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21.
Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The λj,k‐number of G and the radio number of G are respectively the minimum span among all L(j, k)‐labelings, and the minimum span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the λj,k‐number of ∏ K for pairwise relatively prime integers t1 < t2 < … < tq, t1 ≥ 2. We also show the existence of an infinite class of graphs G with radio number |V(G)| for any diameter d(G). © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005 相似文献
22.
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 相似文献
23.
We consider the integrated problem of optimally maintaining an imperfect, deteriorating sensor and the safety‐critical system it monitors. The sensor's costless observations of the binary state of the system become less informative over time. A costly full inspection may be conducted to perfectly discern the state of the system, after which the system is replaced if it is in the out‐of‐control state. In addition, a full inspection provides the opportunity to replace the sensor. We formulate the problem of adaptively scheduling full inspections and sensor replacements using a partially observable Markov decision process (POMDP) model. The objective is to minimize the total expected discounted costs associated with system operation, full inspection, system replacement, and sensor replacement. We show that the optimal policy has a threshold structure and demonstrate the value of coordinating system and sensor maintenance via numerical examples. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 399–417, 2017 相似文献
24.
In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed. 相似文献
25.
Let X1 < X2 <… < Xn denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 - exp (?xp), x > 0. Formulae for computing Cov (Xi, Xj) are well known, but they are difficult to use in practice. A simple approximation to Cov(Xi, Xj) is presented here, and its accuracy is discussed. 相似文献
26.
This paper considers the problem of computing optimal ordering policies for a product that has a life of exactly two periods when demand is random. Initially costs are charged against runouts (stockouts) and outdating (perishing). By charging outdating costs according to the expected amount of outdating one period into the future, a feasible one period model is constructed. The central theorem deals with the n-stage dynamic problem and demonstrates the appropriate cost functions are convex in the decision variable and also provides bounds on certain derivatives. The model is then generalized to include ordering and holding costs. The paper is concluded with a discussion of the infinite horizon problem. 相似文献
27.
28.
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. 相似文献
29.
The minimum storage‐time sequencing problem generalizes many well‐known problems in combinatorial optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propose a new lower bound, based on a Lagrangian relaxation, which can be computed very efficiently. To improve upon this lower bound, we employ a bundle optimization algorithm. We also show that the best bound obtainable by this approach equals the one obtainable from the linear relaxation computed on a formulation whose first Chvàtal closure equals the convex hull of all the integer solutions of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 313–331, 2001 相似文献
30.
We develop a simple algorithm, which does not require convolutions, for computing the distribution of the residual life when the renewal process is discrete. We also analyze the algorithm for the particular case of lattice distributions, and we show how it can apply to an inventory problem. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 435–443, 1999 相似文献