A meta-heuristic based approach for solving the single-item lot-sizing problem with a flow shop with energy and environmental constraints

In our work, we proposed at first an extension of a mathematical model of the capacitated single-item lot-sizing problem with a flow shop configuration and multiple energy suppliers, renewable and non-renewable ones. We used an eco-friendly constraint to push the manufacturer toward getting its electricity from renewable energy suppliers. Even if it's not cost-effective to do so, renewable energy has a much lower carbon footprint. The obtained model was implemented in solver software and simulated annealing meta-heuristic algorithm to compare the two solution approaches. For small-sized instances both approaches proved to be effective in terms of solution quality and compilation time, meanwhile, for large-sized instances, the solver couldn't find the optimal solution within a one-hour compilation time. For the meta-heuristic, it gave satisfactory results, especially in terms of the time needed for compilation.