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

This dissertation consists of two distinct lines of research efforts. 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. [9], 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 effect. We prove that a reference price dependent base-stock policy is optimal even though the single period expected profit may not be concave. In the infinite horizon case, we further show that in the optimal trajectory, reference price converges to a steady state and provide a characterization. Finally, chapter 5 studies a continuous-time dynamic pricing problem under stochastic reference price effect. 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 simplified models.