Susan H. Xu

Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System

This paper considers a multicomponent, multiproduct periodic-review assemble-to-order (ATO) system that uses an independent base-stock policy for inventory replenishment. Product demands in each period are integer-valued correlated random variables, with each product being assembled from multiple units of a subset of components. The system quotes a prespecified response time window for each product and receives a reward if the demand for that product is filled within its response time window. We formulate a two-stage stochastic integer program with recourse to determine the optimal base-stock policy and the optimal component allocation policy for the ATO system. We show that the component allocation problem is a general multidimensional knapsack problem (MDKP) and is NP-hard. We propose a simple, order-based component allocation rule and show that it can be solved in either polynomial or pseudopolynomial time. We also use the sample average approximation method to determine the optimal base-stock levels and compare it with two variations of the equal fractile heuristic. Intensive testing indicates that our solution method for each stage of the stochastic program is robust, effective, and that it significantly outperforms existing methods. Finally, we discuss several managerial implications of our findings.

GREEDY ALGORITHM FOR THE GENERAL MULTIDIMENSIONAL KNAPSACK PROBLEM

In this paper, we propose a new greedy-like heuristic method, which is primarily intended for the general MDKP, but proves itself effective also for the 0-1 MDKP. Our heuristic differs from the existing greedy-like heuristics in two aspects. First, existing heuristics rely on each item’s aggregate consumption of resources to make item selection decisions, whereas our heuristic uses the effective capacity, defined as the maximum number of copies of an item that can be accepted if the entire knapsack were to be used for that item alone, as the criterion to make item selection decisions. Second, other methods increment the value of each decision variable only by one unit, whereas our heuristic adds decision variables to the solution in batches and consequently improves computational efficiency significantly for large-scale problems. We demonstrate that the new heuristic significantly improves computational efficiency of the existing methods and generates robust and near-optimal solutions. The new heuristic proves especially efficient for high dimensional knapsack problems with small-to-moderate numbers of decision variables, usually considered as “hard” MDKP and no computationally efficient heuristic is available to treat such problems.

Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers

Queueing systems managed by ticket technology are widely used in service industries as well as government offices. Upon arriving at a ticket queue, each customer is issued a numbered ticket. The number currently being served is displayed. An arriving customer balks if the difference between his ticket number and the displayed number exceeds his patience level. We propose a Markov chain model of a ticket queue and develop effective evaluation tools. These tools can help management quantify the service level and identify the performance gap between the ticket queue and the conventional physical queue, in which a waiting line is formed. We gain insights about the ways customer service is affected by information loss in the ticket queue. In particular, we show that ticket and physical queues have significantly different balking probabilities when customer patience is low and the system traffic is heavy. We also propose an improvement to the ticket queue that provides each customer with his expected waiting time conditioned on his observed number difference, which is shown to raise the performance of the ticket queue to that of the physical queue.

Managing an Available-to-Promise Assembly System with Dynamic Short-Term Pseudo-Order Forecast

We study an order promising problem in a multiclass, available-to-promise (ATP) assembly system in the presence of pseudo orders. A pseudo order refers to a tentative customer order whose attributes, such as the likelihood of an actual order, order quantity, and confirmation timing, can change dynamically over time. A unit demand from any class is assembled from one manufactured unit and one inventory unit, where the manufactured unit takes one unit of capacity and needs a single period to produce. An accepted order must be filled before a positive delivery lead time. The underlying order acceptance decisions involve trade-offs between committing resources (production capacity and component inventory) to low-reward firm orders and reserving resources for high-reward orders. We develop a Markov chain model that captures the key characteristics of pseudo orders, including demand lumpiness, nonstationarity, and volatility. We then formulate a stochastic dynamic program for the ATP assembly system that embeds the Markov chain model as a short-term forecast for pseudo orders. We show that the optimal order acceptance policy is characterized by class prioritization, resource-imbalance-based rationing, and capacity-inventory-demand matching. In particular, the rationing level for each class is determined by a critical value that depends on the resource imbalance level, defined as the net difference between the production capacity and component inventory levels. Extensive numerical tests underscore the importance of the key properties of the optimal policy and provide operational and managerial insights on the value of the short-term demand forecast and the robustness of the optimal policy. This paper was accepted by Martin Lariviere, operations management.

