Hanqin Zhang

Quantity Flexibility Contracts: Optimal Decisions with Information Updates*

We study single and multiperiod quantity flexibility contracts involving one demand forecast update in each period and a spot market. We obtain the optimal order quantity at the beginning of a period and order quantities on contract and from the spot market at the then prevailing price after the forecast revision and before the demand materialization. The amount that can be purchased on contract is bounded by a given flexibility limit. We discuss the impact of the forecast quality and the level of flexibility on the optimal decisions and managerial insights behind the results.

Inventory Models with Fixed Costs, Forecast Updates, and Two Delivery Modes

This paper is concerned with a periodic review inventory system with fast and slow delivery modes, fixed ordering cost, and regular demand forecast updates. At the beginning of each period, on-hand inventory and demand information are updated. At the same time, decisions on how much to order using fast and slow delivery modes are made. Fast and slow orders are delivered at the end of the current period and at the end of the next period, respectively. A forecast-update-dependent ( s,S)-type policy is shown to be optimal. Also shown are some monotonicity properties of the policy parameters with respect to the costs and information updates.

Trading a mean-reverting asset: Buy low and sell high

This paper is concerned with an optimal trading (buy and sell) rule. The underlying asset price is governed by a mean-reverting model. The objective is to buy and sell the asset so as to maximize the overall return. Slippage cost is imposed on each transaction. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the original optimal stopping problem can be obtained by solving two quasi-algebraic equations. Sufficient conditions are given in the form of a verification theorem. A numerical example is reported to demonstrate the results.

Are Base-Stock Policies Optimal in Inventory Problems with Multiple Delivery Modes?

We present a periodic review inventory model with multiple delivery modes. While base-stock policies are optimal for one or two consecutive delivery modes, they are not so otherwise. For multiple consecutive delivery modes, we show that only the fastest two modes have optimal base stocks, and provide a simple counterexample to show that the remaining ones do not. We investigate why the base-stock policy is or is not optimal in different situations. This note is an abridged version of Feng et al. (2006).

Coordinating dyadic supply chains when production costs are disrupted

This paper studies a supply chain coordination problem under production cost disruptions. When a production cost disruption occurs, the coordination scheme designed for the initially estimated production cost needs to be revised. To resolve this issue, it is necessary to explicitly consider the possible deviation costs caused by any changes in the original production plan. How to model the production cost disruptions and their impacts, and how to design coordination schemes under disruptions is discussed. Results obtained under various scenarios including the cases of a single retailer and multiple retailers, the cases of linear and nonlinear demand-price functions, and different wholesale policies are presented.

Stability of Multiclass Queueing Networks Under Priority Service Disciplines

In this paper, we establish a sufficient condition for the stability of a multiclass fluid network and queueing network under priority service disciplines. The sufficient condition is based on the existence of a linear Lyapunov function, and it is stated in terms of the feasibility of a set of linear inequalities that are defined by network parameters. In all the networks we have tested, this sufficient condition actually gives a necessary and sufficient condition for their stability.

Risk analysis of commitment-option contracts with forecast updates

The standard treatment of supply chain models largely focuses on the optimization of the expected value of a given cost or profit measure. Due to highly uncertain supply and demand conditions, the use of the expected objective measure may not be justified. This article studies a class of commitment–option supply contracts in a mean-variance framework. With structure properties established it is shown that a mean-variance trade-off analysis with advanced reservation can be carried out. Moreover, it is indicated how the corresponding contract decisions differ from decisions for optimizing an expected objective value.

Peeling layers of an onion: inventory model with multiple delivery modes and forecast updates

This paper is concerned with a periodic review inventory system with fast and slow delivery modes and regular demand forecast updates. At the beginning of each period, on-hand inventory and demand information are updated. At the same time, decisions on how much to order using fast and slow delivery modes are made. Fast and slow orders are delivered at the end of the current and the next periods, respectively. It is shown that there exists an optimal Markov policy and that it is a modified base-stock policy.

The Effect of Lead Time and Demand Uncertainties in (r, q) Inventory Systems

We study a single-item (r, q) inventory system, where r is the reorder point and q is the order quantity. The demand is a compound-Poisson process. We investigate the behavior of the optimal policy parameters and the long-run average cost of the system in response to stochastically shorter or less-variable lead times. We show that although some of the properties of the base-stock system can be extended to this more general model, some cannot. The same findings also apply when the comparison is conducted on the lead-time demand distributions.

Spectral Polynomial Algorithms for Computing Bi-Diagonal Representations for Phase Type Distributions and Matrix-Exponential Distributions

In this paper, we develop two spectral polynomial algorithms for computing bi-diagonal representations of matrix-exponential distributions and phase type (PH) distributions. The algorithms only use information about the spectrum of the original representation and, consequently, are efficient and easy to implement. For PH-representations with only real eigenvalues, some conditions are identified for the bi-diagonal representations to be ordered Coxian representations. It is shown that every PH-representation with a symmetric PH-generator has an equivalent ordered Coxian representation of the same or a smaller order. An upper bound of the PH-order of a PH-distribution with a triangular or symmetric PH-generator is obtained.