Longest processing time

The longest processing time first rule, which schedules the jobs in decreasing order of pj, is used as a heuristic for the Pm C 3j problem, which is known to be NP-hard. The importance of the makespan objective lies in the fact that a small makespan is a sign of a good job balance (partition) over the various machines. In order to find a schedule with a relatively small makespan, one orders the jobs in decreasing order of their processing times and puts the jobs on the machines, whenever one is freed, in that order. A worst-case analysis of this heuristic shows that... 

LPT rule, see Longest processing time first rule... 

Another complication in this type of scheduling problem is that the production steps are sequential R S R This means that when a reactor has finished producing a product, the separator should be available to carry out the next step in the process, and, similarly, the precipitator should be available when the separation has finished. This problem was chosen with the assunption that the separator and precipitator are always available to handle the products from the reactor, because the longest processing time for a given piece of equipment is always shorter than the shortest time for the preceding operation (4 < 7, 3 < 4). For this case, the solution to the problem is sinple because the only piece of equipment that must be considered is the reactor the reaction step is the limiting step in each process. 

TeBDE appeared at the longest exposure time (244 hours). In sand, the half-life of DeBDE exposed to UV radiation was between 12 and 37 hours. Lower PBDEs and other compounds (not specified) were found after UV radiation (Sellstrom et al. 1998). In a laboratory study of soil treated with DeBDE and exposed to UV light, a photolysis half-life of 185 hours for DeBDE was measured. The debromination process was the same as that seen for other studies. 

The transition from Eq. (38) to Eq. (40) is only possible if the relaxation process still corresponds to the longest relevant time scale in the system. 

If a mixer is to be used for reactive processes, it should be designed such that the longest mixing time scale (whether micro-, meso-, or macromixing) is significantly shorter than the characteristic time scale of the desired chemical reaction. As mentioned in Section 3, any of the time scales can be rate determining. 

Small business association Debt Longest payback time Complex and competitive process... 

The attrition of solid particles is an unavoidable consequence of the intensive solids motion resulting from the presence of bubbles in the fluidized bed. The attrition problem is especially critical in processes where the bed material needs to remain unaltered for the longest possible time, as in fluidized-bed reactors for heterogeneous catalytic gas-phase reactions. Catalyst attrition is important in the economics of such processes and may even become the critical factor. 

The predictions of the storage and loss moduli that are obtained from these relaxation processes are in excellent agreement with experiment (see Fig. 3-38). The predicted exponential dependences of the longest relaxation time and zero-shear viscosity on the arm molecular weight are also well-confirmed experimentally (Pearson and Helfand 1984 Fetters et al. 1993), as is the insensitivity of these quantities to the number of arms at fixed... 

The relaxation that is not quenched at the glass transition, which is responsible for the partial relaxation in /(, t) even at 0 above 0, is referred to as the yS relaxation. It exists because of incompletely arrested structural relaxation. The longest relaxation time Tp of this /S process is predicted by the mode-coupling theory to become singular at the critical glass concentration, according to the power law ... 

If constraint release were the only process for conformational rearrangement, the initial path motions would be the same as the chain motions of the N-element Rouse model. Equation 4 relates the longest relaxation time Ti to the diffiision coefficient for Rouse chains. The diffusion cxieffident from constraint release is gjven by Eq. 90 with Ns = N. With Eqs. 1, 2, 4 and 9,... 

Here the average is over a sample of reference times that span a region of time that is much larger than the longest coiTelation time of the process. 

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