Otimização do planejamento e programação da produção na indústria de polpa moldada
Pérez Martínez, Karim Yaneth
We study an integrated process configuration, lot-sizing and scheduling problem, which appears in the context of a real production environment in the molded pulp packaging industry. Products are produced by alternative process configurations, which are defined by a combination of molds and a set of products to be produced. The production quantities, setup operations and capacity consumption depend on which process configurations are used, how long they are used for, and in which sequence they are scheduled. The total number of process configurations may be too large and difficult to define beforehand in some production environments, since a set of operational and technological constraints must be satisfied. For the particular case studied here, processes configuration decisions are generated at the same time as lot-sizing and sequencing decisions, which involve sequence-dependent setup costs and times. This research had the important collaboration of a typical molded pulp packaging company located in the São Paulo state, where real data were collected to validate the approaches proposed here. Two mathematical formulations are proposed to represent and optimize the problem, which are different in the way how process configuration decisions are represented. The first formulation is a linear formulation which uses some structures defined in advance to generate feasible process configuration; and the second one is a non-linear formulation which models the technical constraints of the problem to generate the process configurations to be implemented. Some valid inequalities and symmetry-breaking constraints are proposed to strengthen the formulations and improve the performance of the solution methods. The proposed mathematical approaches are solved using a standard mixed integer programming (MIP) solver, specifically the solver CPLEX. A branch-and-cut (B&C) algorithm, which takes into account the particularities of the formulations and implements logic-based Benders cuts in a branch-and-bound framework, and a MIP-based heuiristic are also proposed to solve the problem. Results show that in general, the formulations proposed here represent properly the integrated problem. Computational experiments shows that, although it is is challenging to solve to optimality all the problem instances presented here, the B&C algorithm outperforms the models’ resolution by CPLEX for all of the instances tested. Results also show that the valid inequalities and symmetry-breaking constraints proposed clearly improve the lower bounds of the formulations and the performance of the solution methods, particularly for the B&C algorithm. The heuristic proposed method also seems to be competitive for the problem instances tested, as it found optimal solutions for small instances, better solutions and similar solutions, in the worst case, compared to the ones provided by the exact approaches for large instances and involving much less computing times.