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.

This paper aims to study a real case of an optimization problem derived from a hospital supply chain. The present work focuses on developing operational decision support models and algorithms for production process scheduling in hospital catering. The addressed production system is considered as a flexible job shop system. The objective is to minimize the total flow time. A novel mathematical model and two metaheuristics for the production scheduling of multi-product and multi-stage food processes are developed. These methods have proven their effectiveness for the scheduling of operations of the food production processes and allowed significant improvements in the performance of the studied production system.

This study addresses a new single-item lot-sizing problem for flow-shop configurations by integrating the capacity contract selection problem with multiple energy sources. To the best of our knowledge, this problem has never been tackled before. We introduce a mathematical model which defines optimum production plan and energy contract option regarding the objectives and constraints of the production system and energy supplier contract conditions. Since the problem is NP-Hard, a Fix-and-Relax heuristic is introduced to solve the problem. Two different relaxation procedures are applied and the performance of the solution approach is tested on randomly generated instances. It is seen that the obtained results are quite promising. The applied heuristic approach produces solutions with the optimality gap $0.2\mathrm{\%}$ in average for the small problem sizes such as (N5_T5,N5_T7). For the larger instances, it allows to reach better results than the results obtained by commercial solvers within a shorter time.

This research focuses on an Order Acceptance Scheduling (OAS) problem on a single machine under time-of-use (TOU) tariffs and taxed carbon emissions periods with the objective to maximize total profit minus tardiness penalties and environmental costs. Due to the NP-hardness of the considered problem especially in presence of sequence-dependent setup-times, two fix-and-relax (FR) heuristics based on different time-indexed (TI) formulations are proposed. A metaheuristic based on the Dynamic Island Model (DIM) framework is also employed to tackle this optimization problem. These approached methods show promising results both in terms of solution quality and solving time compared to state-of-the-art exact solving approaches.