A lot sizing problem in deliberated and controlled co-production systems

Abstract

Deliberated and controlled co-production can be defined as the production of different products simultaneously where production parameters are known and co production is deliberate. We study an extension of the lot sizing problem in a deliber ated and controlled co-production system, and show that it is NP-Hard. We investigate special cases of the problem for which it is polynomially solvable, and propose solution techniques for those special cases. We propose four mixed integer programming model formulations based on single item uncapacitated lot sizing and simple plant location formulations. We show that solution spaces of the linear relaxations of the proposed formulations are equal. We propose valid inequalities for the problem and show that our proposed valid inequalities added to the model with a separation algorithm improve the linear relaxation lower bound by more than %20 for all test instances. We propose a pattern fitting heuristic that aims to find initial feasible solutions for a commercial solver. We propose another heuristic based on Wagner-Whitin’s algorithm to create integer feasible solutions from fractional solutions. We show that the average optimal ity gap is reduced by at least %10 with proposed improvements to MIP formulations. We also show that the quality of integer feasible solutions is increased within a given time limit.