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. The online appendix is available at https://doi.org/10.1287/ijoc.2017.0792 .

We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to standard problems encountered in statistics and to a novel inspection scheduling problem in which the aim is to find inspection plans with desirable statistical properties.

In this paper, we address the general multiperiod production/inventory problem with nonstationary stochastic demand and supplier lead time under service-level constraints. A replenishment cycle policy is modeled. We propose two hybrid algorithms that blend constraint programming and local search for computing near-optimal policy parameters. Both algorithms rely on a coordinate descent local search strategy; what differs is the way this strategy interacts with the constraint programming solver. These two heuristics are first, compared for small instances against an existing optimal solution method. Second, they are tested and compared with each other in terms of solution quality and run time on a set of larger instances that are intractable for the exact approach. Our numerical experiments show the effectiveness of our methods.