Modeling and mitigation of supply-demand mismatches

In this thesis, I develop analytical models to price the value of supply chain investments under demand uncer¬tainty. This thesis includes three self-contained papers. In the first paper, we investigate the value of lead-time reduction under the risk of sudden and abnormal changes in demand forecasts. We first consider the risk of a complete and permanent loss of demand. We then provide a more general jump-diffusion model, where we add a compound Poisson process to a constant-volatility demand process to explore the impact of sudden changes in demand forecasts on the value of lead-time reduction. We use an Edgeworth series expansion to divide the lead-time cost into that arising from constant instantaneous volatility, and that arising from the risk of jumps. We show that the value of lead-time reduction increases substantially in the intensity and/or the magnitude of jumps. In the second paper, we analyze the value of quantity flexibility in the presence of supply-chain dis- intermediation problems. We use the multiplicative martingale model and the "contracts as reference points" theory to capture both positive and negative effects of quantity flexibility for the downstream level in a supply chain. We show that lead-time reduction reduces both supply-chain disintermediation problems and supply- demand mismatches. We furthermore analyze the impact of the supplier's cost structure on the profitability of quantity-flexibility contracts. When the supplier's initial investment cost is relatively low, supply-chain disin¬termediation risk becomes less important, and hence the contract becomes more profitable for the retailer. We also find that the supply-chain efficiency increases substantially with the supplier's ability to disintermediate the chain when the initial investment cost is relatively high. In the third paper, we investigate the value of dual sourcing for the products with heavy-tailed demand distributions. We apply extreme-value theory and analyze the effects of tail heaviness of demand distribution on the optimal dual-sourcing strategy. We find that the effects of tail heaviness depend on the characteristics of demand and profit parameters. When both the profit margin of the product and the cost differential between the suppliers are relatively high, it is optimal to buffer the mismatch risk by increasing both the inventory level and the responsive capacity as demand uncertainty increases. In that case, however, both the optimal inventory level and the optimal responsive capacity decrease as the tail of demand becomes heavier. When the profit margin of the product is relatively high, and the cost differential between the suppliers is relatively low, it is optimal to buffer the mismatch risk by increasing the responsive capacity and reducing the inventory level as the demand uncertainty increases. In that case, how¬ever, it is optimal to buffer with more inventory and less capacity as the tail of demand becomes heavier. We also show that the optimal responsive capacity is higher for the products with heavier tails when the fill rate is extremely high.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

JPEG standard uniform quantization error modeling with applications to sequential and progressive operation modes

In this paper we propose a method for computing JPEG quantization matrices for a given mean square error or PSNR. Then, we employ our method to compute JPEG standard progressive operation mode definition scripts using a quantization approach. Therefore, it is no longer necessary to use a trial and error procedure to obtain a desired PSNR and/or definition script, reducing cost. Firstly, we establish a relationship between a Laplacian source and its uniform quantization error. We apply this model to the coefficients obtained in the discrete cosine transform stage of the JPEG standard. Then, an image may be compressed using the JPEG standard under a global MSE (or PSNR) constraint and a set of local constraints determined by the JPEG standard and visual criteria. Secondly, we study the JPEG standard progressive operation mode from a quantization based approach. A relationship between the measured image quality at a given stage of the coding process and a quantization matrix is found. Thus, the definition script construction problem can be reduced to a quantization problem. Simulations show that our method generates better quantization matrices than the classical method based on scaling the JPEG default quantization matrix. The estimation of PSNR has usually an error smaller than 1 dB. This figure decreases for high PSNR values. Definition scripts may be generated avoiding an excessive number of stages and removing small stages that do not contribute during the decoding process with a noticeable image quality improvement.