Flow shop scheduling with earliness,tardiness, and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding), and intermediate (work‐in‐process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two different, but closely related, Dantzig‐Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig‐Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two different lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near‐optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with different types of strongly ????‐hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near‐optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Dynamic inventory and pricing models for competing retailers

We address infinite‐horizon models for oligopolies with competing retailers under demand uncertainty. We characterize the equilibrium behavior which arises under simple wholesale pricing schemes. More specifically, we consider a periodic review, infinite‐horizon model for a two‐echelon system with a single supplier servicing a network of competing retailers. In every period, each retailer faces a random demand volume, the distribution of which depends on his own retail price as well as those charged by possibly all competing retailers. We also derive various comparative statics results regarding the impact several exogenous system parameters (e.g., cost or distributional parameters) have on the equilibrium decisions of the retailers as well as their expected profits. We show that certain monotonicity properties, engrained in folklore as well as in known inventory models for centralized systems, may break down in decentralized chains under retailer competition. Our results can be used to optimize the aggregate profits in the supply chain (i.e., those of the supplier and all retailers) by implementing a specific wholesale pricing scheme. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

基于级库存的维修器材整合供应策略研究

针对传统器材供应模式效率低的问题,借助供应链管理的思想提出了多需求点整合供应模式,并建立了基于级库存策略的整合优化模型,对成本各组成部分分析求解,得到了最优总成本对应的策略参数,其中总成本考虑了供应中心补货成本、库存持有成本、供应成本和供应延迟成本．最后通过算例与直接供应策略进行了比较,证明了整合供应策略的有效性．     

Deterministic inventory lot‐size models under inflation with shortages and deterioration for fluctuating demand

In this paper, we extend the inventory lot‐size models to allow for inflation and fluctuating demand (which is more general than constant, increasing, decreasing, and log‐concave demand patterns). We prove that the optimal replenishment schedule not only exists but is also unique. Furthermore, we show that the total cost associated with the inventory system is a convex function of the number of replenishments. Hence, the search for the optimal number of replenishments is simplified to finding a local minimum. Finally, several numerical examples are provided to illustrate the results. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 144–158, 2001     

Optimal material control in an assembly system with component commonality

Allocation of scarce common components to finished product orders is central to the performance of assembly systems. Analysis of these systems is complex, however, when the product master schedule is subject to uncertainty. In this paper, we analyze the cost—service performance of a component inventory system with correlated finished product demands, where component allocation is based on a fair shares method. Such issuing policies are used commonly in practice. We quantify the impact of component stocking policies on finished product delays due to component shortages and on product order completion rates. These results are used to determine optimal base stock levels for components, subject to constraints on finished product service (order completion rates). Our methodology can help managers of assembly systems to (1) understand the impact of their inventory management decisions on customer service, (2) achieve cost reductions by optimizing their inventory investments, and (3) evaluate supplier performance and negotiate contracts by quantifying the effect of delivery lead times on costs and customer service. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:409–429, 2001     

多级可修备件库存的生灭过程建模与优化

针对VARI-METRIC模型在低可用度下结果不准确的问题,建立基于生灭过程的任意等级、任意层级可修件库存优化模型。通过对各级站点、各类备件需求率与到达率的预测,对每个部件建立其生灭过程模型,并提出基于生灭过程的装备可用度计算方法。以整个保障系统的装备可用度为约束指标,以备件总购置费最低为目标,利用边际算法得到最优备件配置方案,并建立仿真模型对所得优化方案进行评估与调整。结合算例,以仿真结果作为检验标准,选取权威的VMETRIC软件与该解析模型在优化性能、计算精度及适用性上进行对比和说明。结果表明,无论是解析模型还是VMETRIC软件,均存在一定的适用范围,而采用解析与仿真相结合的方法无疑具有更强的适应性。     

Applying a bootstrap approach for setting reorder points in military supply systems

This paper develops and applies a nonparametric bootstrap methodology for setting inventory reorder points and a simple inequality for identifying existing reorder points that are unreasonably high. We demonstrate that an empirically based bootstrap method is both feasible and calculable for large inventories by applying it to the 1st Marine Expeditionary Force General Account, an inventory consisting of $20–30 million of stock for 10–20,000 different types of items. Further, we show that the bootstrap methodology works significantly better than the existing methodology based on mean days of supply. In fact, we demonstrate performance equivalent to the existing system with a reduced inventory at one‐half to one‐third the cost; conversely, we demonstrate significant improvement in fill rates and other inventory performance measures for an inventory of the same cost. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 459–478, 2000     

An optimal recursive method for various inventory replenishment models with increasing demand and shortages

We establish various inventory replenishment policies to solve the problem of determining the timing and number of replenishments. We then analytically compare various models, and identify the best alternative among them based on minimizing total relevant costs. Furthermore, we propose a simple and computationally efficient optimal method in a recursive fashion, and provide two examples for illustration. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 791–806, 1997     

A logistics scheduling model: Inventory cost reduction by batching

Logistics scheduling refers to the problems where the decisions of job scheduling and transportation are integrated in a single framework. In this paper, we discuss a logistics scheduling model where the raw material is delivered to the shop in batches. By making the batching and scheduling decisions simultaneously, the total inventory and batch setup cost can be reduced. We study different models on this issue, present complexity analysis and optimal algorithms, and conduct computational experiments. Some managerial insights are observed. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Emergency transshipment in decentralized dealer networks: When to send and accept transshipment requests

While there has been significant previous literature on inventory transshipment, most research has focused on the dealers' demand filling decision (when to fill transshipment requests from other dealers), ignoring the requesting decision (when to send transshipment requests to other dealers). In this paper we develop optimal inventory transshipment policies that incorporate both types of decisions. We consider a decentralized system in which the dealers are independent of the manufacturer and of each other. We first study a network consisting of a very large number of dealers. We prove that the optimal inventory and transshipment decisions for an individual dealer are controlled by threshold rationing and requesting levels. Then, in order to study the impact of transshipment among independent dealers in a smaller dealer network, we consider a decentralized two‐dealer network and use a game theoretic approach to characterize the equilibrium inventory strategies of the individual dealers. An extensive numerical study highlights the impact of the requesting decision on the dealers' equilibrium behavior in a decentralized setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006