Stochastic lot sizing problems under monopoly

In this thesis, we study stochastic lot sizing problems under monopoly. We consider production planning of a single item using uncapacitated resources over a multi-period time horizon. The demand uncertainty is modeled via a scenario tree structure. Each node of the tree corresponds to a scenario of demand realization with an associated probability. We first consider the stochastic lot sizing problem under monopoly (SLS), which addresses the period based production plan of a manufacturer with uncertain demands and a monopolistic supplier. We propose an exact dynamic programming algorithm to solve the SLS problem in polynomial time. The second problem we consider, the stochastic lot sizing problem with extra ordering (SLSE), is based on two-stage stochastic programming. In addition to the period based production decision variables of the SLS model, there exist scenario based extra ordering decision variables in the problem setting of SLSE. We develop two families of valid inequalities for the feasible region of the introduced SLSE model. The required separation algorithms of both valid inequalities are presented along with their implementations with branch-and-cut algorithm in solving SLSE. An extensive computational analysis with branch-and-cut algorithms shows the effectiveness of these inequalities.