Asymptotics and Sustainability in Operations Management

Organizations today operate in increasingly complex, uncertain, and competitive environments. Operations management equips them with analytical tools to guide informed and effective operational decisions. For example, retailers must effectively manage lost sales to maintain competitiveness. Producers should dynamically select supply modes, and logistics companies must incorporate new features into transportation models to ensure resilience, cost efficiency, and sustainability. Advanced critical systems must remain operational at low maintenance cost by utilizing abundant real-time sensor data. Although these problems arise in different contexts, they can be expressed as mathematical models that reveal their underlying similarities. These mathematical models, however, can become highly complex in representing real-world problems, which makes the identification of optimal decisions difficult. For instance, calculating the optimal ordering decision for a product is straightforward under the assumption that customers wait during a stockout, but dropping this assumption generally transforms the problem into a far greater challenge. Some simplifying assumptions, previously regarded as insignificant, can now pose major risks to organizations. This situation requires research to develop effective and practical solutions for more complex and realistic settings. Economic efficiency, reliability, and sustainability are among the core performance metrics that define excellence in operations. While the first two metrics have long been considered in nearly all operational decisions, sustainability only became an important dimension in the 21st century. Early research in the 1980s, such as Hansen (Hansen and Lebedeff, 1987), provided evidence that CO₂ emissions lead to a rise in global temperatures and emphasized their environmental consequences. Across operational domains, transportation and industry each represent about 22% of the European Union’s CO₂ emissions (European Environment Agency, 2021). Sustainability in operations also includes resource efficiency, which covers the reduction of energy, water, and material consumption in production and logistics processes. Improved resource efficiency reduces waste, lowers operational costs, supports environmental objectives, and strengthens approaches that extend asset life. These observations highlight the critical need to incorporate sustainability into decision-making processes. However, sustainability goals introduce additional costs that organizations must take into account in their operational decisions. Balancing these costs against efficiency, reliability, and other performance objectives requires careful consideration of their trade-offs. Optimization models provide a natural framework to evaluate such trade-offs and help decision makers identify solutions that achieve environmental targets while preserving operational and economic performance. Operational systems are inherently subject to uncertainty in some decision parameters such as demand, supply, and equipment status. Stochastic models capture these uncertainties and allow researchers to model variability and evaluate the performance of different decisions under more realistic conditions. Many stochastic models become highly complex as a key problem parameter grows, which makes exact solution methods infeasible. Asymptotic analysis provides a powerful approach to address this challenge by characterizing the behavior of the system under limiting regimes, such as the high cost of losing a sale in inventory models, the high payload in routing models, and the long lifetime of components in maintenance models. This method allows for the derivation of asymptotically optimal policies that maintain strong performance in non-asymptotic settings, without the computational expense of solving a high-dimensional stochastic model. This thesis addresses two topics: integrating sustainability into certain operations management problems and developing tractable policies through asymptotic analysis of high-dimensional stochastic systems.