Yingdong Lu

Order Fill Rate, Leadtime Variability, and Advance Demand Information in an Assemble-to-Order System

We study an assemble-to-order system with stochastic leadtimes for component replenishment. There are multiple product types, of which orders arrive at the system following batch Poisson processes. Base-stock policies are used to control component inventories. We analyze the system as a set of queues driven by a common, multiclass batch Poisson input, and derive the joint queue-length distribution. The result leads to simple, closed-form expressions of the first two moments, in particular the covariances, which capture the dependence structure of the system. Based on the joint distribution and the moments, we derive easy-to-compute approximations and bounds for the order fulfillment performance measures. We also examine the impact of demand and leadtime variability, and investigate the value of advance demand information.

Order-Based Cost Optimization in Assemble-to-Order Systems

We study a multi-item stochastic inventory system in which customers may order different but possibly overlapping subsets of items, such as a multiproduct assemble-to-order system. The goal is to determine the right base-stock level for each item and to identify the key driving factors. We formulate a cost-minimization model with order-based backorder costs and compare it with the standard single-item, newsvendor-type model with item-based backorder cost. We show that the solution of the former can be bounded by that of the latter with appropriately imputed parameters. Starting with this upper bound, the optimal base-stock levels of the order-based problem can be obtained in a greedy fashion. We also show that the optimal base-stock levels increase in replenishment lead times but may increase or decrease in lead-time variability and demand correlation. Finally, we devise closed-form approximations of the optimal base-stock levels to see more clearly their dependence on the system parameters.

Applications of flexible pricing in business-to-business electronic commerce

The increasingly dynamic nature of business-to-business electronic commerce has produced a recent shift away from fixed pricing and toward flexible pricing. Flexible pricing, as defined here, includes both differential pricing, in which different buyers may receive different prices based on expected valuations, and dynamic-pricing mechanisms, such as auctions, where prices and conditions are based on bids by market participants. In this paper we survey ongoing work in flexible pricing in the context of the supply chain, including revenue management, procurement, and supply-chain coordination. We review negotiation mechanisms for procurement, including optimization approaches to the evaluation of complex, multidimensional bids. We also discuss several applications of flexible pricing on the sell side, including pricing strategies for response to requests for quotes, dynamic pricing in a reverse logistics application, and pricing in the emerging area of hosted applications services. We conclude with a discussion of future research directions in this rapidly growing area.

No-Holdback Allocation Rules for Continuous-Time Assemble-to-Order Systems

This paper analyzes a class of common-component allocation rules, termed no-holdback (NHB) rules, in continuous-review assemble-to-order (ATO) systems with positive lead times. The inventory of each component is replenished following an independent base-stock policy. In contrast to the usually assumed first-come-first-served (FCFS) component allocation rule in the literature, an NHB rule allocates a component to a product demand only if it will yield immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain key performance expressions and compare them to those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems.

Backorder minimization in multiproduct assemble-to-order systems

We consider a multiproduct assemble-to-order system. Components are built to stock with inventory controlled by base-stock rules, but the final products are assembled to order. Customer orders of each product follow a batch Poisson process. The leadtimes for replenishing component inventory are stochastic. We study the optimal allocation of a given budget among component inventories so as to minimize a weighted average of backorders over product types. We derive easy-to-compute bounds and approximations for the expected number of backorders and use them to formulate surrogate optimization problems. Efficient algorithms are developed to solve these problems, and numerical examples illustrate the effectiveness of the bounds and approximations. Contributed by the Supply Chains/Production-Inventory Systems Department

The Stochastic Knapsack Revisited: Switch-Over Policies and Dynamic Pricing

The stochastic knapsack has been used as a model in wide-ranging applications from dynamic resource allocation to admission control in telecommunication. In recent years, a variation of the model has become a basic tool in studying problems that arise in revenue management and dynamic/flexible pricing, and it is in this context that our study is undertaken. Based on a dynamic programming formulation and associated properties of the value function, we study in this paper a class of control that we call switch-over policies---start by accepting only orders of the highest price, and switch to including lower prices as time goes by, with the switch-over times optimally decided via convex programming. We establish the asymptotic optimality of the switch-over policy, and develop pricing models based on this policy to optimize the price reductions over the decision horizon.

Solving a dynamic resource allocation problem through continuous optimization

A class of dynamic resource allocation problems with infinite planning horizon are studied. We observe special structures in the dynamic programming formulation of the problem, which enable us to convert it to continuous optimization problems that can be more easily solved. Structural properties of the problems are discussed, and explicit solutions are given for some special cases.

Optimal control of a fluid network with side constraints

We study the optimal scheduling control of multiclass fluid networks, with constraints on the fluid levels. We present a linear programming-based approach to the general problem, and show that the approach generates the optimal control in a single-station Klimov-like model with side constraints.