Essays on robust optimization, integrated inventory and pricing, and reference price effect

This dissertation consists of two distinct lines of research e orts. Chapter 2 proposes a general methodology to seek robust solution to multi-stage stochastic optimization problems. Chapters 3, 4 and 5 all deal with models that arise from inventory management and dynamic pricing. Chapter 2 introduces the Extended Affinely Adjustable Robust Counterpart(EAARC). We first propose the general steps of extending affine decision rules via re-parameterizing the uncertainty set, then propose the example of splitting-based EAARC. We show that this approach extends the versatility of affine decision rules beyond what has been proposed by Ben-Tal et al. while retaining tractability. Chapter 3 looks at the classical joint inventory-and-pricing model (single product periodic-review) with concave ordering cost. Concave cost structures may often occur in settings with multiple sources of supply. For this model, assuming additive demand uncertainty, we show that a generalized (s; S; p) policy is optimal under certain conditions imposed on the distribution of the random perturbation. Chapter 4 and 5 focus on the reference price effect in which the price impact on demand is no longer instantaneous, but history-dependent. Chapter 4 analyzes a joint inventory-and-pricing model with reference price e ffect. We prove that a reference price dependent base-stock policy is optimal even though the single period expected pro t may not be concave. In the in finite horizon case, we further show that in the optimal trajectory, reference price converges to a steady state and provide a characterization. Chapter 5 represents some initial e orts in modeling heterogeneity in the consumer group, in which we study a continuous-time dynamic pricing problem under stochastic reference price e ffect. Stochastic optimal control theory is applied to the problem to derive an explicit solution. Various comparative statics are then conducted to benchmark our model against a few simpli ed models.