Multistage stochastic capacitated discrete lot-sizing with lead times: problem definition, complexity analysis and tighter formulations

Abstract

A stochastic capacitated discrete procurement problem with lead times, cancellation and postponement is addressed. The problem determines the expected cost minimization of satisfying the uncertain demand of a product during a discrete time planning horizon. The supply of the product is made through the purchase of optional distinguishable orders of fixed size with lead time. Due to the uncertainty of demand, corrective actions, such as order cancellation and postponement, may be taken with associated costs and time limits. The problem is modeled as an extension of a capacitated discrete lot-sizing problem with uncertain demand and lead times through a multistage stochastic mixed-integer programming approach. To improve the resolution of the model by tightening its formulation, valid inequalities are generated based on conventional inequalities. Subsets of approximately non dominated valid inequalities are determined heuristically. A procedure to tighten an upgraded formulation based on a known scheme of pairing of inequalities is proposed. Computational experiments are performed for several instances with different uncertainty information structure. The experimental results allow to conclude that the inclusion of subsets of the generated valid inequalities enable a more efficient resolution of the model.