Sungyong Choi

A risk-averse newsvendor with law invariant coherent measures of risk

For general law invariant coherent measures of risk, we derive an equivalent representation of a risk-averse newsvendor problem as a mean-risk model. We prove that the higher the weight of the risk functional, the smaller the order quantity. Our theoretical results are confirmed by sample-based optimization.

A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk

We consider a multiproduct risk-averse newsvendor under the law-invariant coherent measures of risk. We first establish several fundamental properties of the model regarding the convexity of the problem, the symmetry of the solution, and the impact of risk aversion. Specifically, we show that for identical products with independent demands, increased risk aversion leads to decreased orders. For a large but finite number of heterogeneous products with independent demands, we derive closed-form approximations for the optimal order quantities. The approximations are as simple to compute as the classical risk-neutral solutions. We also show that the risk-neutral solution is asymptotically optimal as the number of products tends to be infinity, and thus risk aversion has no impact in the limit. For a risk-averse newsvendor with dependent demands, we show that positively (negatively) dependent demands lead to lower (higher) optimal order quantities than independent demands. Using a numerical study, we examine the convergence rates of the approximations and develop additional insights into the interplay between dependent demands and risk aversion.

A Multi-Product Risk-Averse Newsvendor with Exponential Utility Function

We consider a multi-product newsvendor using an exponential utility function. We first establish a few basic properties for the newsvendor regarding the convexity of the model and monotonicity of the impact of risk aversion on the solution. When the product demands are independent and the ratio of the degree of risk aversion to the number of products is sufficiently small, we obtain closed-form approximations of the optimal order quantities. The approximations are as easy to compute as the risk-neutral solution. We prove that when this ratio approaches zero, the risk-averse solution converges to the corresponding risk-neutral solution. When the product demands are positively (negatively) correlated, we show that risk aversion leads to lower (higher) optimal order quantities than the solution with independent demands. Using a numerical study, we examine convergence rates of the approximations and thoroughly study the interplay of demand correlation and risk aversion. The numerical study confirms our analytical results and further shows that an increased risk aversion does not always lead to lower order quantities, when demands are strongly negatively correlated.

Ensuring Privacy and Security for LBS through Trajectory Partitioning

The concept of location k-anonymity has been proposed to address the privacy issue of location based services (LBS). Under this notion of anonymity, the adversary only has the knowledge that the LBS request originates from a region containing at least k people, and therefore cannot individually distinguish the requestor. However, new types of LBS services such as continuous nearest neighbor searches require the knowledge of the users trajectory, which can lead to a privacy breach. The longer the adversary can track the users trajectory, the stronger the possibility that the users sensitive information is revealed. To alleviate this problem, we propose algorithms to optimally partition a continuous request into multiple LBS requests with shorter trajectories. This results in increased privacy due to the unlinking of different requests over time and has the added benefit of improving the overall quality of service since the anonymized regions are now smaller. Our experimental results show that significant privacy and QoS benefits can be achieved with nominal computational overhead.

Risk-averse newsvendor models

The multi(or single-) product newsvendor problem is a well-known classical problem in inventory management. The general setting analyzed is as follows. There are multiple (or single) perishable products with random demand in a single-selling season. Given a purchase cost and resale price, the decision maker (aka the newsvendor) chooses the optimal ordering quantity for each product at the beginning of the selling season. If the newsvendor orders too much of any product, all leftovers are sold at salvage value; if the newsvendor orders too little, it incurs lost opportunity of sales. Given uncertain demand, it is obvious that the final profit for the newsvendor is random. Thus prior researchers have focused on maximizing expected profits for the newsvendor in making the ordering decision. Unless there are resource constraints and/or demand substitution effects, most multiproduct newsvendor problems can be decomposed into multiple independent single-product problems. The general solution (for expected profit maximization) is a simple closed-form ratio of the overage and underage ”costs” for the newsvendor’s (cumulative) marginal demand distribution. Given such a straightforward result, this approach has been applied in numerous industry settings to address problems of revenue management and/or overbooking. From a decision-maker’s perspective, maximizing expected profits implies risk neutrality. However, risk neutrality guarantees the best decision only on average. Although the use of this model may be justified by the Law of Large Numbers, one cannot expect that a single realization will be sufficiently close to the expected value. In fact, when actual outcomes deviate greatly from their expected values due to their randomness, it may cause an unacceptably large loss to the newsvendor.

