S Thomas McCormick
Relevant Degree Programs
Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - April 2022)
Chapter 1 is an introductory chapter for this thesis work. It sets the sceneby describing the motivation and industrial setting for each project.In Chapter 2, "Optimal Inventory Replenishment with Two DeliverySizes", we consider a periodic review inventory system where a retailer canorder in multiples of a fixed quantity Q₁, or multiples of Q₂ = 2Q₁, where theper unit material cost is less for ordering Q₂. We extend results of Veinott,and of Fangruo Chen, to show that an optimal replenishment policy has areorder point R, as well as a second parameter controlling when the lastorder should be for Q₁ instead of Q₂ under a linear cost structure.In Chapter 3, "Sequence Optimization in Block Cave Mining" we investigatethe use of integer programming models to aid the practitioner inthe early planning stages of a Block Cave Mine. Given the footprint of theore body divided into draw points or grid squares, sequence optimizationdetermines which draw points to open in which period to meet the physicalconstraints of the mining process and maximize the total net present valueof the mine. Traditionally done by trial and error by experts in the field, thisis a first attempt to use modelling techniques to automate and optimize theprocess. We develop three integer programming models and discuss the challengesof formulating the problem in this framework. Two additional modelsare developed for comparison, one using the Column Generation techniqueand one using a greedy or myopic algorithm. All models are run on two datasets provided by our industrial partner, and the performance and results arecompared. This work demonstrates that integer programming models cangenerate opening sequences but, like many "real life" problems, this one iscomplicated.
This dissertation studies three topics in supply chain management. Consider a decentralized supply chain, where a manufacturer distributes products through competing retailers. Incentive conflicts among players often occur in such supply chains since the players have different objectives. This research seeks to help the manufacturer understand downstream retailers' incentives and provide managerial guidelines such as coordinating mechanisms and optimal strategies under existing contractual agreements.The first essay considers a manufacturer who distributes a product line (consisting of different product variants) through competing retailers. Due to the substitution between different product variants, as well as between different retailers, the incentive problems associated with distributing a product line are more complicated than that of distributing a single product. We characterize retailers' incentive distortions, and construct contracts that achieve channel coordination. Using numerical simulations, we study how the retailers' incentives and contracts are affected by underlying model parameters.The second essay investigates firms' incentives for transshipment in a decentralized supply chain. Transshipment price and the control of transshipment parameters are key factors that affect the manufacturer's and retailers' incentives for transshipment. We identify conditions under which the manufacturer and retailers are better off and worse off under transshipment. We also compare the decentralized retailer supply chain with one where the retailers are under joint ownership (a "chain store"). We obtain two surprising results. First, the manufacturer may prefer dealing with the chain store rather than with decentralized retailers. Second, chain store retailers may earn lower profits than decentralized retailers.The third essay examines the impact of a gray market on the firms in a decentralized supply chain. Under certain conditions, a gray market's positive effect, i.e., the demand generating effect, dominates the negative effect, i.e., the demand loss in authorized channels, and increases the manufacturer's profit. However, the manufacturer also can be hurt by a gray market. In some cases, the manufacturer can use the linear wholesale price to deter retailers from transshipping to a gray market. However, the deterrence may not always be successful, and the manufacturer needs to employ other approaches such as penalty terms to terminate a gray market.
Master's Student Supervision (2010 - 2021)
One of the main results of "Order-Based Cost Optimization in Assemble-to-Order Systems"  by Y. Lu and J-S. Song, Operations Research, 53, 151-169 (2005) is Proposition 1 (c), which states that the cost function of an assemble-to-order inventory system satisfies a discrete convexity property called L♮-convexity. Based on this result, Lu and Song proposed two types of L♮-convex minimization algorithms for finding the optimum policy. We construct a simple assemble-to-order system for which the cost function fails to satisfy L♮-convexity. Using a similar system, we further show that the cost function may not enjoy a more general notion of discrete convexity property called D-convexity. Yet, because of some other properties of the cost function, one can still solve the cost optimization problem using other methods from the literature.