Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution

Accelerated life testing (ALT) is commonly used to obtain reliability information about a product in a timely manner. Several stress loading designs have been proposed and recent research interests have emerged concerning the development of equivalent ALT plans. Step‐stress ALT (SSALT) is one of the most commonly used stress loadings because it usually shortens the test duration and reduces the number of required test units. This article considers two fundamental questions when designing a SSALT and provides formal proofs in answer to each. Namely: (1) can a simple SSALT be designed so that it is equivalent to other stress loading designs? (2) when optimizing a multilevel SSALT, does it degenerate to a simple SSALT plan? The answers to both queries, under certain reasonable model assumptions, are shown to be a qualified YES. In addition, we provide an argument to support the rationale of a common practice in designing a SSALT, that is, setting the higher stress level as high as possible in a SSALT plan. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Formulations for dynamic lot sizing with service levels

In this article, we study deterministic dynamic lot‐sizing problems with a service‐level constraint on the total number of periods in which backlogs can occur over a finite planning horizon. We give a natural mixed integer programming formulation for the single item problem (LS‐SL‐I) and study the structure of its solution. We show that an optimal solution to this problem can be found in \begin{align*}\mathcal O(n^2\kappa)\end{align*} time, where n is the planning horizon and \begin{align*}\kappa=\mathcal O(n)\end{align*} is the maximum number of periods in which demand can be backlogged. Using the proposed shortest path algorithms, we develop alternative tight extended formulations for LS‐SL‐I and one of its relaxations, which we refer to as uncapacitated lot sizing with setups for stocks and backlogs. {We show that this relaxation also appears as a substructure in a lot‐sizing problem which limits the total amount of a period's demand met from a later period, across all periods.} We report computational results that compare the natural and extended formulations on multi‐item service‐level constrained instances. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Bayesian selling problem with partial information

We introduce an optimal stopping problem for selling an asset when the fixed but unknown distribution of successive offers is from one of n possible distributions. The initial probabilities as to which is the true distribution are given and updated in a Bayesian manner as the successive offers are observed. After receiving an offer, the seller has to decide whether to accept the offer or continue to observe the next offer. Each time an offer is observed a fixed cost is incurred. We consider both the cases where recalling a past offer is allowed and where it is not allowed. For each case, a dynamic programming model and some heuristic policies are presented. Using simulation, the performances of the heuristic methods are evaluated and upper bounds on the optimal expected return are obtained. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

面向武器装备体系组合规划的集成决策优化框架

针对当前武器装备体系组合规划存在选择空间规模大、决策目标数量多等问题,提出一种集成决策优化框架,用于组合选择和规划武器装备的发展型号、时间和数量。首先对武器装备体系组合规划问题的NP-Hard和高维多目标性质进行定量化分析和公式化描述;然后采用目标规划方法将该问题构建为双目标优化模型;再基于NSGA-II多目标演化计算方法,开发面向本问题的优化算法,求得该模型的Pareto解集合;最后通过TOPSIS方法,从Pareto解集合中求取符合决策者偏好的满意解。通过某侦察预警监视体系发展规划示例,验证了当给定经验数据和决策者偏好信息后,该框架可获得符合要求的武器装备体系组合规划方案,能够支撑武器装备体系发展论证和规划。     

A produce‐to‐stock system with advance demand information and secondary customers

We consider a manufacturer (i.e., a capacitated supplier) that produces to stock and has two classes of customers. The primary customer places orders at regular intervals of time for a random quantity, while the secondary customers request a single item at random times. At a predetermined time the manufacturer receives advance demand information regarding the order size of the primary customer. If the manufacturer is not able to fill the primary customer's demand, there is a penalty. On the other hand, serving the secondary customers results in additional profit; however, the manufacturer can refuse to serve the secondary customers in order to reserve inventory for the primary customer. We characterize the manufacturer's optimal production and stock reservation policies that maximize the manufacturer's discounted profit and the average profit per unit time. We show that these policies are threshold‐type policies, and these thresholds are monotone with respect to the primary customer's order size. Using a numerical study we provide insights into how the value of information is affected by the relative demand size of the primary and secondary customers. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Joint pricing,assortment, and inventory decisions for a retailer's product line

Consider a set of product variants that are differentiated by some secondary attributes such as flavor, color, or size. The retailer's problem is to jointly determine the set of variants to include in her product line (“assortment”), together with their prices and inventory levels, so as to maximize her expected profit. We model the consumer choice process using a multinomial logit choice model and consider a newsvendor type inventory setting. We derive the structure of the optimal assortment for some important special cases, including the case of horizontally differentiated items, and propose a dominance relationship for the general case that simplifies the search for an optimal assortment. We also discuss structural properties of the optimal prices. Finally, motivated by our analytical results, we propose a heuristic solution procedure, which is shown to be quite effective through a numerical study. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

On optimal system designs in reliability‐economics frameworks

Reliability Economics is a field that can be defined as the collection of all problems in which there is tension between the performance of systems of interest and their cost. Given such a problem, the aim is to resolve the tension through an optimization process that identifies the system which maximizes some appropriate criterion function (e.g. expected lifetime per unit cost). In this paper, we focus on coherent systems of n independent and identically distributed (iid) components and mixtures thereof, and characterize both a system's performance and cost as functions of the system's signature vector (Samaniego, IEEE Trans Reliabil (1985) 69–72). For a given family of criterion functions, a variety of optimality results are obtained for systems of arbitrary order n. Approximations are developed and justified when the underlying component distribution is unknown. Assuming the availability of an auxiliary sample of N component failure times, the asymptotic theory of L‐estimators is adapted for the purpose of establishing the consistency and asymptotic normality of the proposed estimators of the expected ordered failure times of the n components of the systems under study. These results lead to the identification of ε‐optimal systems relative to the chosen criterion function. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Dynamic lot‐sizing model with production time windows

We consider a dynamic lot‐sizing model with production time windows where each of n demands has earliest and latest production due dates and it must be satisfied during the given time window. For the case of nonspeculative cost structure, an O(nlogn) time procedure is developed and it is shown to run in O(n) when demands come in the order of latest production due dates. When the cost structure is somewhat general fixed plus linear that allows speculative motive, an optimal procedure with O(T⁴) is proposed where T is the length of a planning horizon. Finally, for the most general concave production cost structure, an optimal procedure with O(T⁵) is designed. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

On the effectiveness of top‐down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top‐down versus bottom‐up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first‐order univariate autoregressive process. Under the top‐down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom‐up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag‐1 autocorrelation of the demand time series for all the items is identical. We show that when the lag‐1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag‐1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom‐up strategy consistently outperforms the top‐down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag‐1 autocorrelation of the demand processes is not identical. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Collaboration in contingent capacities with information asymmetry

We study the optimal contracting problem between two firms collaborating on capacity investment with information asymmetry. Without a contract, system efficiency is lost due to the profit‐margin differentials among the firms, demand uncertainty, and information asymmetry. With information asymmetry, we demonstrate that the optimal capacity level is characterized by a newsvendor formula with an upward‐adjusted capacity investment cost, and no first‐best solution can be achieved. Our analysis shows that system efficiency can always be improved by the optimal contract and the improvement in system efficience is due to two factors. While the optimal contract may bring the system's capacity level closer to the first‐best capacity level, it prevents the higher‐margin firm from overinvesting and aligns the capacity‐investment decisions of the two firms. Our analysis of a special case demonstrates that, under some circumstances, both firms can benefit from the principal having better information about the agent's costs. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 54:, 2007