The multiplicative representation for multiple objectives optimization with an application for arms procurement

Multiple Objectives Optimization is much seen in combination with linear functions and even with linear programming, together with an adding of the objectives by using weights. With distance functions, normalization instead of weights is used. It is also possible that together with an additive direct influence of the objectives on the utility function a mutual utility of the objectives exists under the form of a multiplicative representation. A critical comment is brought on some representations of this kind. A full‐multiplicative form may offer other opportunities, which will be discussed at length in an effort to exclude weights and normalization. This theoretical approach is followed by an application for arms procurement. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 327–340, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10014     

Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines

We study the assignment of flexible servers to stations in tandem lines with service times that are not necessarily exponentially distributed. Our goal is to achieve optimal or near‐optimal throughput. For systems with infinite buffers, it is already known that the effective assignment of flexible servers is robust to the service time distributions. We provide analytical results for small systems and numerical results for larger systems that support the same conclusion for tandem lines with finite buffers. In the process, we propose server assignment heuristics that perform well for systems with different service time distributions. Our research suggests that policies known to be optimal or near‐optimal for Markovian systems are also likely to be effective when used to assign servers to tasks in non‐Markovian systems. © 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     

Analysis of an Alternative Military Healthcare Benefit Design

Abstract

The Military Compensation and Retirement Modernization Commission was established by the Congress in 2013 to perform a systematic review of military compensation to address rising costs and other trends. Their recommendation for reforming the TRICARE health care program was sweeping, and differed greatly from earlier proposals that focused on increasing beneficiary cost shares. Specifically, the commission proposed overhauling the current benefit delivery model and replacing it with a premium-based insurance model offering a menu of DoD-sponsored private health plans. The analysis presented here is based on work that supported the commission by estimating the budgetary impact of its proposed reforms. Results indicate that movement towards the premium-based model would produce an annual budgetary cost savings in the $2 billion to $4 billion range, with a best savings estimate of $3.2 billion.     

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 sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

New heuristic methods for the capacitated multi‐facility Weber problem

In this paper we consider the capacitated multi‐facility Weber problem with the Euclidean, squared Euclidean, and ?_p‐distances. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the distance between them. We first present a mixed integer linear programming approximation of the problem. We then propose new heuristic solution methods based on this approximation. Computational results on benchmark instances indicate that the new methods are both accurate and efficient. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006     

A parallel sequencing algorithm for minimizing total cost

The problem of sequencing jobs on parallel processors when jobs have different available times, due dates, penalty costs and waiting costs is considered. The processors are identical and are available when the earliest job becomes available and continuously thereafter. There is a processor cost during the period when the processor is available for processing jobs. The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs.). A proof of the algorithm and numerical results are given.     

Optimal location of a single service center of certain types

Hakimi has considered the problem of finding an optimal location for a single service center, such as a hospital or a police station. He used a graph theoretic model to represent the region being serviced. The communities are represented by the nodes while the road network is represented by the ares of the graph. In his work, the objective is one of minimizing the maximum of the shortest distances between the vertices and the service center. In the present work, the region being serviced is represented by a convex polygon and communities are spread over the entire region. The objective is to minimize the maximum of Euclidian distances between the service center and any point in the polygon. Two methods of solution presented are (i) a geometric method, and (ii) a quadratic programming formulation. Of these, the geometric method is simpler and more efficient. It is seen that for a class of problems, the geometric method is well suited and very efficient while the graph theoretic method, in general, will give only approximate solutions in spite of the increased efforts involved. But, for a different class of problems, the graph theoretic approach will be more appropriate while the geometric method will provide only approximate solutions though with ease. Finally, some feasible applications of importance are outlined and a few meaningful extensions are indicated.