Narrow Results

This work investigates a new semi-online scheduling problem with lookahead. We focus on job scheduling on two identical parallel machines, where deterministic online algorithms only know the information of $k$ initial jobs (i.e., the initial-lookahead information), while the following jobs still arrive one-by-one in an over-list fashion. We consider makespan minimization as the objective. The study aims at revealing the value of knowing $k$ initial jobs, which are used to improve the competitive performance of those online algorithms without such initial-lookahead information. We provide the following findings: (1) For the scenario where the $k$ initial jobs are all the largest jobs with length $\mathrm{\Delta }$, we prove that the classical LIST algorithm is optimal with competitive ratio $(k+3)/(k+2)$; (2) For the scenario where the total length of these $k(>1)$ jobs is at least $\mathrm{\Delta }$, we show that any online algorithm has a competitive ratio at least 3/2, implying that the initial-lookahead knowledge is powerless since there exists a 3/2-competitive online algorithm without such information; (3) For the scenario where the total length of these $k(>\alpha )$ jobs is at least $\alpha \mathrm{\Delta }$ ($\alpha \ge 2$), we propose an online algorithm, named as LPT-LIST, with competitive ratio of $(\alpha +2)/(\alpha +1)$, implying that the initial-lookahead information indeed helps to improve the competitiveness of those online algorithms lacking such information.

Multi-period risk functionals assign a risk value to discrete-time stochastic processes. While convexity and monotonicity extend in straightforward manner from the single-period case, the role of information is more problematic in the multi-period situation. In this paper, we define multi-period functionals in such a way that the development of available information over time (expressed as a filtration) enters explicitly the definition of the functional. This allows to define and study the property of information monotonicity, i.e. monotonicity w.r.t. increasing filtrations. On the other hand, time consistency of valuations is a favorable property and it is well-known that this requirement essentially leads to compositions of conditional mappings. We demonstrate that generally spoken the intersection of time consistent and information monotone valuation functionals is rather sparse, although both classes alone are quite rich. In particular, the paper gives a necessary and sufficient condition for information monotonicity of additive compositions of positively homogeneous risk/acceptability mappings. Within the class of distortion functionals only compositions of expectation or essential infima are information monotone. Furthermore, we give a sufficient condition and examples for compositions of nonhomogeneous mappings exhibiting information monotonicity.

The article summarises findings from a qualitative study that was conducted in rural Uganda, East Africa. The main aim of the study was to investigate the accessibility and use of health information in the lower echelons of Primary Health Care (PHC). Women, as PHC providers in an African family, were focussed on, as well as health workers. An interview schedule that consisted of open questions and one relating to health information critical incidents was used. A holistic inductive paradigm was adopted with a grounded theory analysis. The findings highlight a model of information behaviour that was driven by the value and impact of information unlike previous information models, which have been driven by information needs. The value and effect of information on PHC was as experienced and reported by the interviewees. Implications of the study and areas for further research are highlighted.