“…Inequalities in Equations ( 10) and ( 11) are analogous to the constraints in Equations ( 8) and ( 9), but in this case are applied to the last product produced in the week. To assure the existence of a last product v to be produced on the line l in week s, there must be a production of said product v. Furthermore, Equation (9) guarantees that the existing last product is unique. The constraint in Equation ( 12) forces the variable w s v,l to take the value 1 only if the production of product v is split on two weeks, i.e., product v is the last product of week s and the first of the week s + 1 for the production line l. The inequality in Equation ( 13) controls the cleaning variable c s l , which indicates whether a cleaning is saved on production line l for week s. The sum of variables c s l appears in the objective function with a negative sign, therefore, the optimization model presses for this quantity to have the maximum possible value.…”