  This paper addresses the single-item single-stocking location non-stationary
stochastic lot-sizing problem under a reorder point -- order quantity control
strategy. The reorder points and order quantities are chosen at the beginning
of the planning horizon. The reorder points are allowed to vary with time and
we consider order quantities either to be a series of time-dependent constants
or a fixed value; this leads to two variants of the policy: the (st,Qt) and the
(st,Q) policies, respectively. For both policies, we present stochastic dynamic
programs (SDP) to determine optimal policy parameters and introduce mixed
integer non-linear programming (MINLP) heuristics that leverage
piecewise-linear approximations of the cost function. Numerical experiments
demonstrate that our solution method efficiently computes near-optimal
parameters for a broad class of problem instances.
