On a CP approach to solve a MINLP inventory model

One of the most important policies adopted in inventory control is the replenishment cycle pol­ icy. Such a policy provides an effective means of dampening planning instability and coping with demand uncertainty. We describe a constraint programming approach for computing optimal re­ plenishment cycle policy parameters under non­stationary stochastic demand, ordering, holding and shortage costs. Our solution approach exploits the convexity of the cost­function to dynamically compute during search the cost associated with a given decision variable assignment. By using our model we gauge the quality of an existing approximate mixed integer linear programming approach that exploits a piecewise linear approximation for the complex cost function. Furthermore, our computational experience shows that our approach can solve realistic instances in a fraction of a second.