Risk-Based Perspectives and Methodologies for Managing Disproportionate Demand and Supply

In this dissertation, we focus on risks directly related to retailers facing disproportionate demand and supply due to demand uncertainty under social initiatives. In terms of risk-based methodologies, our interest is in stochastic approaches subject to complete or incomplete information which includes conditional value-at-risk (CVaR) and robust optimization, respectively. Through both avenues, we look to examine new problems of practical relevance in the retail industry. One immediate consequence of disproportionate demand and supply is a stockout. Despite a large body of literature on the foundational newsvendor (NV) framework (which is also essential for the purposes of this dissertation), no previous work examines the impact of risk-based decision-making under alternative stockout policies (SOPs). Hence, to set the stage for a comprehensive investigation of risk-based perspectives and methodologies, we first revisit the traditional NV setting and explicitly incorporate contrasting approaches for handling excess demand. In doing so, we consider both risk-neutral (expected profit maximization) and risk-averse (CVaR minimization) preferences of the retailer and aim to produce a complete comparative analysis characterizing the optimal SOP. Next, we extend the problem setting of interest to consider a popular representation of Corporate Social Responsibility (CSR). The specific initiative of interest is called buy-one-give-one (BOGO), under which the impact of disproportional demand and supply must be managed with care for corporate credibility. As BOGO resembles the social initiative of focus throughout this dissertation, we formulate several problems through the lens of the retailer, all of which are new to the literature. We implement demand uncertainty in the context of retailers offering BOGO initiatives while subject to alternative assumptions regarding knowledge of the demand distribution. We extend the risk-based scheme by employing the CVaR criterion while also emphasizing the complete information assumption tied to such modeling approaches. This recognition leads to our final portion of work involving incomplete information and demand uncertainty. The ensuing work involves distributionally robust optimization (DRO) and enables us to study various structural properties of the corresponding optimal policy and offer multiple operational insights on how BOGO initiatives can affect firms’ sourcing policies. We expand on the vast collection of optimization literature that incorporates risk-neutrality and/or risk-aversion within the traditional NV setting. We also make a general distinction between the NV settings which do and do not allow recourse production. In turn, this distinction aligns precisely with two common practices for handling stockout scenarios. We develop methodology to compute the optimal order quantities and discover the optimal SOP for both risk-neutral (RN) and risk-averse (RA) attitudes and counterpart modeling approaches. Additionally, we highlight the prevalence of CSR as well as the growing list of firms offering BOGO initiatives. Although a number of firms employ BOGO initiatives, we identify a significant gap in the inventory management literature and become the first to explicitly address related problems from a risk-averse or distribution-free standpoint. Our contributions are of practical value as SOPs are applicable to any retail setting, risk attitudes are more aligned to risk-averse preferences, and limited demand information is typically more realistic than complete demand distribution knowledge. Overall, a compelling case is made in terms of the convenience, realizable social benefit, and expected profit performance of the optimal inventory policies delineated throughout this work.