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731.
Single- and multi-facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi-facility problems with lp distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods. 相似文献
732.
George E. Monahan 《海军后勤学研究》1986,33(2):293-307
This article examines the problem of optimally selecting from several unknown rewards when there are given alternative, costly sources of information. The optimal rule, indicating the information to be purchased and the reward to be selected, is specified as a function of the decision maker's prior probabilities regarding the value of each alternative. The rule is surprisingly complex, balancing prior beliefs, the “informativeness” of the relevant information system, and the cost of acquiring information. 相似文献
733.
Lakshman S. Thakur 《海军后勤学研究》1986,33(2):325-358
We implement a solution procedure for general convex separable programs where a series of relatively small piecewise linear programs are solved as opposed to a single large one, and where, based on bound calculations developed in [13] and [14], the ranges of linearization are systematically reduced for successive programs. The procedure inherits ε-convergence to the global optimum in a finite number of steps, but perhaps its most distinct feature is the rigorous way in which ranges containing an optimal solution are reduced from iteration to iteration. This paper describes the procedure, called successive approximation, discusses its convergence, tightness of the bounds, bound-calculation overhead, and its robustness. It presents a computer implementation to demonstrate its effectiveness for general problems and compares it (1) with the more standard separable programming approach and (2) with one of the recent augmented Lagrangian methods [10] included in a comprehensive study of nonlinear programming codes [12]. It seems clear from over 130 cases resulting from 80 distinct problems studied here that significant savings in terms of computational effort can be realized by a judicious use of the procedure, and the ease with which it can be used is appreciably increased by the robustness it shows. Moreover, for most of these problems, the advantage increases as the size, nonlinearity, and the degree of desired accuracy increase. Other important benefits include significantly smaller storage requirements, the ability to estimate the error in the current solution, and to terminate the algorithm as soon as the acceptable level of accuracy has been achieved. Problems requiring up to about 10,000 nonzero elements in their specification and about 45,000 nonzero elements in the generated separable programs resulting from up to 70 original nonlinear variables and 70 nonlinear constraints are included in the computations. 相似文献
734.
J. E. Angus 《海军后勤学研究》1986,33(3):385-390
An alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function Fi, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let Ui(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (Ui(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞. 相似文献
735.
Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A2 statistic calculated from a set zi of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A2 is recommended overall; the mean also gives good power in many situations, but can be nonconsistent. 相似文献
736.
We present variants of a convergent Lagrangean relaxation algorithm for minimizing a strictly convex separable quadratic function over a transportation polytope. The algorithm alternately solves two “subproblems,” each of which has an objective function that is defined by using Lagrange multipliers derived from the other. Motivated by the natural separation of the subproblems into independent and very easily solved “subsubproblems,” the algorithm can be interpreted as the cyclic coordinate ascent method applied to the dual problem. We exhibit our computational results for different implementations of the algorithm applied to a set of large constrained matrix problems. 相似文献
737.
In many decision-making situations, each activity that can be undertaken may have associated with it both a fixed and a variable cost. Recently, we have encountered serveral practical problems in which the fixed cost of undertaking an activity depends upon which other activities are also undertaken. To our knowledge, no existing optimization model can accomodate such a fixed cost structure. To do so, we have therefore developed a new model called the interactive fixed charge linear programming problem (IFCLP). In this paper we present and motivate problem (IFCLP), study some of its characteristics, and present a finite branch and bound algorithm for solving it. We also discuss the main properties of this algorithm. 相似文献
738.
We consider the optimal replacement problem for a fault tolerant system comprised of N components. The components are distingushable, and the state of the system is given by knowing exactly which components are operationl and which have failed. The individual component failure rates depend on the state of the entire system. We assume that the rate at which the system produces income decreases as the system deteriorates and the system replacement cost rises. Individual components cannot be replaced. We give a greedy-type algorithm that produces the replacement policy that maximizes the long-run net system income per unit time. 相似文献
739.
Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β1 in one tail and no more than β2 in the other tail with probability γ may be computed for any size sample. They are computed from X? - k1S and X? - k2S, where X? and S are the usual sample mean and standard deviation and k1 and k2 are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X? – k1S) and (X? + k2S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′. 相似文献
740.