A simple and accurate spectrophotometric method is proposed for the determination of tannins in tea and beer samples based on the reduction of iron(III) to iron(II) by tannins at 80 degrees C for 20 min. The iron(II) was then reacted with 1,10-phenanthroline at pH 4.4 to form a coloured complex. Background correction could be effected by precipitating the tannins in the sample solution twice with gelatin and kaolin. Absorbance measurements were made at 540 nm and the calibration graph was linear from 0 to 5.5 micrograms ml-1 of tannic acid with a slope of 0.213 A p.p.m.-1. The precision for the determination of tannins in a tea sample containing 9.45% of tannins was 1.8%. Most of the ingredients commonly found in tea and beer samples do not interfere with the determination. Several tea and beer samples were analysed for their tannin content using the proposed method.
In this paper, we introduce a variant of the relocation problem, which was formulated from a public house redevelopment project in Boston. In the problem of interest, given some initial resources in a common pool there is a set of jobs to be processed on a two-machine flowshop. Each job acquires a specific number of resources to start its processing and will return a number of resources to the pool at its completion. The resource consumption and resource recycle processes are performed on machine one and machine two, respectively, in a twomachine flowshop style. Abiding by the resource constraints, the problem seeks to find a feasible schedule whose makespan is minimized. In this paper, we first present NP-hardness proofs for some special cases. Three heuristic algorithms are designed to compose approximate schedules. Two lower bounds are developed and then used to test the performance of our proposed heuristics. Numerical results from computational experiments suggest that the proposed heuristics can produce quality solutions in a reasonable time.
a b s t r a c tThe paper considers makespan minimization on a single machine subject to release dates in the relocation problem, originated from a resource-constrained redevelopment project in Boston. Any job consumes a certain amount of resource from a common pool at the start of its processing and returns to the pool another amount of resource at its completion. In this sense, the type of our resource constraints extends the well-known constraints on resumable resources, where the above two amounts of resource are equal for each job. In this paper, we undertake the first complexity analysis of this problem in the case of arbitrary release dates. We develop an algorithm, based on a multi-parametric dynamic programming technique (when the number of parameters that undergo enumeration of their values in the DP-procedure can be arbitrarily large). It is shown that the algorithm runs in pseudo-polynomial time when the number m of distinct release dates is bounded by a constant. This result is shown to be tight: (1) it cannot be extended to the case when m is part of the input, since in this case the problem becomes strongly NP-hard, and (2) it cannot be strengthened up to designing a polynomial time algorithm for any constant m > 1, since the problem remains NP-hard for m = 2. A polynomial-time algorithm is designed for the special case where the overall contribution of each job to the resource pool is nonnegative. As a counterpart of this result, the case where the contributions of all jobs are negative is shown to be strongly NP-hard.
This paper investigates the talent scheduling problem in film production, which is known as rehearsal scheduling in music and dance performances. The first lower bound on the minimization of talent hold cost is based upon the outside-in branching strategy. We introduce two approaches to add extra terms for tightening the lower bound. The first approach is to formulate a maximum weighted matching problem. The second approach is to retrieve structural information and solve a maximum weighted 3-grouping problem. We make two contributions: First, our results can fathom the matrix of a given partial schedule. Second, our second approach is free from the requirement to schedule some shooting days in advance for providing anchoring information as in the other approaches, i.e., a lower bound can be computed once the input instance is given. The lower bound can fit different branching strategies. Moreover, the second contribution provides a state-of-the-art research result for this problem. Computational experiments confirm that the new bounds are much tighter than the original one.
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