Probabilistic analysis of an asymptotically optimal solution for the completion time variance problem

Scheduling a set of n jobs on a single machine so as to minimize the completion time variance is a well‐known NP‐hard problem. In this paper, we propose a sequence, which can be constructed in O(n log n) time, as a solution for the problem. Our primary concern is to establish the asymptotical optimality of the sequence within the framework of probabilistic analysis. Our main result is that, when the processing times are randomly and independently drawn from the same uniform distribution, the sequence is asymptotically optimal in the sense that its relative error converges to zero in probability as n increases. Other theoretical results are also derived, including: (i) When the processing times follow a symmetric structure, the problem has 2^{⌊(n−1)/2⌋} optimal sequences, which include our proposed sequence and other heuristic sequences suggested in the literature; and (ii) when these 2^{⌊(n−1)/2⌋} sequences are used as approximate solutions for a general problem, our proposed sequence yields the best approximation (in an average sense) while another sequence, which is commonly believed to be a good approximation in the literature, is interestingly the worst. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 373–398, 1999     

Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties

We examine the problem of scheduling n jobs with a common due date on a single machine. The processing time of each job is a random variable, which follows an arbitrary distribution with a known mean and a known variance. The machine is not reliable; it is subject to stochastic breakdowns. The objective is to minimize the expected sum of squared deviations of job completion times from the due date. Two versions of the problem are addressed. In the first one the due date is a given constant, whereas in the second one the due date is a decision variable. In each case, a general form of the deterministic equivalent of the stochastic scheduling problem is obtained when the counting process related to the machine uptime distribution is a generalized Poisson process. A sufficient condition is derived under which optimal sequences are V-shaped with respect to mean processing times. Other characterizations of optimal solutions are also established. Based on the optimality properties, algorithms with pseudopolynomial time complexity are proposed to solve both versions of the problem. © 1996 John Wiley & Sons, Inc.     

Multi-period airline overbooking with multiple fare classes

Consider a multi-period multi-fare class airline overbooking problem that relates to a single-leg flight. Passengers may cancel their reservations at any time, including being no-shows at flight-time. Canceling passengers receive a refund that depends on their fare class, e.g., supersaver, coach, etc. At flight-time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. A continuous state-space dynamic programming model is developed in which the state is the numbers of reservations currently on hand in each fare class. In each period, reservation requests occur in only one fare class and the fraction of reservations canceling in each class is independent of the number of reservations therein. A booking-limit policy is optimal, i.e., in each period the airline accepts reservation requests up to a booking limit if the number of initial reservations in the fare class is less than the booking limit, and declines reservation requests otherwise. The booking limits for each class depend on the numbers of reservations in the other classes. When there are two fare classes the optimal booking limits in each class decrease with the number of reservations in the other class. © 1996 John Wiley & Sons, Inc.     

基于数据分发服务的无人机任务载荷综合仿真平台研究

现代无人机在军用、民用等领域都有着越来越广泛的应用,而载荷是无人机完成特定重要任务的必要设备,对载荷设备的选型和验证是非常重要的一个环节.针对无人机载荷选型以及载荷试验过程复杂、试验周期长、试验成本高的问题,设计了一种基于数据分发服务通信技术的无人机任务载荷综合仿真平台.该平台以载荷仿真为主体,同时结合任务仿真、通信仿...     

On the solution of a stochastic bottleneck assignment problem and its variations

In this article, we study the stochastic version of the so-called bottleneck assignment problem. Our primary objective is to maximize the probability that the bottleneck value satisfies a specified target. Under general stochastic assumptions, we show that the solution in this case is easily obtained by solving a linear assignment problem. We next examine the situation where the target is to be minimized, given that the probability of satisfying the target exceeds a specified threshold. Finally, we address extensions to the original problem where a second objective is also considered.     

Inference for the maximum cell probability under multinomial sampling

This article investigates inference for p_max, the largest cell probability in multinomial trials for the case of a small to moderate number of trials. Emphasis focuses on point and interval estimation. Both frequentist and Bayesian approaches are developed. The results of extensive simulation investigation are included as well as the analysis of a set of crime data for the city of New Orleans taken from the National Crime Survey.     

Optimal clustering: A model and method

Classifying items into distinct groupings is fundamental in scientific inquiry. The objective of cluster analysis is to assign n objects to up to K mutually exclusive groups while minimizing some measure of dissimilarity among the items. Few mathematical programming approaches have been applied to these problems. Most clustering methods to date only consider lowering the amount of interaction between each observation and the group mean or median. Clustering used in information systems development to determine groupings of modules requires a model that will account for the total group interaction. We formulate a mixed-integer programming model for optimal clustering based upon scaled distance measures to account for this total group interaction. We discuss an efficient, implicit enumeration algorithm along with some implementation issues, a method for computing tight bounds for each node in the solution tree, and a small example. A computational example problem, taken from the computer-assisted process organization (CAPO) literature, is presented. Detailed computational results indicate that the method is effective for solving this type of cluster analysis problem.     

Estimation for dirichlet mixed models

Dirichlet mixed models find wide application. Estimation is usually achieved through the method of moments. Here we present an iterative hybrid algorithm for obtaining the maximum likelihood estimate employing both modified Newton-Raphson and E-M methods. This successful MLE algorithm enables calculation of a jack-knife MLE. Simulation comparison of the three estimates is provided. The MLE substantially improves upon the moments estimator particularly with increasing dimension. The jack-knife MLE in turn offers dramatic improvement over the MLE.     

Due-date assignment and early/tardy scheduling on identical parallel machines

This article examines the problem of simultaneously assigning a common due date to a set of independent jobs and scheduling them on identical parallel machines in such a way that the costs associated with the due date and with the earliness or tardiness of the jobs are minimized. We establish that, for certain values of the due-date cost, an optimal schedule for this problem is also optimal for an early/tardy scheduling problem studied by Emmons. We discuss the solution properties for the two problems, and show that both problems are NP-hard even for two machines. We further show that these problems become strongly NP-hard if the number of machines is allowed to be arbitrary. We provide a dynamic programming solution for the problems, the complexity of which indicates that the problems can be solved in pseudopolynomial time as long as the number of machines remains fixed. Finally, we present the results of a limited computational study. © 1994 John Wiley & Sons, Inc.     

Simulating nonhomogeneous poisson processes with proportional intensities

The purpose of this research is to investigate simulation algorithms for nonhomogeneous Poisson processes with proportional intensities. Two algorithmic approaches are studied: inversion and thinning. Motivated by industrial practices, the covariate vector involved in the simulation is permitted to change after every event (or observation). The algorithms are extended to permit the simulation of general nonhomogeneous Poisson processes with possible discontinuities both in baseline intensity and covariate vector. This latter extension can be used to facilitate a wide range of failure situations that can arise with repairable systems. © 1994 John Wiley & Sons, Inc.