Scheduling parallel dedicated machines with the speeding-up resource

We consider a problem of scheduling jobs on m parallel machines. The machines are dedicated, i.e., for each job the processing machine is known in advance. We mainly concentrate on the model in which at any time there is one unit of an additional resource. Any job may be assigned the resource and this reduces its processing time. A job that is given the resource uses it at each time of its processing. No two jobs are allowed to use the resource simultaneously. The objective is to minimize the makespan. We prove that the two-machine problem is NP-hard in the ordinary sense, describe a pseudopolynomial dynamic programming algorithm and convert it into an FPTAS. For the problem with an arbitrary number of machines we present an algorithm with a worst-case ratio close to 3/2, and close to 3, if a job can be given several units of the resource. For the problem with a fixed number of machines we give a PTAS. Virtually all algorithms rely on a certain variant of the linear knapsack problem (maximization, minimization, multiple-choice, bicriteria). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Transporting jobs through a two-machine open shop

We consider the two-machine open shop scheduling problem in which the jobs are brought to the system by a single transporter and moved between the processing machines by the same transporter. The purpose is to split the jobs into batches and to find the sequence of moves of the transporter so that the time by which the completed jobs are collected together on board the transporter is minimal. We present a 7/5-approximation algorithm. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009

Aspects of the in vitro bioactivity of hydraulic calcium (alumino)silicate cement

In response to a burgeoning interest in the prospective clinical applications of hydraulic calcium (alumino)silicate cements, the in vitro bioactivity and dissolution characteristics of a white Portland cement have been investigated. The formation of an apatite layer within 6 h of contact with simulated body fluid was attributed to the rapid dissolution of calcium hydroxide from the cement matrix and to the abundance of pre-existing Si-OH nucleation sites presented by the calcium silicate hydrate phase. A simple kinetic model has been used to describe the rate of apatite formation and an apparent pseudo-second-order rate constant for the removal of HPO42- ions frorn solultion has been calculated (k(2) = 5.8 x 10(-4) g mg(-1)). Aspects of the chemistry of hydraulic cements are also discussed with respect to their potential use in the remedial treatment of living tissue. (C) 2008 Wiley Periodicals, Inc. J Biomed Mater Res 90A: 166-174, 2009