A multistage stochastic lot-sizing problem with cancellation and postponement under uncertain demands

¹ Depto. de Investigación Operativa, Instituto de Computación, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, 11.300 Montevideo, Uruguay
² Depto. de Industrias, Campus Santiago Vitacura, Universidad Técnica Federico Santa María, Avda. Santa María 6400, Vitacura, Santiago, Chile

^* Corresponding author: ctesturi@fing.edu.uy

Received: 7 December 2020
Accepted: 11 March 2021

Abstract

A multistage stochastic capacitated discrete procurement problem with lead times, cancellation and postponement is addressed. The problem determines the procurement of a product under uncertain demand at minimal expected cost during a time horizon. The supply of the product is made through the purchase of optional distinguishable orders of fixed size with delivery time. Due to the unveiling of uncertainty over time it is possible to make cancellation and postponement corrective decisions on order procurement. These decisions involve costs and times of implementation. A model of the problem is formulated as an extension of a discrete capacitated lot-sizing problem under uncertain demand and lead times through a multi-stage stochastic mixed-integer linear optimization approach. Valid inequalities are generated, based on a conventional inequalities approach, to tighten the model formulation. Experiments are performed for several problem instances with different uncertainty information structure. Their results allow to conclude that the incorporation of a subset of the generated inequalities favor the model solution.