Youhua (Frank) Chen

Technical Note---A Risk-Averse Newsvendor Model Under the CVaR Criterion

The classical risk-neutral newsvendor problem is to decide the order quantity that maximizes the one-period expected profit. In this note, we consider a risk-averse newsvendor with stochastic price-dependent demand. We adopt Conditional Value-at-Risk ( CVaR ), a risk measure commonly used in finance, as the decision criterion. The aim of our study is to investigate the optimal pricing and ordering decisions in such a setting. For both additive and multiplicative demand models, we provide sufficient conditions for the uniqueness and existence of the optimal policy. Comparative statics show the monotonicity properties and other characteristics of the optimal pricing and ordering decisions. We also compare our results with those of the newsvendor with a risk-neutral attitude and a general utility function.

The myopic Order-Up-To policy with a proportional feedback controller

We develop a discrete control theory model of a myopic Order-Up-To (OUT) policy reacting to a stochastic demand pattern with Auto Regressive and Moving Average (ARMA) components. We show that the bullwhip effect arises with such a policy despite the fact that it is optimal when the ordering cost is linear. We then derive a set of z-transform transfer functions of a modified OUT policy that allows us to avoid the bullwhip problem by incorporating a proportional controller into the inventory position feedback loop. With this technique, the order variation can always be reduced to the same level as the demand variation. However, bullwhip-effect avoidance always comes at the cost of holding extra inventory. When the ordering cost is piece-wise linear and increasing, we compare the total cost per period under the two types of control policies: with and without bullwhip-effect reduction. Numerical examples reveal that the cost saving can be substantial if the order variance is reduced by using the proportional controller.

Ordering Policies for Periodic-Review Inventory Systems with Quantity-Dependent Fixed Costs

We consider a stochastic periodic-review inventory control system in which the fixed cost depends on the order quantity. In particular, we investigate the optimal ordering policies under three fixed cost structures. The first structure is motivated by transportation and production contracts and considers two fixed costs: if the order size is within a specified limit C, then the fixed cost is K1; otherwise, it is K2, where K1 ≼ K2. The second structure contains multiple fixed costs in which the same incremental fixed cost K is incurred for any additional order quantity up to a given identical batch capacity C. In the third structure, in addition to the K incurred as in the previous case, a common fixed cost is charged for any nonzero order size. An example of the former case arises when an order is shipped with a homogeneous fleet of trucks with per-truck fixed costs. A situation in which a fixed administrative cost plus a quantity-dependent trucking cost is incurred for each shipment exemplifies the latter case. For the first cost structure, we separate the analysis according to the conditions (1) K1 ≼ K2 ≼ 2K1 and (2) K1 ≼ K2. Under condition (1), we introduce a new concept called C-(K1, K2)-convexity, which enables us to almost completely characterize the optimal ordering policy. Under the general condition (2), we utilize a modified notion to provide a partial characterization of the optimal policy and propose a heuristic policy that performs well under a wide variety of model parameters. For the second cost structure, we show that it is optimal to order an integer multiple of the batch capacity to raise the inventory level to a specified range or band of length C, and then to order an additional full or partial batch size depending on the cost function, with no ordering required above the band. We also characterize a similar optimal policy for the third cost structure. Using different techniques, our study extends or redevelops several existing results in the literature.

Optimal inventory and admission policies for drop-shipping retailers serving in-store and online customers

This article studies the optimal inventory and dynamic admission policies of two physical retailers who, besides selling through their traditional in-store channels, also act as drop-shippers for an online retailer (e-tailer). The e-tailer carries no inventory of its own and always turns to one of the two physical retailers for order fulfillment. The considered scenario is the one in which retailer 1 (R1) and retailer 2 (R2) act as the primary and secondary drop-shippers of the e-tailer, respectively. While trying to maximize their respective revenues, both retailers face the problem of whether or not to accept the e-tailers order-fulfillment request. It is initially assumed that the initial inventory levels of each retailer are fixed and that R1 shares his inventory information with R2. By adopting a revenue management framework, the dynamic admission policies of both retailers are studied and it is shown that R1 and R2 should implement one-dimensional and two-dimensional threshold policies, respectively. The scenario in which R1 does not share his inventory information with R2 is considered. For this scenario two heuristic policies for R2 are proposed and they are compared to the optimal policy when information is shared. A detailed sensitivity analysis for varying parameter value is presented, which shows the impact of information sharing between the two retailers. Finally, the assumption of fixed initial inventory levels is relaxed and the optimal initial inventory levels of each retailer that maximize their expected profits are determined.

Optimal Pricing and Inventory Control Policy with Quantity-Based Price Differentiation

A firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon. In addition to the regular unit selling price, the firm can utilize quantity discounts to increase sales. We refer to this dual-pricing strategy as quantity-based price differentiation. At the beginning of each period, the firm needs to make three decisions: replenish the inventory, set the unit selling price if the unit sales mode is deployed, and set the quantity-discount price if the quantity-sales mode is deployed (or the combination of the two modes of sales). We identify conditions under which the optimal inventory control policy and selling/pricing strategy is well structured. Remarkably, under a utility-based demand framework, these conditions can be unified by a simple regularity assumption that has long been used in the auction and mechanism design literature. Moreover, sharper structural results are yielded for the optimal selling strategy. We also examine the comparative advantag...

On a semi-dynamic pricing and seat inventory allocation problem

Motivated by the practice of airlines, this paper considers the following problem. Tickets are offered at a limited number of predetermined price levels, and the price is only allowed to change monotonically. Management needs to determine the number of seats to be sold at each discount fare with an objective of maximizing the revenue. Such a semi-dynamic pricing and seat allocation approach improves the static pricing approach, as it allows a certain degree of pricing flexibility, but it compromises the potential revenue maximization of the dynamic pricing approach. Therefore, a natural question is what is the magnitude of the revenue loss by such a semi-dynamic approach? The primary objective of this paper is to gain insights into this question. Based on structural results, numerical experiments show that the semi-dynamic pricing approach generates near-optimal revenue.

Outpatient appointment scheduling with unpunctual patients

This study examines the design of appointment scheduling policies with considerations of not only the conventional factors, for example, the random consultation time and multiple patient types, but also of a new factor, particularly, patient unpunctuality, that is, one patient may arrive earlier or later than the appointment time. Patient unpunctuality negatively affects the appointment scheduling system, for example, such behaviour, reduces provider productivity and clinical efficiency, increases health care costs, and limits the ability of a clinic to serve its patients population by reducing the clinic’s effective capacity. In this study, while considering patient unpunctuality, we first introduce an analytical model and show the optimality of a fixed-interval policy for a simplified two-patient model. Motivated by the result, we propose an easy-to-implement heuristic policy with a simple structure using a simulation framework to improve the performance of the appointment scheduling system. The simulation result shows that our policy is overwhelmingly preponderant in current practice. We also measure the effect of patient unpunctuality and other factors. Actual data are used to add realism to the input parameters, and practical guidelines are developed for appointment scheduling.