Compliance of the L5-S1 spinal unit: a comparative study between an unconstrained and a partially constrained system

A comparison between an unconstrained and a partially constrained system for in vitro biomechanical testing of the L5-S1 spinal unit was conducted. The objective was to compare the compliance and the coupling of the L5-S1 unit measured with an unconstrained and a partially constrained test for the three major physiological motions of the human spine. Very few studies have compared unconstrained and partially constrained testing systems using the same cadaveric functional spinal units (FSUs). Seven human L5-S1 units were therefore tested on both a pneumatic, unconstrained, and a servohydraulic, partially constrained system. Each FSU was tested along three motions: flexion-extension (FE), lateral bending (LB) and axial rotation (AR). The obtained kinematics on both systems is not equivalent, except for the FE case, where both motions are similar. The directions of coupled motions were similar for both tests, but their magnitudes were smaller in the partially constrained configuration. The use of a partially constrained system to characterize LB and AR of the lumbosacral FSU decreased significantly the measured stiffness of the segment. The unconstrained system is today's "gold standard" for the characterization of FSUs. The selected partially constrained method seems also to be an appropriate way to characterize FSUs for specific applications. Care should be taken using the latter method when the coupled motions are important.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

Batch scheduling in process industries: an application of resource-constrained project scheduling

The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time.