Dynamic decision-making under uncertainties: algorithms based on linear decision rules and applications in operating models

This thesis is to propose efficient and robust algorithms based on Linear Decision Rule (LDR), which expand the applicability of the existing LDR methods. Representative and complex operation models are analyzed and solved by the proposed approaches. The research motivation and scope are provided in Chapter 1. Chapter 2 introduces the generic LDR method and the contributions of this thesis to the LDR literature. To extend the LDR method to nonlinear objectives, two methods are proposed. The first is an iterative LDR (ILDR) method that tackles general concave differentiable nonlinear terms in the objective function. The second treats quadratic terms in the objective function by a Second-Order Cone approximation. The details and implementation of the proposed methods are presented in Chapter 3 and Chapter 4. Chapter 3 utilizes the Robust Optimization approach to derive an ILDR solution for a multi-period hydropower generation problem that has a nonlinear objective function. The methodology results in tractable second-order cone formulations. The performance of the ILDR approach is compared with the Sampling Stochastic Dynamic Programming (SSDP) policy derived using historical data. In Chapter 4, a joint pricing and inventory control problem of a perishable product with a fixed lifetime is analyzed. Both the backlogging and lost-sales cases are discussed. The analytic results shed new light on perishable inventory management, and the proposed approach provides a significantly simpler proof of a classical structural result in the literature. Two heuristics were proposed, one of which is a modification and improvement of an existing heuristic. The other one is an LDR based approach, which approximates the dynamics and the objective function by robust counterparts. The robust counterpart for the backlogging case is tight, and it leads to a satisfactory performance of less than 1% loss of optimality. Although the robust counterpart for the lost-sales case is not tight in the current numerical study, the gap between the LDR method and the SDP benchmark is less than 5% on average. Chapter 5 summarizes the contributions of the thesis and discusses about potential improvements. One important working project, an approximate dynamic programming based on LDR (ADP-LDR) approach, is introduced for future research

Coordinating inventory control and pricing strategies for perishable products

We analyze a joint pricing and inventory control problem for a perishable product with a fixed lifetime over a finite horizon. In each period, demand depends on the price of the current period plus an additive random term. Inventories can be intentionally disposed of, and those that reach their lifetime have to be disposed of. The objective is to find a joint pricing, ordering, and disposal policy to maximize the total expected discounted profit over the planning horizon taking into account linear ordering cost, inventory holding and backlogging or lost-sales penalty cost, and disposal cost. Employing the concept of L♮-concavity, we show some monotonicity properties of the optimal policies. Our results shed new light on perishable inventory management, and our approach provides a significantly simpler proof of a classical structural result in the literature. Moreover, we identify bounds on the optimal order-up-to levels and develop an effective heuristic policy. Numerical results show that our heuristic policy performs well in both stationary and nonstationary settings. Finally, we show that our approach also applies to models with random lifetimes and inventory rationing models with multiple demand classes

All-optical multi-level phase quantization based on phase sensitive amplification with low-order harmonics

A novel scheme is proposed for all-optical multi-level phase quantization by mixing two lower-order harmonics, rather than mixing the signal with its conjugate (M�1)th harmonic, which is difficult to be generated but necessary for the traditional quantization method. The low-order harmonics used in the proposed scheme are determined as the conjugate (M/2�1)th and the (M/2+1)thharmonics for M=4n , or the conjugate (M/2�2)th and the (M/2+2)th harmonics for M=4n+2, or the conjugate [(M�1)/2]th and the [(M+1)/2]th harmonics for M=2n+1, n=1,2,3�The simulations show the effectiveness of the scheme for the eight- and nine-level all-optical phase quantization. Furthermore, the application of the scheme to the all-optical phase regeneration is validated. An improved method with two cascading stages is also proposed and validated to achieve a monotonic step-like phase�phase transfer characteristic for the optimized all-optical phase quantization. This proposed scheme provides a new way for multi-level phase quantization and multi-level phase shift keying regeneration to meet the ever increasing demand for the bandwidth in fiber optic communications

640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser

An ultra-fast physical random number generator is demonstrated utilizing a photonic integrated device based broadband chaotic source with a simple post data processing method. The compact chaotic source is implemented by using a monolithic integrated dual-mode amplified feedback laser (AFL) with self-injection, where a robust chaotic signal with RF frequency coverage of above 50 GHz and flatness of ±3.6 dB is generated. By using 4-least significant bits (LSBs) retaining from the 8-bit digitization of the chaotic waveform, random sequences with a bit-rate up to 640 Gbit/s (160 GS/s × 4 bits) are realized. The generated random bits have passed each of the fifteen NIST statistics tests (NIST SP800-22), indicating its randomness for practical applications