The building evacuation problem with shared information

In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP‐hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real‐world network representing a four‐story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Approximation results for min‐max path cover problems in vehicle routing

This article studies a min‐max path cover problem, which is to determine a set of paths for k capacitated vehicles to service all the customers in a given weighted graph so that the largest path cost is minimized. The problem has wide applications in vehicle routing, especially when the minimization of the latest service completion time is a critical performance measure. We have analyzed four typical variants of this problem, where the vehicles have either unlimited or limited capacities, and they start from either a given depot or any depot of a given depot set. We have developed approximation algorithms for these four variants, which achieve approximation ratios of max{3 ‐ 2/k,2}, 5, max{5 ‐ 2/k,4}, and 7, respectively. We have also analyzed the approximation hardness of these variants by showing that, unless P = NP , it is impossible for them to achieve approximation ratios less than 4/3, 3/2, 3/2, and 2, respectively. We have further extended the techniques and results developed for this problem to other min‐max vehicle routing problems.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Mean residual life of coherent systems consisting of multiple types of dependent components

Mean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components’ lifetimes are also defined and studied.     

Nonperiodic preventive maintenance for repairable systems

As a complex system with multiple components usually deteriorates with age, preventive maintenance (PM) is often performed to keep the system functioning in a good state to prolong its effective age. In this study, a nonhomogeneous Poisson process with a power law failure intensity is used to describe the deterioration of a repairable system, and the optimal nonperiodic PM schedule can be determined to minimize the expected total cost per unit time. However, since the determination of such optimal PM policies may involve numerous uncertainties, which typically make the analyses difficult to perform because of the scarcity of data, a Bayesian decision model, which utilizes all available information effectively, is also proposed for determining the optimal PM strategies. A numerical example with a real failure data set is used to illustrate the effectiveness of the proposed approach. The results show that the optimal schedules derived by Bayesian approach are relatively more conservative than that for non‐Bayesian approach because of the uncertainty of the intensity function, and if the intensity function are updated using the collected data set, which indicates more severe deterioration than the prior belief, replacing the entire system instead of frequent PM activities before serious deterioration is suggested. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Dynamic server assignment policies for assembly‐type queues with flexible servers

We seek dynamic server assignment policies in finite‐capacity queueing systems with flexible and collaborative servers, which involve an assembly and/or a disassembly operation. The objective is to maximize the steady‐state throughput. We completely characterize the optimal policy for a Markovian system with two servers, two feeder stations, and instantaneous assembly and disassembly operations. This optimal policy allocates one server per station unless one of the stations is blocked, in which case both servers work at the unblocked station. For Markovian systems with three stations and instantaneous assembly and/or disassembly operations, we consider similar policies that move a server away from his/her “primary” station only when that station is blocked or starving. We determine the optimal assignment of each server whose primary station is blocked or starving in systems with three stations and zero buffers, by formulating the problem as a Markov decision process. Using this optimal assignment, we develop heuristic policies for systems with three or more stations and positive buffers, and show by means of a numerical study that these policies provide near‐optimal throughput. Furthermore, our numerical study shows that these policies developed for assembly‐type systems also work well in tandem systems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

New inequalities for finite and infinite group problems from approximate lifting

In this paper, we derive new families of facet‐defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem include two‐ and three‐slope facet‐defining inequalities as well as the first family of four‐slope facet‐defining inequalities. The new valid inequalities for the infinite group problem include families of two‐ and three‐slope extreme inequalities. These new inequalities not only illustrate the diversity of strong inequalities for the finite and infinite group problems, but also provide a large variety of new cutting planes for solving integer and mixed‐integer programming problems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Exact algorithms for scheduling multiple families of jobs on parallel machines

In many practical manufacturing environments, jobs to be processed can be divided into different families such that a setup is required whenever there is a switch from processing a job of one family to another job of a different family. The time for setup could be sequence independent or sequence dependent. We consider two particular scheduling problems relevant to such situations. In both problems, we are given a set of jobs to be processed on a set of identical parallel machines. The objective of the first problem is to minimize total weighted completion time of jobs, and that of the second problem is to minimize weighted number of tardy jobs. We propose column generation based branch and bound exact solution algorithms for the problems. Computational experiments show that the algorithms are capable of solving both problems of medium size to optimality within reasonable computational time. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 823–840, 2003.     

Nonrobustness of the normal approximation of lead‐time demand in a (Q,R) system

For computing an optimal (Q, R) or kindred inventory policy, the current literature provides mixed signals on whether or when it is safe to approximate a nonnormal lead‐time‐demand (“LTD”) distribution by a normal distribution. The first part of this paper examines this literature critically to justify why the issue warrants further investigations, while the second part presents reliable evidence showing that the system‐cost penalty for using the normal approximation can be quite serious even when the LTD‐distribution's coefficient of variation is quite low—contrary to the prevalent view of the literature. We also identify situations that will most likely lead to large system‐cost penalty. Our results indicate that, given today's technology, it is worthwhile to estimate an LTD‐distribution's shape more accurately and to compute optimal inventory policies using statistical distributions that more accurately reflect the LTD‐distributions' actual shapes. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model

Instead of measuring a Wiener degradation or performance process at predetermined time points to track degradation or performance of a product for estimating its lifetime, we propose to obtain the first‐passage times of the process over certain nonfailure thresholds. Based on only these intermediate data, we obtain the uniformly minimum variance unbiased estimator and uniformly most accurate confidence interval for the mean lifetime. For estimating the lifetime distribution function, we propose a modified maximum likelihood estimator and a new estimator and prove that, by increasing the sample size of the intermediate data, these estimators and the above‐mentioned estimator of the mean lifetime can achieve the same levels of accuracy as the estimators assuming one has failure times. Thus, our method of using only intermediate data is useful for highly reliable products when their failure times are difficult to obtain. Furthermore, we show that the proposed new estimator of the lifetime distribution function is more accurate than the standard and modified maximum likelihood estimators. We also obtain approximate confidence intervals for the lifetime distribution function and its percentiles. Finally, we use light‐emitting diodes as an example to illustrate our method and demonstrate how to validate the Wiener assumption during the testing. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008