Most operations management textbooks use the following simple approximation to illustrate the computation of the capacity of a process: the capacity of each resource is first calculated by examining that resource in isolation; process capacity is then defined as the smallest among the capacities of the resources, that is, bottleneck capacity. In a recent paper, Gurvich and Van Mieghem [Gurvich I, Van Mieghem JA (2015) Collaboration and multitasking in networks: Architectures, bottlenecks, and capacity. Manufacturing Service Oper. Management 17(1):16–33.] show that, in the presence of collaboration and multitasking, this “bottleneck formula” can be significantly inaccurate, and they obtain a necessary and sufficient condition under which it correctly determines process capacity. We provide further clarity on determining process capacity by showing that it is hard to compute process capacity exactly and also to approximate it to within a reasonable factor. These results are based on a novel characterization, which we establish, of process capacity that relates it to the fractional chromatic number of the associated “collaboration graph.” An important implication is that it is unlikely that we can replace the bottleneck formula with a simple but close approximation of process capacity. On the positive side, we show that capacity can be efficiently computed for processes for which the collaboration graph is a perfect graph. From a practical viewpoint, our analysis for general processes results in a natural hierarchy of subclasses of policies that require an increasing amount of sophistication in implementation and management: while process capacity is the maximum long-term process rate achievable over all feasible policies, we provide a precise expression for the maximum process rate over policies in each subclass of this hierarchy, thus highlighting the trade-off between operational difficulty and the achievable process rate. The online appendix is available at https://doi.org/10.1287/msom.2017.0689 .
As a common kind of failure, crack damages account for major losses in plastic pipeline systems, which are now increasingly being used. In this study, a crack detection method for plastic pipes using piezoelectric transducers based on nonlinear ultrasonic modulation is developed. First, the low frequency and the high frequency (HF) inputs generated by two lead zirconate titanate (PZT) transducers that are bonded to the outer surface of a plastic pipe are used to induce stress waves along the pipe. For the response signal detected by another PZT, the first spectral sideband is extracted using filtering and synchronous demodulation and then modified by a proposed mean equalization method. Subsequently, by applying wavelet packet analysis, the wavelet energy of the signal can be obtained and is used as an index to determine the damaged state. Finally, a series of experiments on plastic pipes of different crack damaged states were conducted using several ways to verify their effectiveness. Experimental results show that wavelet energy of the response signal decreases as the crack grows and it is mainly determined by the HF component of the response signal, while the wavelet energy of the modified first spectral sideband tends to become larger when the crack grows. Among the investigated approaches, it is found that the first spectral sideband can detect the crack damage state effectively.
This paper aims to realize the extensive application of Internet of things technology in urban waterlogging prevention management system, and has analyzed the security requirement and security architecture of Internet of things technology, and discussed the demand of urban waterlogging prevention management system in combination with the key technology of Internet of things technology, to do the overall design and functional design well during designing of urban waterlogging prevention management system. Finally, the application process of the Internet of things technology in Chongqing waterlogging prevention management system is summarized. The application result shows that the flood control and drainage function of Chongqing is gradually improved with smooth drainage facilities; the inspection and maintenance management is gradually standardized; operation monitoring and early warning management is fully strengthened. There is visual management for emergency command and dispatch, and at the same time, the drainage pipe network assessment management can be conducted correctly.
we investigate a multidimensional system described by a set of stochastic differential equations in which the multiplicative noise is assumed to be an O-U noise. With the help of the projection operator technique, we derive an integrodifferential equation for the probability density and an approximate equation for the mean first-passage time (MFPT). Under some approximation, we obtain an effective Fokker-Planck equation and apply the equation to the single mode laser problem. The concrete calculations of MFPT are made with an important example.
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