Robust Solutions for the Resource-Constrained Project Scheduling Problem: Understanding and Improving Robustness in Partial Order Schedules produced by the Chaining algorithm

Robustness is essential for schedules if they are being executed under uncertain conditions. In this thesis we research robustness in Partial Order Schedules, which represent sets of solutions for instances of the Resource-Constrained Project Scheduling Problem. They can be generated using a greedy procedure called Chaining, which can be easily adapted to use various heuristics. We use an empirical method to gain understanding of robustness and how the chaining procedure adds to this. Based on the findings of an exploratory study we develop three models, each capturing aspects of robustness on a different level. The first model describes how a single activity is affected by various disturbances. The second model predicts how structural properties of Partial Order Schedules can reduce the effect of these disturbances. The third model describes how heuristics for the chaining procedure can influence these properties. Using experimental evaluation, we found that the model is not complete. Experimental results did conform to the expectations set by the third model, but not of the second model. We therefore suspect that it is too simplistic for accurate predictions, but since it does match earlier observations we believe it is a good starting point for further understanding.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc

Distributing flexibility to enhance robustness in task scheduling problems

Temporal scheduling problems occur naturally in many diverse application domains such as manufacturing, transportation, health and education. A scheduling problem arises if we have a set of temporal events (or variables) and some constraints on those events, and we have to find a schedule, which is an assignment of values to the variables that satisfies the constraints. The execution of schedules in practice is typically surrounded by uncertainty, so that it makes sense to assign intervals rather than fixed times to events. Such a schedule is hypothesized to be more robust to disruptions, as it leaves room for adapting the assignment of exact times to events, to disturbances occurring during execution. In previous work, we have shown how to efficiently compute an assignment of intervals to the variables in a temporal scheduling problem, that maximizes the sum of the lengths of the intervals. We empirically evaluated whether we can further improve the robustness of such a schedule by changing the distribution of intervals. In the current paper, we investigate in more detail how characteristics of the input instances affect different scheduling methods\u92 robustness properties. From this investigation, we derive three new methods for designing interval schedules, and show them to provide similar or improved robustness

Evaluation and Improvement of Laruelle-Widgrén Inverse Banzhaf Approximation

Voting is a popular way of reaching decisions in multi-agent systems. Weighted voting in particular allows different agents to have varying levels of influence on the decision taken: each agent’s vote carries a weight, and a proposal is accepted if the sum of the weights of the agents in favor of the proposal is at least equal to a given quota. Unfortunately, there is no clear and unambiguous relation between a player’s weight and the extent of her influence on the outcome of the decision making process. Different measures of ‘power’ have been proposed, such as the Banzhaf and the Shapley-Shubik indices. Here we consider the ‘inverse’ problem: given a vector of desired power indices for the players, how should we set their weights and the quota such that the players’ power in the resulting game comes as close as possible to the target vector? There has been some work on this problem, both heuristic and exact, but little is known about the approximation quality of the heuristics for this problem. The goal of this paper is to empirically evaluate the heuristic algorithm for the Inverse Banzhaf Index problem by Laruelle and Widgrén. We analyze and evaluate the intuition behind this algorithm. We found that the algorithm can not handle general inputs well, and often fails to improve inputs. It is also shown to diverge after only tens of iterations. Based on our analysis, we present three alternative extensions of the algorithm that do not alter the complexity but can result in up to a factor 6.5 improvement in solution quality.Software Computer TechnologyElectrical Engineering, Mathematics and Computer Scienc