The resource constrained project scheduling problem with multiple crashable modes: An exact solution method

We introduce a formulation and an exact solution method for a nonpreemptive resource constrained project scheduling problem in which the duration/cost of an activity is determined by the mode selection and the duration reduction (crashing) within the mode. This problem is a natural combination of the time/cost tradeoff problem and the resource constrained project scheduling problem. It involves the determination, for each activity, of its resource requirements, the extent of crashing, and its start time so that the total project cost is minimized. We present a branch and bound procedure and report computational results with a set of 160 problems. Computational results demonstrate the effectiveness of our procedure. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 107–127, 2001     

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。     

Effectiveness of (R,Q) policies in one‐warehouse multiretailer systems with deterministic demand and backlogging

Consider a distribution system with a central warehouse and multiple retailers. Customer demand arrives at each of the retailers continuously at a constant rate. The retailers replenish their inventories from the warehouse which in turn orders from an outside supplier with unlimited stock. There are economies of scale in replenishing the inventories at both the warehouse and the retail level. Stockouts at the retailers are backlogged. The system incurs holding and backorder costs. The objective is to minimize the long‐run average total cost in the system. This paper studies the cost effectiveness of (R, Q) policies in the above system. Under an (R, Q) policy, each facility orders a fixed quantity Q from its supplier every time its inventory position reaches a reorder point R. It is shown that (R, Q) policies are at least 76% effective. Numerical examples are provided to further illustrate the cost effectiveness of (R, Q) policies. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 422–439, 2000     

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     

Optimal (τ, T) opportunistic maintenance of a k‐out‐of‐n:G system with imperfect PM and partial failure

The opportunistic maintenance of a k‐out‐of‐n:G system with imperfect preventive maintenance (PM) is studied in this paper, where partial failure is allowed. In many applications, the optimal maintenance actions for one component often depend on the states of the other components and system reliability requirements. Two new (τ, T) opportunistic maintenance models with the consideration of reliability requirements are proposed. In these two models, only minimal repairs are performed on failed components before time τ and the corrective maintenance (CM) of all failed components are combined with PM of all functioning but deteriorated components after τ; if the system survives to time T without perfect maintenance, it will be subject to PM at time T. Considering maintenance time, asymptotic system cost rate and availability are derived. The results obtained generalize and unify some previous research in this area. Application to aircraft engine maintenance is presented. © 2000 John Wiley & Sons;, Inc. Naval Research Logistics 47: 223–239, 2000     

Optimal policies for M/M/m queue with two different kinds of (N,T)‐policies

In this paper, two different kinds of (N, T)‐policies for an M/M/m queueing system are studied. The system operates only intermittently and is shut down when no customers are present any more. A fixed setup cost of K > 0 is incurred each time the system is reopened. Also, a holding cost of h > 0 per unit time is incurred for each customer present. The two (N, T)‐policies studied for this queueing system with cost structures are as follows: (1) The system is reactivated as soon as N customers are present or the waiting time of the leading customer reaches a predefined time T, and (2) the system is reactivated as soon as N customers are present or the time units after the end of the last busy period reaches a predefined time T. The equations satisfied by the optimal policy (N*, T*) for minimizing the long‐run average cost per unit time in both cases are obtained. Particularly, we obtain the explicit optimal joint policy (N*, T*) and optimal objective value for the case of a single server, the explicit optimal policy N* and optimal objective value for the case of multiple servers when only predefined customers number N is measured, and the explicit optimal policy T* and optimal objective value for the case of multiple servers when only predefined time units T is measured, respectively. These results partly extend (1) the classic N or T policy to a more practical (N, T)‐policy and (2) the conclusions obtained for single server system to a system consisting of m (m ≥ 1) servers. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 240–258, 2000     

Note: On the two‐machine no‐idle flowshop problem

In this short note we study a two‐machine flowshop scheduling problem with the additional no‐idle feasibility constraint and the total completion time criterion function. We show that one of the few papers which deal with this special problem contains incorrect claims and suggest a way how these claims can be rectified. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:353–358, 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