The stochastic single resource service‐provision problem

The service‐provision problem described in this paper comes from an application of distributed processing in telecommunications networks. The objective is to maximize a service provider's profit from offering computational‐based services to customers. The service provider has limited capacity and must choose which of a set of software applications he would like to offer. This can be done dynamically, taking into consideration that demand for the different services is uncertain. The problem is examined in the framework of stochastic integer programming. Approximations and complexity are examined for the case when demand is described by a discrete probability distribution. For the deterministic counterpart, a fully polynomial approximation scheme is known 2 . We show that introduction of stochasticity makes the problem strongly NP‐hard, implying that the existence of such a scheme for the stochastic problem is highly unlikely. For the general case a heuristic with a worst‐case performance ratio that increases in the number of scenarios is presented. Restricting the class of problem instances in a way that many reasonable practical problem instances satisfy allows for the derivation of a heuristic with a constant worst‐case performance ratio. Worst‐case performance analysis of approximation algorithms is classical in the field of combinatorial optimization, but in stochastic programming the authors are not aware of any previous results in this direction. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems

Clustering problems are often difficult to solve due to nonlinear cost functions and complicating constraints. Set partitioning formulations can help overcome these challenges, but at the cost of a very large number of variables. Therefore, techniques such as delayed column generation must be used to solve these large integer programs. The underlying pricing problem can suffer from the same challenges (non‐linear cost, complicating constraints) as the original problem, however, making a mathematical programming approach intractable. Motivated by a real‐world problem in printed circuit board (PCB) manufacturing, we develop a search‐based algorithm (Rank‐Cluster‐and‐Prune) as an alternative, present computational results for the PCB problem to demonstrate the tractability of our approach, and identify a broader class of clustering problems for which this approach can be used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

On the exponentially weighted moving variance

MacGregor and Harris (J Quality Technol 25 (1993) 106–118) proposed the exponentially weighted mean squared deviation (EWMS) and the exponentially weighted moving variance (EWMV) charts as ways of monitoring process variability. These two charts are particularly useful for individual observations where no estimate of variability is available from replicates. However, the control charts derived by using the approximate distributions of the EWMS and EWMV statistics are difficult to interpret in terms of the average run length (ARL). Furthermore, both control charting schemes are biased procedures. In this article, we propose two new control charts by applying a normal approximation to the distributions of the logarithms of the weighted sum of chi squared random variables, which are respectively functions of the EWMS and EWMV statistics. These new control charts are easy to interpret in terms of the ARL. On the basis of the simulation studies, we demonstrate that the proposed charts are superior to the EWMS and EWMV charts and they both are nearly unbiased for the commonly used smoothing constants. We also compare the performance of the proposed charts with that of the change point (CP) CUSUM chart of Acosta‐Mejia (1995). The design of the proposed control charts is discussed. An example is also given to illustrate the applicability of the proposed control charts. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

A branch‐and‐cut algorithm for the nonpreemptive swapping problem

In the Swapping Problem (SP), we are given a complete graph, a set of object types, and a vehicle of unit capacity. An initial state specifies the object type currently located at each vertex (at most one type per vertex). A final state describes where these object types must be repositioned. In general, there exist several identical objects for a given object type, yielding multiple possible destinations for each object. The SP consists of finding a shortest vehicle route starting and ending at an arbitrary vertex, in such a way that each object is repositioned in its final state. This article exhibits some structural properties of optimal solutions and proposes a branch‐and‐cut algorithm based on a 0‐1 formulation of the problem. Computational results on random instances containing up to 200 vertices and eight object types are reported. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Sojourn times in G/M/1 fork‐join networks

We consider a processing network in which jobs arrive at a fork‐node according to a renewal process. Each job requires the completion of m tasks, which are instantaneously assigned by the fork‐node to m task‐processing nodes that operate like G/M/1 queueing stations. The job is completed when all of its m tasks are finished. The sojourn time (or response time) of a job in this G/M/1 fork‐join network is the total time it takes to complete the m tasks. Our main result is a closed‐form approximation of the sojourn‐time distribution of a job that arrives in equilibrium. This is obtained by the use of bounds, properties of D/M/1 and M/M/1 fork‐join networks, and exploratory simulations. Statistical tests show that our approximation distributions are good fits for the sojourn‐time distributions obtained from simulations. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Bayesian enhanced decision making for deteriorating repairable systems with preventive maintenance

Since a system and its components usually deteriorate with age, preventive maintenance (PM) is often performed to restore or keep the function of a system in a good state. Furthermore, PM is capable of improving the health condition of the system and thus prolongs its effective age. There has been a vast amount of research to find optimal PM policies for deteriorating repairable systems. However, such decisions involve numerous uncertainties and the analyses are typically difficult to perform because of the scarcity of data. It is therefore important to make use of all information in an efficient way. In this article, a Bayesian decision model is developed to determine the optimal number of PM actions for systems which are maintained according to a periodic PM policy. A non‐homogeneous Poisson process with a power law failure intensity is used to describe the deteriorating behavior of the repairable system. It is assumed that the status of the system after a PM is somewhere between as good as new for a perfect repair and as good as old for a minimal repair, and for failures between two preventive maintenances, the system undergoes minimal repairs. Finally, a numerical example is given and the results of the proposed approach are discussed after performing sensitivity analysis. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Steady‐state diffusion approximations for discrete‐time queue in hospital inpatient flow management

In this article, we analyze a discrete‐time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count has no explicit form and is difficult to compute in certain parameter regimes. Using the Stein's method framework, we identify a continuous random variable to approximate the steady‐state customer count. The continuous random variable corresponds to the stationary distribution of a diffusion process with state‐dependent diffusion coefficients. We characterize the error bounds of this approximation under a variety of system load conditions—from lightly loaded to heavily loaded. We also identify the critical role that the service rate plays in the convergence rate of the error bounds. We perform extensive numerical experiments to support the theoretical findings and to demonstrate the approximation quality. In particular, we show that our approximation performs better than those based on constant diffusion coefficients when the number of servers is small, which is relevant to decision making in a single hospital ward.     

舰炮一维修正弹校正诸元误差和预测误差试射

由于工作原理不同,舰炮使用传统无控弹试射方法不适用于一维弹道修正弹。分析了舰炮使用一维弹道修正弹射击误差构成和试射的必要性,提出了一维弹道修正弹校正射击诸元误差和预测误差试射新方法。首先通过分析对海射击以实际观测弹着水柱与提前点偏差作为发射诸元误差的精度,以及以预测弹着落点与实际观测弹着水柱偏差作为预测误差的精度,提出了求取诸元误差和预测误差的方法,论证了试射发数;然后从距离上和方向上校正诸元误差和预测误差。假设各误差值,通过仿真计算表明,按新方法试射能够显著提高射击精度。     

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of single‐commodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worst‐case cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worst‐case cost using budgeted uncertainty sets. We develop cutting‐plane algorithms for solving the mixed‐integer nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and real‐world networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154–173, 2017     

Many‐server loss models with non‐poisson time‐varying arrivals

This article proposes an approximation for the blocking probability in a many‐server loss model with a non‐Poisson time‐varying arrival process and flexible staffing (number of servers) and shows that it can be used to set staffing levels to stabilize the time‐varying blocking probability at a target level. Because the blocking probabilities necessarily change dramatically after each staffing change, we randomize the time of each staffing change about the planned time. We apply simulation to show that (i) the blocking probabilities cannot be stabilized without some form of randomization, (ii) the new staffing algorithm with randomiation can stabilize blocking probabilities at target levels and (iii) the required staffing can be quite different when the Poisson assumption is dropped. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 177–202, 2017