Dynamic inventory management with cash flow constraints

In this article, we consider a classic dynamic inventory control problem of a self‐financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Optimum step‐stress accelerated life test plans for log‐location‐scale distributions

This article presents new tools and methods for finding optimum step‐stress accelerated life test plans. First, we present an approach to calculate the large‐sample approximate variance of the maximum likelihood estimator of a quantile of the failure time distribution at use conditions from a step‐stress accelerated life test. The approach allows for multistep stress changes and censoring for general log‐location‐scale distributions based on a cumulative exposure model. As an application of this approach, the optimum variance is studied as a function of shape parameter for both Weibull and lognormal distributions. Graphical comparisons among test plans using step‐up, step‐down, and constant‐stress patterns are also presented. The results show that depending on the values of the model parameters and quantile of interest, each of the three test plans can be preferable in terms of optimum variance. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Waiting time analysis for a queueing system with time‐limited service and exponential timer

We consider a single‐queue with exhaustive or gated time‐limited services and server vacations, in which the length of each service period at the queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes empty, whichever occurs first, and then takes vacations. The customer whose service is interrupted due to the timer expiration may be attended according to nonpreemptive or preemptive service disciplines. For the M/G/1 exhaustive/gated time‐limited service queueing system with an exponential timer and four typical preemptive/nonpreemptive service disciplines, we derive the Laplace—Stieltjes transforms and the moment formulas for waiting times and sojourn times through a unified approach, and provide some new results for these time‐limited service disciplines. © John Wiley & Sons, Inc. Naval Research Logistics 48: 638–651, 2001.     

Generating Pareto‐optimal boundary points in multiparty negotiations using constraint proposal method

In this paper a constraint proposal method is developed for computing Pareto‐optimal solutions in multiparty negotiations over continuous issues. Constraint proposal methods have been previously studied in a case where the decision set is unconstrained. Here we extend the method to situations with a constrained decision set. In the method the computation of the Pareto‐optimal solutions is decentralized so that the DMs do not have to know each others' value functions. During the procedure they have to indicate their optimal solutions on different sets of linear constraints. When the optimal solutions coincide, the common optimum is a candidate for a Pareto‐optimal point. The constraint proposal method can be used to generate either one Pareto‐optimal solution dominating the status quo solution or several Pareto‐optimal solutions. In latter case a distributive negotiation among the efficient points can be carried out afterwards. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 210–225, 2001     

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     

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     

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     

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