Flow Shop Scheduling (FSS) problem constitutes a major part of production planning in every manufacturing organization. It aims at determining the optimal sequence of processing jobs on available machines within a given customer order. In this research, a novel bi-objective Mixed-Integer Linear Programming (MILP) model is proposed for FSS with an outsourcing option and Just-in-Time (JIT) delivery in order to simultaneously minimize total cost of the production system and total energy consumption. Each job is considered to be either scheduled in-house or to be outsourced to one of the possible subcontractors. To efficiently solve the problem, a hybrid technique is proposed based on an interactive fuzzy solution technique and a Self-Adaptive Artificial Fish Swarm Algorithm (SAAFSA). The proposed model is treated as a single objective MILP using a Multi-Objective Fuzzy Mathematical Programming (MOFMP) technique based on the e-constraint, and SAAFSA is then applied to provide Pareto optimal solutions. The obtained results demonstrate the usefulness of the suggested methodology and high efficiency of the algorithm in comparison with CPLEX solver in different problem instances. Finally, a sensitivity analysis is implemented on the main parameters to study the behavior of the objectives according to the real-world conditions.

In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors.