A discussion on the conservatism of robust linear optimization problems

In 2004, Bertsimas and Sim proposed a robust approach that can control the degree of conservatism by applying a limitation Γ to the maximum number of parameters that are allowed to change. However, the robust approach can become extremely conservative even when Γ is relatively small. In this paper, we provide a theoretical analysis to explain why this extreme conservatism occurs. We further point out that the robust approach does not reach an extremely conservative state when Γ is less than k, where k is the number of nonzero components of the optimal solution of the extremely conservative robust approach. This research also shows that care must be taken when adjusting the value of Γ to control the degree of conservatism because the approach may result in greater conservatism than was intended. We subsequently apply our analysis to additive combinatorial optimization problems. Finally, we illustrate our results on numerical simulations.     

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Clustered interval-censored failure time data often arises in medical studies when study subjects come from the same cluster. Furthermore, the failure time may be related to the cluster size. A simple and common approach is to simplify interval-censored data due to the lack of proper inference procedures for direct analysis. For this reason, we proposed the within-cluster resampling-based method to consider the case II interval-censored data under the additive hazards model. With-cluster resampling is simple but computationally intensive. A major advantage of the proposed approach is that the estimator can be easily implemented when the cluster size is informative. Asymptotic properties and some simulation results are provided and indicate that the proposed approach works well.     

Queueing systems with different types of server interruptions

We consider a queueing system with disruptive and non-disruptive server interruptions. Both disruptive and non-disruptive interruptions may start when there is a customer in service. The customer repeats its service after a disruptive interruption, and continues its service after a non-disruptive interruption. Using a transform approach, we obtain various performance measures such as the moments of the queue content and waiting times. We illustrate our approach by means of some numerical examples.     

An epidemiological approach to model the viral propagation of memes

An epidemiological approach is adopted to develop a model of viral meme propagation. The successful implementation in the modelling of meme spread as reflected in Internet search data shows that memes may be treated as infectious entities when modelling their propagation over time and across societies.     

A Simulation and Learning Technique for Generating Knowledge about Manufacturing Systems Behavior

One of the most important difficulties when developing knowledge based systems in manufacturing scheduling or control, is finding the required knowledge. We address here the problem of acquiring knowledge about the behavior of manufacturing systems. Learning algorithms are proposed to generate, from simulation experiments, a set of production rules. This set may be considered as a simulation meta-model, and may be used either directly by the shop manager, or inserted into a knowledge base. This approach is illustrated by the use of the learning program GENREG. It generates rules related to the behavior of a simplified flow shop when different dispatching rules are applied.     

The tolerance approach in multiobjective linear fractional programming

When solving a multiobjective programming problem by the weighted sum approach, weights represent the relative importance associated to the objectives. As these values are usually imprecise, it is important to analyze the sensitivity of the solution under possible deviations on the estimated values. In this sense, the tolerance approach provides a direct measure of how weights may vary simultaneously and independently from their estimated values while still retaining the same efficient solution. This paper provides an explicit expression to the maximum tolerance on weights in a multiobjective linear fractional programming problem when all the denominators are equal. An application is also presented to illustrate how the results may help the decision maker to choose a most satisfactory solution in a production problem.     

A note on optimal assignment of slack due-dates in single-machine scheduling

This paper extends T.C.E. Cheng's approach for optimal assignment of slack due-dates and sequencing in the single-machine shop to the case when preemption is allowed and there are precedence constraints and ready times of jobs. It is shown that under special conditions the presented algorithm may be used when preemption is not allowed.     

Robust planning of blending activities at refineries

Refinery operation planning is a complex task since refinery processes and inventories are tightly interconnected. We study refinery planning when ships are loaded with a blend of components and where arrival times of ships are uncertain. Any delay in ship arrival may result in overfull component tanks which results in less efficient blending alternatives, reduced process operations or even shut downs. We propose a planning approach where we use robust optimization as a decision tool. By using robust optimization uncertainty in arrival times is explicitly dealt with and the resulting plan and schedule will always be feasible. The approach includes a flexible way to describe and model uncertainties. To compare the robust approach with a traditional deterministic approach, we use a simulation process. Computational results from a case study and simulations show that the proposed methodology is substantially better than a deterministic approach.     

Solving arc routing problems with turn penalties

In several arc routing problems, it is necessary to take turn penalties into account when designing a solution. Traditionally, this is done through a transformation of the arc routing problem into an equivalent vertex routing problem. In this paper it is shown that a more direct approach, not resorting to such a transformation, may be more efficient.     

EMPIRICAL LIKELIHOOD APPROACH FOR LONGITUDINAL DATA WITH MISSING VALUES AND TIME-DEPENDENT COVARIATES

Missing data and time-dependent covariates often arise simultaneously in longitudinal studies, and directly applying classical approaches may result in a loss of efficiency and biased estimates. To deal with this problem, we propose weighted corrected estimating equations under the missing at random mechanism, followed by developing a shrinkage empirical likelihood estimation approach for the parameters of interest when time-dependent covariates are present. Such procedure improves efficiency over generalized estimation equations approach with working independent assumption, via combining the independent estimating equations and the extracted additional information from the estimating equations that are excluded by the independence assumption. The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries. We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart follow central chi-square distributions asymptotically when evaluated at the true parameter. The practical performance of our approach is demonstrated through numerical simulations and data analysis.     

