Co-ordinated supply chain management and optimal control problems

Abstract

The thesis is divided into two parts: Supply Chain Co-ordinated Model and Optimal Control Problems. The first part of the thesis examines co-ordinated supply chain model. From classical inventory theory, the economic ordering quantity (EOQ) concept has been widely applied. Under EOQ, a buyer determines the optimal ordering size that minimizes its total cost. In a two-level supply chain, under individual optimal policies, the buyer orders at the EOQ and the vendor determines its own optimal production lot size, i.e. economic production quantity (EPQ). However, independent optimization may not be optimal for the whole supply chain system. Such an independent policy is known as the non-cooperation system. Many researchers, beginning in the 1970's, started to explore modes of co-ordination that performs better than the non-cooperation system in terms of total system cost. Motivated by a recently developed co-ordination model, the synchronized cycles model, this part of the thesis further explores some characteristics on this model that enhances the co-ordination between the buyers and the vendor. A hybrid heuristic is developed to solve the synchronized cycles supply chain problem. By numerous numerical examples, the hybrid heuristic is successful in searching for a better "near-optimal" solution than the synchronized cycles algorithm developed by Chan and Kingsman (2005, 2007). Further investigations are carried out to explore the characteristics of the model and some bounds are developed on certain decision variables in order to enhance the synchronized cycles algorithm. In addition, modification to the synchronized cycles model by including vehicle scheduling is considered. The performance of the synchronized cycles model is compared to the independent policy. By the "synchronization" characteristic, the synchronized cycles model out-performs the independent policy both in shipment and delivery scheduling and total system cost. Finally, while many of the past researches emphasized on the co-ordination that minimizes the total system cost in the supply chain system, the thesis investigates how the demand heterogeneity, e.g. different values of mean demand, variance and skewness, would affect the performance of the synchronized cycles model. This is a novel investigation in the field of supply chain management. Numerical experiments are carried out to identify conditions of the demand heterogeneity that work well for the synchronized cycles model. The second part of the thesis consists of four open optimal control problems applying to different areas. Optimal control techniques are developed in this thesis and applied to solve the mathematical and computational difficulties encountered by these problems. The optimal control software package, MISER3, is intensively used. Numerical examples are provided to demonstrate the effectiveness of the methods developed. Results obtained are significant. 1. Modeling of a supply chain system with Ornstein Uhlenbeck demand process This demand process is seldom considered in the field of supply chain management and has not yet been analytically derived using the Pontryagin's maximum principle. A single-vendor-single-buyer supply chain system is formulated. Both co-ordinated and non-cooperative supply chain models are considered. 2. The isoperimetric pillar-construction problem The problem is to find an enclosed cross-sectional/base region of a pillar defined by a simple closed curve of fixed perimeter, such that the volume of the pillar, bounded above by a given surface, is maximized. Solutions to the single pillar and multiple pillars cases are considered. For multiple pillars case, a novel elliptic separation constraint technique is used to separate the overlapping of different pillars. 3. Modeling of the design of a flexible rotating beam The problem considers a rotating beam which carries an end mass and rotates in a vertical plane under the effect of gravity by means of a time-varying driving torque. The problem is posed as a continuous-time optimal control problem for the ACLD treatment. Such a computational optimal control approach is a novel technique in the design of the ACLD treated rotating beam. In addition, the accurate time of the switching points are determined which has not been considered in previous similar researches. 4. Nonlinear model of quarter-car suspension problem Vehicle active suspension system has been a popular issue in road vehicle applications. Many researchers have dedicated effort in the modeling and the design of controlled suspension system to ensure a smooth ride. A quarter-car suspension model with state dependent ODE system of equations is considered. Computational method with enhanced switching controls is used to solve the problem.