A Stochastic Control Theory Perspective On Supply Chain Management Under Uncertainty

A supply chain is rife with many uncertainties, such as volatile demand, unknown lead time and inaccurate inventory data. Theses information uncertainties may lead to incorrect supply chain decisions, thus hinder the effective material flow. In recent decades, advances in information technology (IT) and expanding IT infrastructure introduce new possibilities to improve supply chain decisions under uncertainty. However, there is a lack of firm understanding of the value of information (the opposite of uncertainty) in supply chain management (SCM). In this thesis, we consider a supply chain as a linear time invariant dynamic system whose inputs and outputs are stochastic processes. We propose a unified stochastic control theory framework for supply chain decision-making in uncertain and dynamic business environment. In this framework, we systematically design SCM strategies, such as demand forecasting, replenishment rules and optimal estimators. Given these strategies, we analytically investigate the stochastic properties of the supply chain. This thesis may help readers understand uncertainty and the value of information in SCM. The main contents of this thesis are as follows:1) Chapter 2 addresses demand uncertainty and its propagation in supply chains. The supply chain is considered as a linear time invariant (LTI) system driven by stochastic customer demand. Under general ARMA demand patterns and arbitrary fixed lead times, a unified and structured framework based on the classical minimum variance control theory is proposed for decentralized supply chain management Optimal forecasting, the traditional Order-up-to policy and the generalized Order-up-to policy are directly derived according to the minimum variance criterion. Given these strategies, stochastic properties of the supply chain are studied using LTI system theory in both the time and the frequency domain. Findings from previous literatures are re-interpreted from a control-theory-oriented perspective and new characteristics of the generalized Order-up-to policy are deduced and analyzed. On the basis of the statistical analysis, an optimization model is constructed to minimize the variable operation costs which are related to the parameters of the SCM strategies.2) Chapter 3 addresses lead time uncertainty in supply chains. The supply chain includes a markovian lead time model of the supply system. Since the lead time varies with time, the dynamic characteristic of the supply chain is different from that used in demand uncertainty research. We analyze these new characteristics and continue to adopt the minimum variance control methodology for SCM design and analysis. We derive the exact formulas of the Order-up-to policy and the generalized Order-up-to policy under supply chain lead time uncertainty. Also, we provide the variant forms of the above strategies when the lead time information is incomplete. Moreover, given the replenishment rules, we analytically investigate the statistical properties of the inventory and the orders of the supply chain. On the basis of these results, we quantify the effect of lead time uncertainty and the effect of lead time information completeness on supply chain performance.3) Chapter 4 addresses the problem of inaccurate inventory data in supply chains. We firstly provide a mathematical description of the impact of inaccurate inventory data on supply chain operations to explain the necessity of data reconciliation technology. Then we present a new framework for data reconciliation in generalized linear dynamic systems, in which the well-known Kalman filter is inadequate for filtering. In contrast to the classical formulation, the proposed framework is in a more concise form but still remains the same filtering accuracy. This comes from the properties of linear dynamic systems and the features of the linear equality constrained least squares solution. Meanwhile, the statistical properties of the framework offer new potentials for dynamic measurement bias detection and identification techniques. On the basis of this new framework, a filtering formula is re-derived directly and the generalized likelihood ratio (GLR) method is modified for generalized linear dynamic systems. Simulation studies of a material network present the effects of both the techniques and emphatically demonstrate the characteristics of the identification approach. Moreover, the new framework provides some insights about the connections between linear dynamic data reconciliation (LDDR), linear steady state data reconciliation (LSSDR) and Kalman filter (KF).4) Chapter 5 extends the linear supply chain configuration (one upstream and one downstream member) for a network supply chain configuration (multiple upstream and downstream members) under ARMA demand patterns. We inherit the minimum variance control method to design the SCM strategy for multivariable systems. From the perspective of the state space model and the linear stochastic optimal control theory, we describe the supply chain dynamics, construct the demand predictor and design replenishment rules in a new manner.