Planning annualised hours with a finite set of weekly working hours and cross-trained workers

Annualising working hours (i.e., the possibility of irregularly distributing the total number of working hours over a year) permits companies to adapt capacity to fluctuations in demand, thus reducing overtime, temporary workers and inventory costs. Since annual hours can lead to a worsening of the staff's working conditions, many laws and collective bargaining agreements contain constraints that affect the distribution of working time. This paper proposes an MILP model to solve an annualised working hours planning problem in which workers are considered to be cross-trained, and in which the number of weekly working hours must belong to a previously agreed finite set. A computational experiment demonstrates the effectiveness of the model.