Random waves are generated by wind in the first half of a wind-wave flume. The latter half of the flume is kept free from wind to measure the waves unaffected by the wind and wind-generated current. The random waves in the latter area are measured with a linear array of wave gauges, and their phase velocities and coherences are determined by a usual technique of the cross-spectral analysis. The measured results are compared with the nonlinear theory of two-dimensional random waves, which has been presented in part 1 of this paper (Masuda, Kuo & Mitsuyasu 1979). Agreement between the theory and the experiment is satisfactory, and observed characteristics of the phase velocity and coherence of the spectral components can be attributed to the effects of the nonlinearity and angular dispersion of the random waves.
A theoretical framework is given, upon which to examine the dispersion relation of random gravity waves. First a weakly nonlinear theory is developed to the third-order for a statistically stationary and homogeneous field of random gravity waves. Both the spectrum of forced waves and the nonlinear dispersion relation are expressed in terms of the spectrum of free waves under the assumption of the Gaussian process for the first-order surface displacement. Next a method is proposed by which to separate each of the spectra of free and forced waves from the measured spectrum. This gives practical and powerful means of investigating the statistical structure of wind waves.
This study investigates the effect of random scrap rate on multi-item Finite Production Rate (FPR) model with multi-shipment policy. The classic FPR model considers production planning for single product, a perfect condition during the production run and a continuous inventory issuing policy. However, in real life manufacturing environments, in order to maximize machine utilization, vendors often make plan to produce m products in turn on a single machine. Also, in any given production run due to various different factors, generation of nonconforming items is inevitable. In this study, it is assumed that these defective items cannot be repaired, thus they must be scrapped with an additional cost and delivery of finished products is under a practical multiple shipment policy. Our objective is to determine an optimal common production cycle time that minimizes the long-run average cost per unit time and to investigate the effect of random scrap rate on the optimal common cycle time. Mathematical modeling is employed and renewal reward theorem is used to cope with the variable cycle length. The expected system cost for the proposed multi-item FPR model is derived and its convexity is proved. A closed-form optimal common production cycle time is obtained. A numerical example and sensitivity analysis is provided to demonstrate the practical use of the obtained results.
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