Managing a Single-Product Assemble-to-Order System with Technology Innovations

We consider a multicomponent, single-product assemble-to-order (ATO) system that faces frequent, component-based technology innovations. For each component, there are two technologies with overlapping life cycles coexisting in the market. All cost parameters associated with each technology (procurement cost, salvage value, etc.) evolve dynamically. We investigate two technology-inventory coordination schemes, one is at the strategic level, where technology and inventory decisions are sequentially made using partial information, and another is at the operational level, where technology and inventory decisions are jointly made using full information. The performance gap between the two coordination schemes quantifies the value of incorporating dynamic inventory information in technology management. We develop effective solution techniques and approximation methods and characterize their policy structures. Our numerical study indicates that the strategic-level technology-inventory coordination is generally sufficient, but the operational-level coordination becomes necessary when demand variability is high and salvage loss is heavy. We also propose a hybrid technology-inventory coordination scheme, whereby the firm adopts a technology management plan using the strategic-level coordination scheme, but executes it dynamically by adapting to inventory information, using a heuristic proposed in this paper. Our numerical study suggests that the hybrid strategy can virtually achieve the performance of the optimal operational level coordination. Our analysis provides guidelines for the effective technology-adoption and inventory-control coordination strategies in the ATO system with rapid innovations.

Stochastic methods in reliability and risk management

This volume focuses on stochastic methods developed for reliability modeling and risk analysis. Reliability theory and risk analysis have been closely related, and stochastic methods that are commonly used in both fields serve as a natural conduit through which useful concepts and best practices can migrate from one field to the other. This special volume highlights this convergence of reliability modeling and risk analysis, that forms the core of the science of analyzing hazards and its applications to various fields. Most of papers appearing in this volume were selected from the presentations given at the 7th International Conference on Mathematical Methods in Reliability (MMR2011), held in Beijing, China, June 20–24, 2011. The conference was co-chaired by Yiming Wei (Beijing Institute of Technology, China), N. Balakrishnan (McMaster, Canada), and N. Limnios (UTC, France). The papers have been significantly extended from the conference presentations and all papers have been refereed according to the standards of Annals of Operations Research. The MMR2011 is the seventh in a series of international conferences on Mathematical Methods in Reliability. Since 1997, when the first of MMR conferences was held in Bucharest, Romania, the MMR has become a major international gathering of researchers from the international reliability community. The MMR conferences intend to serve as a forum for discussing fundamental issues and recent advances in reliability theory and risk analysis methods, as well as their applications, and have attracted an increasing number of participants from every continent in the world. The Beijing conference focused on all aspects

Asymptotic analysis of simultaneous damages in spatial Boolean models

A notion of the positive spatial association is introduced in this paper to analyze spatial dependence of Boolean models with the focus on estimating the long-range spatial dependence. The explicit tail estimates for probabilities of simultaneous damage to two distant spatial regions are obtained using the regular variation method, and the long-range spatial covariance for the Boolean models with heavy-tailed grains is shown to decay at the power-law rate that is smaller than the tail decay rate of grains. Examples and applications to spatial reliability modeling are also discussed.

A Near-Optimal Order-Based Inventory Allocation Rule in an Assemble-To-Order System and its Applications to Resource Allocation Problems

Assemble-to-order (ATO) manufacturing strategy has taken over the more traditional make-to-stock (MTS) strategy in many high-tech firms. ATO strategy has enabled these firms to deliver customized demand timely and to benefit from risk pooling due to component commonality. However, multi-component, multi-product ATO systems pose challenging inventory management problems. In this chapter, we study the component allocation problem given a specific replenishment policy and realized customer demands. We model the problem as a general multi-dimensional knapsack problem (MDKP) and propose the primal effective capacity heuristic (PECH) as an effective and simple approximate solution procedure for this NP-hard problem. Although the heuristic is primarily designed for the component allocation problem in an ATO system, we suggest that it is a general solution method for a wide range of resource allocation problems. We demonstrate the effectiveness of the heuristic through an extensive computational study which covers problems from the literature as well as randomly generated instances of the general and 0–1 MDKP. In our study, we compare the performance of the heuristic with other approximate solution procedures from the ATO system and integer programming literature.