Die Bonding Issues on Silicon Carbide Diodes

We report on the die bonding processes and how the surface roughness and metallization schemes affect the processes of die bonding in 4H-SiC device fabrication using a soldering test and die shear test (DST) with differently prepared 4H-SiC samples. The first set of samples (FZ#1 and FZ#2) was capped with sequentially evaporated Ti and Au on an annealed Ni layer. The second set of samples (FZ#3 and FZ#4) and the third set of samples (FZ#5 and FZ#6) were prepared by 4μm-thick Au electroplating on an annealed Ni layer and an un-annealed Ni layer, respectively. The quality of the soldering, such as the solder coverage, void, and adhesion, was characterized by optical microscope, X-ray microprobe, and DST. We found that the samples (FZ#4 and FZ#6) deposited by Au electroplating on C-face (bottom-side) 4H-SiC provided a satisfactory result for the tests of solder coverage, void, and DST and also realized the cleaning process prior to the electroplating and soldering was the most crucial in the die packaging processes of vertical structure devices. The void fraction measured by X-ray microprobe for the samples, FZ#4 and FZ#6 was 2.2% (average for 5 samples) and 0.8% (average for 3 samples), respectively.

A Newsvendor Analysis of Binomial Yield Production Process

Abstract We study a binomial yield production process using a newsvendor approach by considering the mismatch costs between a given demand and a non-defective yield amount. Using a normal approximation, we reformulate the original discrete and exact model as a continuous and approximate model. We conduct a comparative static analysis of the parameters in the approximate model and derive the monotone properties of the (approximate) optimal solution in the case that the given demand is sufficiently large. The analytical results are all consistent with our insights and are also supported by economic explanations. Our numerical study with sample-based optimization indicates that the approximate model is sufficiently close to the exact model in most real-world examples, with some limiting cases included. Then, a simple and naive solution is found to have significant suboptimality. Finally, the results of a sensitivity analysis of the model parameters are confirmed numerically.

An Analysis of Binomial Yield Production Process considering Salvage Value

We study how to determine the optimal lot size in a production process with binomial yield. First, we review the precedent studies in binomial yield production processes in inventory management literature. In results, an extended new model is presented to consider salvage values for leftover inventories. We initially formulate it as a discrete (unconstrained) optimization model, and then convert it as a corresponding continuous (unconstrained) optimization model by the normal approximation. Finally, we prove the concavity of the model, and examine the impact of salvage value on the optimal lot size. All of these analytical results are also confirmed computationally with the numerical examples generated by Monte Carlo simulation.

Entry Deterrence and Price Competition under Asymmetric Information

We study limit pricing in a price-based duopoly market under asymmetric information on the demand state. An incumbent, who is a monopolist in the initial period, has complete information on the size of a market, while a potential entrant only knows it partially. After observing the sales price of the incumbent in the first period, the entrant decides whether to enter a duopoly market and the sales price if she chooses to. We present a separating perfect Bayesian equilibrium, which indicates that limit pricing can deter the entry of a potential entrant under price competition when there is information asymmetry about the demand state.

A Risk-Averse Inventory Model with Markovian Purchasing Costs

We study a few dynamic risk-averse inventory models using additive utility functions. We add Markovian behavior of purchasing costs in our models. Such Markovian purchasing costs can reflect a market situation in a global supply chain such as fluctuations at exchange rates or the existence of product spot markets. We provide our problem formulations with finite and infinite MDP (Markovian Decision Process) problems. For finite time models, we first prove (joint) concavity of the model for each state and obtain a (modified) base-stock optimal policy. Then, we conduct comparative static analysis for model parameters and derive monotone properties to the optimal solutions. For infinite time models, we show the existence of stationary base-stock optimal policies and the inheritance of the monotone properties proven at our finite time models.