Mixed integer linear programming formulation for flexibility instruments in capacity planning problems

• We study a capacity planning problem with flexibility instruments and a case study.
• We present a MILP formulation and conduct an extensive numerical study.
• Significant cost benefits of combining the flexibility instruments are found.
• We show the applicability of the model by solving it with (non-) commercial solvers.

We present a mixed integer linear programming (MILP) approach for an aggregate production planning (APP) problem of an electronics manufacturer. A multi-item, multi-facility, multi-stage capacity planning problem over a finite planning horizon with deterministic demand is considered. We include the flexibility instruments shift planning, overtime account, and flexible maintenance. We present an extensive computational study where the proposed model is applied in a real-world case study and for randomly generated instances. Using a full factorial experimental design we evaluate the cost saving potentials of the flexibility instruments and their combinations. The computational efficiency of the proposed model formulation is investigated by different MILP solvers.