Robust stock assortment and cutting under defects in automotive glass production

Abstract

We address an assortment-and-cutting problem arising in the glass industry. The objective is to provide minimum waste solutions that are robust against such raw material imperfections as those possibly occurring with float glass production technology. The stochastic realization of defects is modeled as a spatial Poisson point process. A mixed integer program in the classical vein of robust optimization is presented and tested on data taken from a real plant application. Defective final products must in any case be discarded as waste but, if a recourse strategy is adopted, faults in glass sheets can sometimes be recovered. Closed forms for the computation of faulty item probabilities are provided in simple cases, and obtained via Monte Carlo simulation in more complex ones. The computational results demonstrate the benefits of the robust approach in terms of the reduction of back-orders and overproduction, thereby showing that recourse strategies can enable nonnegligible improvements. Encouraged by this result, the management is presently evaluating the possibility of adopting the proposed model in plant operation.