The Price of Anarchy for Minsum Related Machine Scheduling

We address the classical uniformly related machine scheduling problem with minsum objective. The problem is solvable in polynomial time by the algorithm of Horowitz and Sahni. In that solution, each machine sequences its jobs shortest first. However when jobs may choose the machine on which they are processed, while keeping the same sequencing rule per machine, the resulting Nash equilibria are in general not optimal. The price of anarchy measures this optimality gap. By means of a new characterization of the optimal solution, we show that the price of anarchy in this setting is bounded from above by 2. We also give a lower bound of e/(e-1). This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem, where the price of anarchy equals 4. Interestingly, as Nash equilibria coincide with shortest processing time first (SPT) schedules, the same bounds hold for SPT schedules. Thereby, our work also fills a gap in the literature

Artificial Intelligence techniques to support cognitive rehabilitation

In recent years, the Guttmann Institute has incorporated an intelligent assistant as a predicted and personalized decision support system (PPDSS). This PPDSS helps plan rehabilitation sessions for patients suffering from acquired brain injury (ABI). Results show questionable planning when comparing patient profiles and their assigned tasks. The distribution of percentage of effort does not perfectly match the distribution of the cognitive profile. This paper provides a thorough analysis of the patient profiles, showing that a patient’s initial profile and the task execution scores during their first few sessions can be used to better predict their final improvement, to a certain degree of accuracy. Furthermore, results show that more executions of tasks does not automatically lead to improvement. Practice does not seem to make perfect. The proposed technique involves the incorporation of task-weights in the new scheduler

Grenswaarden voor het N- en P-gehalte in vaste mest

The variation and limiting values of the N and P content of solid livestock manure were determined from the composition of manure that was transported from 2008 to 2010 as registered by the Dutch Regulation Service. The realibility of the data was evaluated on the basis of N- and P excreted by livestock and manure volumes

"Jo treballo els meus fantasmes". Entrevista a Joan Prat

En aquesta ocasió el Projecte Entrevistes2 ha sortit més enllà de les parets de la UAB per arribar-se fins a Tarragona, on ha entrevistat el catedràtic recent jubilat de la Universitat Rovira i Virgili, el Dr. Joan Prat. A través de l'agradable conversa que vam mantenir amb ell, el professor Prat ens explicà els seus inicis en l'antropologia, els temes que han marcat la seva trajectòria intel·lectual i la seva visió general de la disciplina. Però paral·lelament, al llarg de la seva biografia apareix també el relat de com foren els inicis de l'antropologia a Catalunya. I més específicament, com es generà i desenvolupà l'actual nucli de potent creació intel·lectual i de recerca antropològica que existeix a la URV.En esta ocasión, el Projecte Entrevistes3 se ha desplazado más allá del marco de la UAB para ir hasta Tarragona, donde ha entrevistado al catedrático recién jubilado de la Universitat Rovira i Virgili, el Dr. Joan Prat. En la agradable conversación que mantuvimos con él, el profesor Prat nos explicó sus inicios en la antropología, los temas que han marcado su trayectoria intelectual, y su visión general de la disciplina. Paralelamente al relato biográfico descubrimos también los inicios de la antropología en Cataluña. Y más específicamente, como se generó y desarrolló el actual núcleo de potente creación intelectual y de investigación antropológica que se halla en la URV

Decomposition algorithm for the single machine scheduling polytope

Given an $n$-vector $p$ of processing times of jobs, the single machine scheduling polytope $C$ arises as the convex hull of completion times of jobs when these are scheduled without idle time on a single machine. Given a point (x\ud in C), Carathéodory's theorem implies that $x$ can be written as convex combination of at most $n$ vertices of $C$. We show that this convex combination can be computed from $x$ and $p$ in time O(n2), which is linear in the naive encoding of the output. We obtain this result using essentially two ingredients. First, we build on the fact that the scheduling polytope is a zonotope. Therefore, all of its faces are centrally symmetric. Second, instead of $C$, we consider the polytope $Q$ of half times and its barycentric subdivision. We show that the subpolytopes of this barycentric subdivison of $Q$ have a simple, linear description. The final decomposition algorithm is in fact an implementation of an algorithm proposed by Grötschel, Lovász, and Schrijver applied to one of these subpolytopes

Kunstmestvervangers onderzocht; Monitoring installaties

Onderzoek naar installaties die worden ingezet bij de verwerking van mes

A QPTAS for the General Scheduling Problem with Identical Release Dates

The General Scheduling Problem (GSP) generalizes scheduling problems with sum of cost objectives such as weighted flow time and weighted tardiness. Given a set of jobs with processing times, release dates, and job dependent cost functions, we seek to find a minimum cost preemptive schedule on a single machine. The best known algorithm for this problem and also for weighted flow time/tardiness is an O(loglog P)-approximation (where P denotes the range of the job processing times), while the best lower bound shows only strong NP-hardness. When release dates are identical there is also a gap: the problem remains strongly NP-hard and the best known approximation algorithm has a ratio of e+epsilon (running in quasi-polynomial time). We reduce the latter gap by giving a QPTAS if the numbers in the input are quasi-polynomially bounded, ruling out the existence of an APX-hardness proof unless NPsubseteq DTIME(2^polylog(n)). Our techniques are based on the QPTAS known for the UFP-Cover problem, a particular case of GSP where we must pick a subset of intervals (jobs) on the real line with associated heights and costs. If an interval is selected, its height will help cover a given demand on any point contained within the interval. We reduce our problem to a generalization of UFP-Cover and use a sophisticated divide-and-conquer procedure with interdependent non-symmetric subproblems. We also present a pseudo-polynomial time approximation scheme for two variants of UFP-Cover. For the case of agreeable intervals we give an algorithm based on a new dynamic programming approach which might be useful for other problems of this type. The second one is a resource augmentation setting where we are allowed to slightly enlarge each interval

LevensCyclusAnalyse (LCA) pilot mineralenconcentraten = Life Cycle Assessment (LCA) mineral concentrates pilot

This study assessed the change in the environmental impact of producing and using the end products, including mineral concentrate, from several pilot facilities as mineral fertilizer and substrate for anaerobic digestion. The LCA methodology was applied to assess the environmental consequences of four pig and dairy cattle slurry scenario’s. The scenarios were compared to a reference. Results showed that no mineral fertilizer was replaced in the scenarios. Without anaerobic digestion, no change in the environmental performance was observed for fattening pig slurry. Digestion reduced greenhouse gas emissions and fossil energy use. The sensitivity analysis showed higher ammonia and particulate matter emissions in all scenarios when processing more manure than only a surplus