energy. The creation of renewable energy communities (REC) is among the solutions used to increase this transition. This study presents 16 different configurations for energy self-consumption in RECs containing different industrial factories. One mathematical model is proposed for each configuration, and they have been solved according to different criteria. The comparisons are made between these configurations according to economic, environmental, technical, and social criteria. Then, four multi-criteria decision-making (MCDM) methods are used to choose the best configurations considering all the criteria. For this purpose, the achieved results from the mathematical models are used as input for the MCDM methods. The findings demonstrate that the most effective configurations combine both individual and collective self-consumption. Furthermore, the inclusion of collective production results in multiple advantages, including a 64.71% rise in economic gains, a 26.95% decrease in CO₂ emissions, a 21.39% improvement in self-sufficiency, and a significant increase in job creation by 175.24%. In addition, incorporating storage enables a substantial rise in the degree of self-sufficiency, leading to reduced reliance on the power grid and consequent reduction in CO₂ emissions.

This paper addresses the workload balancing problem in identical parallel machines context. The problem consists of assigning n different jobs to m identical parallel machines in order to minimize the workload imbalance among the different machines. This problem is formulated as a linear mixed integer program to minimize the difference between the greatest and smallest workload assigned to each machine. Based on some numerical examples reported in the literature, we establish that the classical formulation which consists of minimizing the greatest machine completion time does not provide the optimal workload repartition. That is why we consider a new mathematical formulation based on the minimization of the difference between the workload of the bottleneck machine and the workload of the fastest machine. The proposed programming method is also used to provide optimal solutions in reasonable computational times for different test problems presented in the literature by Raghavendra and Murthy 10 to test their genetic algorithm.