The combination of a NEH heuristic and an LP metric to solve a flow-shop scheduling problem taking into account energy consumption and production costs: a case study

In this work, we study a multi-objective problem in a pharmaceutical production unit composed of several production stations that produce several kinds of products. The goal of this work, in a first step, is to propose a scheduling at the production unit in order to establish a synchronization of the different tasks on the m-machines. The problem can be formulated by the scheduling of a multi-product flow-shop.Then, we take into account the energy constraints of each task to be done. The problem can be formulated by a linear multi-objective MILP program, where the first objective is to determine the best sequence that minimizes the production and launch costs. In addition, the second objective is to find the best sequence that minimizes energy consumption. The problem is formulated and solved by combining the NEH heuristic and the LP-metric method to determine an intermediate solution between minimizing production costs and minimizing energy consumption