Pre-emption in resource-constrained project scheduling

The Resource-Constrained Project Scheduling Project (RCPSP), together with some of its extensions, has been widely studied. A fundamental assumption in this basic problem is that activities in progress are non-preemptable. Very little effort has been made to uncover the potential benefits of discrete activity pre-emption, and the papers dealing with this issue have reached the conclusion that it has little effect on project length when constant resource availability levels are defined. In this paper we show how three basic elements of many heuristics for the RCPSP – codification, serial SGS and double justification – can be adapted to deal with interruption. The paper is mainly focussed on problem 1_PRCPSP, a generalization of the RCPSP where a maximum of one interruption per activity is allowed. However, it is also shown how these three elements can be further adapted to deal with more general pre-emptive problems. Computational experiments on the standard j30 and j120 sets support the conclusion that pre-emption does help to decrease project length when compared to the no-interruption case. They also prove the usefulness of the justification in the presence of pre-emption. The justification is a RCPS technique that can be easily incorporated into a wide range of algorithms for the RCPSP, increasing their solution quality – maintaining the number of schedules calculated.     

Skilled workforce scheduling in Service Centres

The Skilled Workforce Project Scheduling Problem (SWPSP) is a complex problem of task scheduling and resource assignment that comes up in the daily management of many company Service Centres (SC). The SWPSP considers many real characteristics faced daily by the SC: client-company service quality agreements that establish maximum dates for the beginning and the end of tasks with penalties for delays, criticality levels indicating the client-priority in processing each task, generalized precedence relationships that can produce cycle structures, time period and percentage time lags and variable task durations depending on the worker executing the task. Furthermore, the SC workforce is made up of specialist workers characterised by efficiency levels showing their efficiency and speed executing the several types of tasks. Each worker has his or her own timetable.     

A Population-Based Approach to the Resource-Constrained Project Scheduling Problem

We present a population-based approach to the RCPSP. The procedure has two phases. The first phase handles the initial construction of a population of schedules and these are then evolved until high quality solutions are obtained. The evolution of the population is driven by the alternative application of an efficient improving procedure for locally improving the use of resources, and a mechanism for combining schedules that blends scatter search and path relinking characteristics. The objective of the second phase is to explore in depth those vicinities near the high quality schedules. Computational experiments on the standard j120 set, generated using ProGen, show that our algorithm produces higher quality solutions than state-of-the-art heuristics for the RCPSP in an average time of less than five seconds.     

Confinement of monopole field lines in a superconductor at T ≠ 0

We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity.     

One-dimensional metal-organic framework with unprecedented heptanuclear copper units

The reaction of copper(II) sulfate, copper(II) chloride, 3,5-diacetylamino-1,2,4-triazole, and 3-acetylamino-5-amino-1,2,4-triazole in water yields green, plate-shaped crystals of [[{Cu3(mu3-OH(1/2))L(H2O)2Cl}2{mu-Cu(H2O)2Cl2}].12H2O]n (1), where L is a new triazole-derived macrocyclic ligand. The structure of 1 consists of heptanuclear (H)OCuII(3)-CuII-CuII(3)O(H) entities linked in pairs through symmetric mu3-O...H...O-mu3 hydrogen bonds to form a double-stranded one-dimensional network. A significant overall antiferromagnetic behavior has been observed for 1.     

Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.