An algorithm is developed for sequencing jobs on a single processor in order to minimize maximum lateness, subject to ready times and due dates. The method that we develop could be classified as branch-and-bound. However, it has the unusual feature that a complete solution is associated with each node of the enumeration tree.

The branch-and-bound technique has been applied to the three machine flow shop problem where the objective is to minimize makespan. A new method of obtaining the bound has been developed. Rules for ordering the machines and listing the jobs prior to application of the algorithm have been proposed. Computational results are given for a large number of job sets up to 10 jobs, and for a few cases up to 45 jobs.

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A family of algorithms is described for finding optimum schedules for job-shops. The algorithms are of a branch and bound type but have a complete schedule associated with each node of the search tree. Branching from nodes is based on important conflicts in the schedule. Some results are provided.production/scheduling: job shop, deterministic

A number of interval sorption experiments have been made and analyzed, assuming Fick's law; diffusion coefficients were derived. These coefficient have been used to predict the behavior in integral sorption; the disagreement between prediction and experiment is discussed. Integral sorption experiments have also been carried out on horse hairs of various diameters to trace the influence of diameter on the sorption rate. GeneralThe general shape of the'water sorption curve by wcx~l for small changes of relative humidity is well known I 1], 22 ~ ; it is very similar to those for water in cethnoso 18, 20) and for organic vapors in cellulose acetate 2 ~ . These curves may best he doscrihed in terms of a two-stage sorption process in which the first stage corresponds to H irkian diffusion and the second stage to a further uptake of sorhate the rate of which is not controlled ltv diffusion hut hy a molecular relaxation process of the sorbent.The exact nature of this relaxation process is not yet fully understood, although an approximate calcutation 121 has shown that it may he due to the relaxation of the elastic strain imposed on the polymer network 1>v the volume swotting accompanying the firat stage of sorption.In an attempt to analyze the observed kinetics of water sorption by wool, perhaps the most outstanding feature which requires explanation is the difference in the form of the uptake curves for small and large steps in relative hunndity. In the absence of a more appropriate theory, an analysis in terms of Fick's law has to 1>e undertaken. It has been shown by Crank 151 that, at least yualitativelv, the major characteristics of the sorption behavior of many polymer systems can be explained in terms of 1: ick's s law provided the diffusion coefficient is made a function of (a) the concentration, (b) I the time. and (c) the strain set up in the sorbent.The only available data for diffusion coemcients which may be applicable to the wool-water systemhave been reported hy King 17 J for horn keratin using a steady-state permeability method. King found that the steady-state diffusion coefbcient was a function of the concentration of the water in the keratin and published the curve relating regain and diffusion roefhcient. L'nfortunately, the physical form of the wool fiber makes it impossibte to devise a steady-state experiment hy which the concentration dependence of the diffusion coefhrient can he measured. One is forced, therefore, to aplroximate the required conditions of the measurement hy making the step of concentration as small as possible and assuming that. over the small range used, the coefficient is constant This type of experiment, however, does not rule out time or ,train effects.The small-step sorption experiments reported here were undertaken with a twofold purpose in view: to check whether agreement could be ohtained between diffusion coefficients for wool keratin and Iving'~ published figures for horn keratin and to find to what extent the sorption and desorption curves predicted by the concentration-...