In this paper we apply emerging theories in probability and statistics to examine the value of pooling of inventories under arbitrary non-normal dependent demand structures. Eppen (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands; using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between the components of a random vector. For broad classes of distributions with arbitrary marginals, we confirm that pooling of inventories is more valuable when demands are less positively dependent.

Several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be accomplished through the reduction of the number of products or stock-keeping units (SKUs), through postponement of differentiation, or in other ways. These approaches are well known and becoming widely applied in practice. However, theoretical analyses of the pooling effect assume an optimal inventory policy before pooling and after pooling, and, in most cases, that demand is normally distributed. In this article, we address the effect of nonoptimal inventory policies and the effect of nonnormally distributed demand on the value of pooling. First, we show that there is always a range of current inventory levels within which pooling is better and beyond which optimizing inventory policy is better. We also find that the value of pooling may be negative when the inventory policy in use is suboptimal. Second, we use extensive Monte Carlo simulation to examine the value of pooling for nonnormal demand distributions. We find that the value of pooling varies relatively little across the distributions we used, but that it varies considerably with the concentration of uncertainty. We also find that the ranges within which pooling is preferred over optimizing inventory policy generally are quite wide but vary considerably across distributions. Together, this indicates that the value of pooling under an optimal inventory policy is robust across distributions, but that its sensitivity to suboptimal policies is not. Third, we use a set of real (and highly erratic) demand data to analyze the benefits of pooling under optimal and suboptimal policies and nonnormal demand with a high number of SKUs. With our specific but highly nonnormal demand data, we find that pooling is beneficial and robust to suboptimal policies. Altogether, this study provides deeper theoretical, numerical, and empirical understanding of the value of pooling.

Decision-makers have access to better environmental information through tools like life-cycle assessment (LCA). However, these methods often implicitly assume that decision-makers make rational assessments when weighing environmental criteria. The impacts of behavioral biases and context effects on decisions remain less recognized, despite being well-documented in behavioral science. Current sustainability approaches offer little guidance in finding optimal solutions when decision-makers' preferences are unknown. Unlike traditional trade-offs involving economic factors, sustainability trade-offs involve intangible and emotionally charged dimensions. Firms aiming for sustainability lack clear guidelines for trading-off environmental and social impacts. This dissertation seeks to assist decision-makers in the context of sustainability from behavioral and optimization-based perspectives.We first conduct an experiment to test whether decision makers are subjected to two context effects, namely attraction and compromise effects, when faced with environmental trade-offs. Our results show that these context effects are prevalent and substantial in both environmental and non-environmental settings, which highlights the need to integrate behavioral science into environmental decision-making. We introduce an interactive optimization method that aims to help decision makers with difficult trade-offs when their value function is not known. This method involves asking decision makers pairwise comparison questions to identify the optimal solution. The approach minimizes the cognitive burden on decision makers by asking fewer, easier questions while still guaranteeing an optimal solution. We test the method in the context of sustainable sourcing in the apparel industry, demonstrating its effectiveness in converging to optimal solutions with fewer decision-making steps compared to traditional methods. Initial feedback from industry practitioners is promising. An interactive approach like this is uncommon in decision-making in sustainable operations. A more conventional approach would be to elicit the decision-maker's weights and then use a traditional optimization method using those weights. To test which method decision-makers prefer, we also develop an experimental framework, using oTree, to compare the performance of the proposed interactive optimization method with a more traditional approach, eliciting weights through direct rating and then optimizing. Although the experimental framework is initially designed specifically to assess our interactive algorithm, the framework highlights more generally how experiments can be designed that combine Gurobi-based optimization within the experimental environment provided by oTree.

In this thesis, we empirically examine different strategies that firms pursue to develop sustainable and safe operations. In the first chapter, we evaluate the profitability of carbon abatement projects that firms implement over time. We find that the average payback period and marginal abatement cost of carbon abatement opportunities do not deteriorate quickly, if at all. Firms that focus more on opportunities that are directly related to their core operations (e.g., optimizing production processes) experience more favorable payback trends compared to those that focus on opportunities that are not directly related to their core operations (e.g., lighting fixtures or building insulation). In the second chapter, we measure the impact of conducting Probabilistic Risk Assessments on safety performance at nuclear plants. We find that the adoption of risk assessments is associated with a 15% decrease in the frequency of safety-related events. We show that this is associated with a 1.6 billion USD increase in annual revenue from avoided lost production. In the third chapter, we examine the impact of automating bill payments on electricity conservation behavior. Many utility companies want to increase the convenience of paying the bill, but we find that there are unintended implications on energy conservation in doing so. We find that enrollment in automatic billing is associated with a 5% increase in energy use. This suggests that the way we pay our bills may influence the salience of electricity costs. We find evidence that providing real-time feedback may counteract this effect.