Randomized Algorithms for Robust Stability and Guaranteed Cost Control of Stochastic Jump Parameter Systems with Uncertain Switching Policies

It has been suggested recently that the uncertainty randomization approach may offer numerical advantages when applied to robust control problems. This paper investigates new possibilities which this approach may offer in relation to the robust stability and control of stochastic systems governed by uncertain discrete-state Markov processes.This work was supported by the Australian Research Council.The author thanks Professors R. Tempo and B. Polyak for discussions concerning possible applications of the results of Refs. 9--10. Also, technical discussions with Professor R. Tempo and Dr. Y. Fujisaki during the author visit to IRITI-CNR, Torino, Italy are gratefully acknowledged.     

Spurious regression and lurking variables

We present asymptotic and finite-sample arguments to study the spurious regression problem. This problem may be solved by introducing a lurking variable in the specification even if it is merely a proxy variable. Moreover, this approach is also valid if the lurking variable is a trending mechanism, as when the spurious regression is due to nonstationarities in the variables.     

Visual Interactive (Computer) Solutions for the Travelling Salesman Problem

A visual interactive method of improving solutions for the travelling salesman problem is described. The travelling or multiple travelling salesman problem, when constraints are included, forms the core of the local delivery routing problem. The approach described in this note may be modified to give a visual interactive method of investigating practical physical distribution problem situations.     

An additive-multiplicative rates model for multivariate recurrent events with event categories missing at random

Multivariate recurrent event data arises when study subjects may experience more than one type of recurrent events. In some situations, however, although event times are always observed, event categories may be partially missing. In this paper, an additive-multiplicative rates model is proposed for the analysis of multivariate recurrent event data when event categories are missing at random. A weighted estimating equations approach is developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a model-checking technique is presented to assess the adequacy of the model. Simulation studies are conducted to evaluate the finite sample behavior of the proposed estimators, and an application to a platelet transfusion reaction study is provided.     

Optimal Policies for Multi-server Non-preemptive Priority Queues

We consider a multi-server non-preemptive queue with high and low priority customers, and a decision maker who decides when waiting customers may enter service. The goal is to minimize the mean waiting time for high-priority customers while keeping the queue stable. We use a linear programming approach to find and evaluate the performance of an asymptotically optimal policy in the setting of exponential service and inter-arrival times.     

快件配送地址变化的干扰管理模型研究

快件配送过程中客户的配送地址发生变化后,继续按初始方案进行配送将不再最优甚至不可行,此时如何快速产生应对扰动的新方案,是当前研究的难点。结合客户消费行为的相关研究手段,将客户分为敏感型客户、容忍型客户和抱怨型客户,在考虑每类客户特点的基础上,将问题的处理分为两个阶段;采用干扰管理和运筹学的相关理论与方法,在每一阶段构建干扰管理子模型并进行求解。算例实验表明:在考虑客户行为及偏好的情况下,与其他重调度方法相比,本文方法生成的应对方案更为有效。     

Wait or buy? The strategic consumer: Pricing and profit implications

Using tools from operations research, airlines have, for many years, taken a strategic approach to pricing the seats available on a particular flight based on demand forecasts and information. The result of this approach is that the same seat on the same flight is often offered at different fares at different times. Setting of these prices using yield-management approaches is a major activity for many airlines and is well studied in the literature. However, consumers are becoming increasingly aware of the existence of pricing strategies used by airlines. In addition, the availability of airline travel pricing on the Internet affords consumers the opportunity to behave more strategically when making purchase decisions. The onset of the information age makes it possible for an informed consumer or a third party, such as a travel agent, to obtain demand information similar to that used by the airlines. In particular, it is possible for consumers or travel agents to purchase historical data or to obtain it by monitoring the seats that are available at various prices for a given flight. If a consumer understands the pricing strategy and has access to demand information, he/she may decide to defer purchase of a ticket because they believe that a cheaper seat may yet become available. If consumers were to make use of this information to make such strategic purchasing decisions, what would be the impact on airline revenues? The purpose of this paper is to investigate these impacts. This work indicates that use of standard yield management approaches to pricing by airlines can result in significantly reduced revenues when buyers are using an informed and strategic approach to purchasing. Therefore, when airlines are setting or presenting prices, they should investigate the effect of strategic purchasing on their decisions.     

Multiscale deflation solvers for flow in porous media

This work describes a novel physics-based deflation preconditioner approach for solving porous media flow problems characterized by highly heterogeneous media. The approach relies on high-conductivity block solutions after rearranging the linear system coefficients into high-conductive and low condutive blocks from a given physically driven threshold value. This rearranging relies on the Hoshen-Kopelman (H-K) algorithm that is commonly used to determine percolation clusters. The resulting preconditioner may alternatively be combined with a deflation preconditioning stage. The proposed approach is coined as a physics-based 2-stage deflation preconditioner (P2SDP). Numerical experiments on different permeability distributions reveal that P2SDP is a powerful means to solve pressure systems when compared to more conventional algebraic approaches such as the incomplete Cholesky factorization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)