An extended mixed-integer programming formulation and dynamic cut generation approach for the stochastic lot-sizing problem

We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function-as is the case in earlier formulations-it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach.