Applications of Stochastic Inventory Control in Market - Making and Robust Supply Chains

This dissertation extends the classical inventory control model to address stochastic inventory control problems raised in market-making and robust supply chains. In the financial market, market-makers assume the role of a counterpart so tbat investors can trade any fixed amounts of assets at quoted bid or ask prices at any time. Market-makers )ellefit from the spread between the bid and ask prices. but they have to carry inventories of assets which expose them to potential losses when the market price moves in an undesirable direction. One approach to reduce the risk associated with price uncertainty is to actively trade with other mlarket-imakers at the price of losing potential spread gain. WVe propose a dynamic programming model to determine the optimal active trading quantity., which mnaximnizes the imarket-imiaker's expected utility. For a single-asset model. we show that a threshold inventory control policy is optimal with respect to both an exponential utility criterion and a mean-variance tradeoff objective. Special properties such as synmetry and monotonicity of the threshold levels are also investigated. For a miultiple-asset model. the imean-variance analysis suggests that there exists a connected no-trade region such that the imarket-illaker does not need to actively trade with other market-makers if the inventory falls in the no-trade region. Outside the no-trade region. the optinal way to adjust inventory levels can be obtained from the boundaries of the no-trade region. These properties of the optimal policy lead to practically efficient algorithms to solve the problem. The dissertation also considers the stochastic inventory control model in robust supply chain systems. Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control policy using the estimated (listributions. which often leads to fragile solutions in case the preselected fainily of distributions was inadequate. In this work. we propose a inillimax robust model that inltegrates data fitting and inventory optimization for the single iteim multi-period periodic review stochastic lot-sizing problem. Unlike the classical stochastic inventory models, where demand distribution is known, we assume that histograms are part of the input. The robust model generalizes Bayesian model, and it can be interpreted as ininunizing history dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular., we analyze the robust rnodels based on the chi-square goodness-of-fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under general conditions. Thesis Supervisor: David Simchi-Levi Title: Professor of Civil and Environmental Engineering