  This paper introduces an integrated lot sizing and scheduling problem
inspired from a real-world application in off-the-road tire industry. This
problem considers the assignment of different items on parallel machines with
complex eligibility constraints within a finite planning horizon. It also
considers a large panel of specific constraints such as: backordering, a
limited number of setups, upstream resources saturation and customers
prioritization. A novel mixed integer formulation is proposed with the
objective of optimizing different normalized criteria related to the inventory
and service level performance. Based on this mathematical formulation, a
problem-based matheuristic method that solves the lot sizing and assignment
problems separately is proposed to solve the industrial case. A computational
study and sensitivity analysis are carried out based on real-world data with up
to 170 products, 70 unrelated parallel machines and 42 periods. The obtained
results show the effectiveness of the proposed approach on improving the
company's solution. Indeed, the two most important KPIs for the management have
been optimized of respectively 32% for the backorders and 13% for the
overstock. Moreover, the computational time have been reduced significantly.
