Zhan Pang

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.

Hedging Against Uncertainty: A Tale of Internet Data Center Operations Under Smart Grid Environment

Internet Data Center (IDC) supports the reliable operations of many important online services. As the demand of Internet services and cloud computing keep increasing in recent years, the power usage associated with IDC operations had been surging significantly. Such mass power consumption has brought heavy burden on IDC operators. Recently there are extensive research on power management for IDCs. However, one important challenge faced by IDC operators has been overlooked. How to handle the uncertainties in IDC operations is a challenging task. The uncertainties come from both the dynamic workload and time-varying electricity prices. In this paper, we systematically investigate the problem of minimizing the operation risk of IDCs against those uncertainties at the same time guaranteeing quality of service under deregulated electricity market environment. We propose a novel hedging scheme and model the operation risk minimization problem as a bilevel programming. We also design an optimal hedging algorithm. We conduct extensive evaluations based on real-life workload data from Google and electricity price data from deregulated electricity market for multiple IDC locations. Results show that our scheme can significantly reduce the operation risk by countering the uncertainties.

Technical Note---A Note on the Structure of Joint Inventory-Pricing Control with Leadtimes

We consider a joint inventory-pricing control problem for a periodic-review, single-stage inventory system with a positive order leadtime and a linear order cost. Demands in consecutive periods are independent, but their distributions depend on the price in accordance with a stochastic demand function of additive form. Pricing and ordering decisions are made simultaneously at the beginning of each period. The objective is to maximize the total expected discounted profit over a finite horizon. We partially characterize the structure of the optimal joint ordering and pricing policies. We also show that our structural analysis can be extended to a multistage (or serial) inventory system with constant or stochastic leadtimes and an assemble-to-order system with price-sensitive demand.

Optimal dynamic pricing and inventory control with stock deterioration and partial backordering

This paper studies the optimal dynamic pricing and inventory control policies in a periodic-review inventory system with fixed ordering cost and additive demand. The inventory may deteriorate over time and the unmet demand may be partially backlogged. We identify two sufficient conditions under which (s,S,p) policies are optimal.

Performance-Based Contracts for Outpatient Medical Services

In recent years, the performance-based approach to contracting for medical services has been gaining popularity across different healthcare delivery systems, both in the United States (under the name of “pay for performance”) and abroad (“payment by results” in the United Kingdom). The goal of our research is to build a unified performance-based contracting (PBC) framework that incorporates patient access-to-care requirements and that explicitly accounts for the complex outpatient care dynamics facilitated by the use of an online appointment scheduling system. We address the optimal contracting problem in a principal--agent framework where a service purchaser (the principal) minimizes her cost of purchasing the services and achieves the performance target (a waiting-time target) while taking into account the response of the provider (the agent) to the contract terms. Given the incentives offered by the contract, the provider maximizes his payoff by allocating his outpatient service capacity among three patient groups: urgent patients, dedicated advance patients, and flexible advance patients. We model the appointment dynamics as that of an M/D/1 queue and analyze several contracting approaches under adverse selection (asymmetric information) and moral hazard (private actions) settings. Our results show that simple and popular schemes used in practice cannot implement the first-best solution and that the linear performance-based contract cannot implement the second-best solution. To overcome these limitations, we propose a threshold-penalty PBC approach and show that it coordinates the system for an arbitrary patient mix and that it achieves the second-best performance for the setting where all advance patients are dedicated.

Optimal control of price and production in an assemble-to-order system

We study the optimal control of an assembly system that produces one assembled-to-order final product with multiple made-to-stock components and sells it at variable price. It is shown that a threshold control on component production, product price, and product orders maximizes total discounted profit over an infinite horizon.

Dynamic Pricing and Inventory Control in a Make-to-Stock Queue With Information on the Production Status

This paper addresses the dynamic pricing problem of a single-item, make-to-stock production system. Demand arrives according to Poisson processes with changeable arrival rate dependent on the selling price. Item processing times follow an Erlang distribution, which allows to use the information on the production status in a tractable way. The objective is to identify a dynamic control policy that decides production and adjusts the price to maximize the long-run total discounted profit. An optimal policy is based on the so-called work-storage level that captures the information of the inventory level and the status of ongoing production process. Specifically, we show that: 1) the finished goods inventory is optimally managed by a critical stage level policy: when the inventory is below a certain work-storage level, production is started if the system is currently idle and 2) the price is optimally set by threshold levels: a certain price is posted when the work-storage level is at or below a threshold corresponding to that level of price. Moreover, we develop an efficient algorithm to compute the optimal policy.

Network capacity management under competition

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model to address the competitive network revenue management problem. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and investigate the uniqueness of a Nash equilibrium for the Nash game. We provide some further uniqueness and comparative statics analysis when the network is reduced to a single-leg flight structure with two products. The comparative statics analysis reveals some useful insights on how Nash equilibrium booking limits change monotonically in the prices of products. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes.

Dynamic booking control for car rental revenue management: A decomposition approach

This paper considers dynamic booking control for a single-station car rental revenue management problem. Different from conventional airline revenue management, car rental revenue management needs to take into account not only the existing bookings but also the lengths of the existing rentals and the capacity flexibility via fleet shuttling, which yields a high-dimensional system state space. In this paper, we formulate the dynamic booking control problem as a discrete-time stochastic dynamic program over an infinite horizon. Such a model is computationally intractable. We propose a decomposition approach and develop two heuristics. The first heuristic is an approximate dynamic program (ADP) which approximates the value function using the value functions of the decomposed problems. The second heuristic is constructed directly from the optimal booking limits computed from the decomposed problems, which is more scalable compared to the ADP heuristic. Our numerical study suggests that the performances of both heuristics are close to optimum and significantly outperform the commonly used probabilistic non-linear programming (PNLP) heuristic in most of the instances. The dominant performance of our second heuristic is evidenced in a case study using sample data from a major car rental company in the UK.

Optimal Control of a Single-Product Assemble-to-Order System With Multiple Demand Classes and Backordering

We analyze the optimal control problem for a continuous-review assemble-to-order (ATO) system with multiple demand classes and backordering. The objective is to minimize total discounted cost over an infinite horizon. It remains an open question of the production control literature what optimal policy structure of such a system is. Using the concept of