Inventory Management with Order Errors, Optimal Investment to Reduce Emissions, and Generalized Cluster-wise Linear Regression

The first part of the thesis combines empirical and analytical methods to study the influence of purchase order (PO) fulfillment errors on a retailer's inventory order policy and cost. PO errors can be corrected through rework at the retailer's distribution center. Using data from a large retail chain, we determine key properties of these errors, in particular, how they vary with order complexity, including average order quantity per stock keeping unit (SKU) and number of items per PO. We propose one deterministic and one stochastic (Q, R) inventory model for POs with a single SKU that account for these correctable errors. We study the deterministic model analytically, and the stochastic model numerically, with parameters estimated from real retail data. We compare the performance of our adjusted order policy with standard policies that ignore correctable PO errors, and provide qualitative guidance in identifying SKUs more prone to these errors. The second part of the thesis studies joint production capacity and investment decisions under command-and-control and market-based carbon regulations (including carbon tax and cap-and-trade) for an emissions intensive firm with stochastic demand. We analytically compare the firm's performance along four dimensions, including profit, total emissions, investment amount, and investment timing. We find that a firm can perform better under either command-and-control and cap-and-trade along any of these four dimensions, depending on the firm's investment cost and emissions regulation parameters. The third part of the thesis proposes several algorithms for solving the generalized cluster-wise linear regression problem, including an exact mathematical programming based approach relying on column generation, a column generation based heuristic algorithm that clusters groups of entities, a metaheuristic genetic algorithm with adapted K-Means, and a two-stage approach that performs clustering first and regression second. We examine the performance of our algorithms on a SKU clustering problem faced by a large supermarket chain. We find that our GA-KMeans algorithm performs the best, and is able to generate clusters of SKUs with distinctive seasonal patterns effectively and efficiently.