duration uncertainty
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Currently, there is a lack of developer-friendly software tools to formally address multi-robot coordination problems and obtain robust, efficient, and predictable strategies. This paper introduces a software toolbox that encapsulates, in one single package, modeling, planning, and execution algorithms. It implements a state-of-the-art approach to representing multi-robot systems: generalized Petri nets with rewards (GSPNRs). GSPNRs enable capturing multiple robots, decision states, action execution states and respective outcomes, action duration uncertainty, and team-level objectives. We introduce a novel algorithm that simplifies the model design process as it generates a GSPNR from a topological map. We also introduce a novel execution algorithm that coordinates the multi-robot system according to a given policy. This is achieved without compromising the model compactness introduced by representing robots as indistinguishable tokens. We characterize the computational performance of the toolbox with a series of stress tests. These tests reveal a lightweight implementation that requires low CPU and memory usage. We showcase the toolbox functionalities by solving a multi-robot inspection application, where we extend GSPNRs to enable the representation of heterogeneous systems and system resources such as battery levels and counters.

Background As healthcare-related data proliferate, there is need to annotate them expertly for the purposes of personalized medicine. Crowdworking is an alternative to expensive expert labour. Annotation corresponds to diagnosis, so comparing unlabeled records to labeled ones seems more appropriate for crowdworkers without medical expertise. We modeled the comparison of a record to two other records as a triplet annotation task, and we conducted an experiment to investigate to what extend sensor-measured stress, task duration, uncertainty of the annotators and agreement among the annotators could predict annotation correctness. Materials and methods We conducted an annotation experiment on health data from a population-based study. The triplet annotation task was to decide whether an individual was more similar to a healthy one or to one with a given disorder. We used hepatic steatosis as example disorder, and described the individuals with 10 pre-selected characteristics related to this disorder. We recorded task duration, electro-dermal activity as stress indicator, and uncertainty as stated by the experiment participants (n = 29 non-experts and three experts) for 30 triplets. We built an Artificial Similarity-Based Annotator (ASBA) and compared its correctness and uncertainty to that of the experiment participants. Results We found no correlation between correctness and either of stated uncertainty, stress and task duration. Annotator agreement has not been predictive either. Notably, for some tasks, annotators agreed unanimously on an incorrect annotation. When controlling for Triplet ID, we identified significant correlations, indicating that correctness, stress levels and annotation duration depend on the task itself. Average correctness among the experiment participants was slightly lower than achieved by ASBA. Triplet annotation turned to be similarly difficult for experts as for non-experts. Conclusion Our lab experiment indicates that the task of triplet annotation must be prepared cautiously if delegated to crowdworkers. Neither certainty nor agreement among annotators should be assumed to imply correct annotation, because annotators may misjudge difficult tasks as easy and agree on incorrect annotations. Further research is needed to improve visualizations for complex tasks, to judiciously decide how much information to provide, Out-of-the-lab experiments in crowdworker setting are needed to identify appropriate designs of a human-annotation task, and to assess under what circumstances non-human annotation should be preferred.

Just like any physical system, projects have entropy that must be managed by spending energy. The entropy is the project’s tendency to move to a state of disorder (schedule delays, cost overruns), and the energy process is an inherent part of any project management methodology. In order to manage the inherent uncertainty of these projects, accurate estimates (for durations, costs, resources, …) are crucial to make informed decisions. Without these estimates, managers have to fall back to their own intuition and experience, which are undoubtedly crucial for making decisions, but are are often subject to biases and hard to quantify. This paper builds further on two published calibration methods that aim to extract data from real projects and calibrate them to better estimate the parameters for the probability distributions of activity durations. Both methods rely on the lognormal distribution model to estimate uncertainty in activity durations and perform a sequence of statistical hypothesis tests that take the possible presence of two human biases into account. Based on these two existing methods, a new so-called statistical partitioning heuristic is presented that integrates the best elements of the two methods to further improve the accuracy of estimating the distribution of activity duration uncertainty. A computational experiment has been carried out on an empirical database of 83 empirical projects. The experiment shows that the new statistical partitioning method performs at least as good as, and often better than, the two existing calibration methods. The improvement will allow a better quantification of the activity duration uncertainty, which will eventually lead to a better prediction of the project schedule and more realistic expectations about the project outcomes. Consequently, the project manager will be able to better cope with the inherent uncertainty (entropy) of projects with a minimum managerial effort (energy).

In real-world project scheduling applications, activity durations are often uncertain. Proactive scheduling can effectively cope with the duration uncertainties, by generating robust baseline solutions according to a priori stochastic knowledge. However, most of the existing proactive approaches assume that the duration uncertainty of an activity is not related to its scheduled start time, which may not hold in many real-world scenarios. In this paper, we relax this assumption by allowing the duration uncertainty to be time-dependent, which is caused by the uncertainty of whether the activity can be executed on each time slot. We propose a stochastic optimization model to find an optimal Partial-order Schedule (POS) that minimizes the expected makespan. This model can cover both the time-dependent uncertainty studied in this paper and the traditional time-independent duration uncertainty. To circumvent the underlying complexity in evaluating a given solution, we approximate the stochastic optimization model based on Sample Average Approximation (SAA). Finally, we design two efficient branch-and-bound algorithms to solve the NP-hard SAA problem. Empirical evaluation confirms that our approach can generate high-quality proactive solutions for a variety of uncertainty distributions.