Minimizing mean absolute deviation of completion times about a common due date

We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.     

Continuous-time markov decision processes with nonzero terminal reward

In this article we consider a continuous-time Markov decision process with a denumerable state space and nonzero terminal rewards. We first establish the necessary and sufficient optimality condition without any restriction on the cost functions. The necessary condition is derived through the Pontryagin maximum principle and the sufficient condition, by the inherent structure of the problem. We introduce a dynamic programming approximation algorithm for the finite-horizon problem. As the time between discrete points decreases, the optimal policy of the discretized problem converges to that of the continuous-time problem in the sense of weak convergence. For the infinite-horizon problem, a successive approximation method is introduced as an alternative to a policy iteration method.     

纳米级精密机械的设计及特性

最近,Queensgate仪器有限公司研制出一系列超精定位机械,它们将Queensgate的压电及纳米级传感器技术融合为具有亚纳米级定位精度能力的多轴定位控制器。在这篇论文中,将介绍和讨论在这些机械的研制中所用到的一些技术,以解释如何获得纳米或亚纳米级水平的计量能力。     

A dual criteria sequencing problem with earliness and tardiness penalties

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020     

Single batch machine scheduling with deliveries

We consider the problem of scheduling a set of n jobs on a single batch machine, where several jobs can be processed simultaneously. Each job j has a processing time p_j and a size s_j. All jobs are available for processing at time 0. The batch machine has a capacity D. Several jobs can be batched together and processed simultaneously, provided that the total size of the jobs in the batch does not exceed D. The processing time of a batch is the largest processing time among all jobs in the batch. There is a single vehicle available for delivery of the finished products to the customer, and the vehicle has capacity K. We assume that K = rD, where and r is an integer. The travel time of the vehicle is T; that is, T is the time from the manufacturer to the customer. Our goal is to find a schedule of the jobs and a delivery plan so that the service span is minimized, where the service span is the time that the last job is delivered to the customer. We show that if the jobs have identical sizes, then we can find a schedule and delivery plan in time such that the service span is minimum. If the jobs have identical processing times, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most 11/9 times the optimal service span. When the jobs have arbitrary processing times and arbitrary sizes, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most twice the optimal service span. We also derive upper bounds of the absolute worst‐case ratios in both cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 470–482, 2015     

Optimal service‐capacity allocation in a loss system

We consider a loss system with a fixed budget for servers. The system owner's problem is choosing the price, and selecting the number and quality of the servers, in order to maximize profits, subject to a budget constraint. We solve the problem with identical and different service rates as well as with preemptive and nonpreemptive policies. In addition, when the policy is preemptive, we prove the following conservation law: the distribution of the total service time for a customer entering the slowest server is hyperexponential with expectation equal to the average service rate independent of the allocation of the capacity. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 81–97, 2015     

On the uncapacitated K‐commodity network design problem with zero flow‐costs

Extending Sastry's result on the uncapacitated two‐commodity network design problem, we completely characterize the optimal solution of the uncapacitated K‐commodity network design problem with zero flow costs for the case when K = 3. By solving a set of shortest‐path problems on related graphs, we show that the optimal solutions can be found in O(n³) time when K = 3, where n is the number of nodes in the network. The algorithm depends on identifying a list of “basic patterns”; the number of basic patterns grows exponentially with K. We also show that the uncapacitated K‐commodity network design problem can be solved in O(n³) time for general K if K is fixed; otherwise, the time for solving the problem is exponential. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Inference from accelerated life tests using eyring type re-parameterizations

Least squares estimators of the parameters of the generalized Eyring Model are obtained by using data from censored life tests conducted at several accelerated environments. These estimators are obtained after establishing that the Gauss-Markov conditions for least squares estimation are satisfied. Confidence intervals for the hazard rate at use conditions are obtained after empirically showing that the logarithm of the estimate of the hazard rate at use conditions is approximately normally distributed. The coverage probabilities of the confidence intervals are also verified by a Monte Carlo experiment. The techniques are illustrated by an application to some real data.     

The fractional fixed-charge problem

Fractional fixed-charge problems arise in numerous applications, where the measure of economic performance is the time rate of earnings or profit (equivalent to an interest rate on capital investment). This paper treats the fractional objective function, after suitable transformation, as a linear parametric fixed-charge problem. It is proved, with wider generality than in the case of Hirsch and Dantzig, that some optimal solution to the generalized linear fixed-charge problem is an extreme point of the polyhedral set defined by the constraints. Furthermore, it is shown that the optimum of the generalized fractional fixed-charge problem is also a vertex of this set. The proof utilizes a suitable penalty function yielding an upper bound on the optimal value of the objective function; this is particularly useful when considering combinations of independent transportation-type networks. Finally, it is shown that the solution of a fractional fixed-charge problem is obtainable through that of a certain linear fixed-charge one.     

Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006