A global constraint for total weighted completion time for cumulative resources

The criterion of total weighted completion time occurs as a sub-problem of combinatorial optimization problems in such diverse areas as scheduling, container loading and storage assignment in warehouses. These applications often necessitate considering a rich set of requirements and preferences, which makes constraint programming (CP) an effective modeling and solving approach. On the other hand, basic CP techniques can be inefficient in solving models that require inference over sum type expressions. In this paper, we address increasing the solution efficiency of constraint-based approaches to cumulative resource scheduling with the above criterion. Extending previous results for unary capacity resources, we define the COMPLETIONm global constraint for propagating the total weighted completion time of activities that require the same cumulative resource. We present empirical results in two different problem domains: scheduling a single cumulative resource, and container loading with constraints on the location of the center of gravity. In both domains, the proposed constraint propagation algorithm out-performs existing propagation techniques

The energy scheduling problem: Industrial case-study and constraint propagation techniques

This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem,the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search.Finally,computational results are provided

Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

A tabu search procedure for generating robust project baseline schedules under stochastic resource availabilities.

The majority of research efforts in project scheduling assume a static and deterministic environment with complete information. In practice, however, these assumptions will hardly, if ever, be satisfied. Proactive scheduling aims at the generation of robust baseline schedules that are as much as possible protected against anticipated disruptions that may occur during project execution. In this paper, we focus on disruptions that may be caused by stochastic resource availabilities and aim at generating stable baseline schedules, where the solution robustness (stability) of the baseline schedule is measured by the weighted deviation between the planned and the actually realized activity starting times during project execution. We present a tabu search procedure that operates on a surrogate free slack based objective function. The effectiveness of the procedure is demonstrated by extensive computational results obtained on a set of randomly generated test instances.

A tabu search procedure for developing robust predicitive project schedules.

Proactive scheduling aims at the generation of robust baseline schedules that are as much as possible protected against disruptions that may occur during project execution. In this paper, we focus on disruptions caused by stochastic resource availabilities and aim at generating stable baseline schedules. A schedule’s robustness (stability) is measured by the weighted deviation between the planned and the actually realized activity starting times during project execution. We present a tabu search procedure that operates on a surrogate, free slack based objective function. Its effectiveness is demonstrated by extensive computational results obtained on a set of randomly generated test instances.Project scheduling; Robustness; Proactive; Stability;

Exact and suboptimal reactive strategies for resource-constrained project scheduling with uncertain resource availabilities.

In order to cope with the uncertainty inherent in practical project management, proactive and/or reactive strategies can be used. Proactive strategies try to anticipate future disruptions by incorporating slack time or excess resource availability into the schedule, whereas reactive strategies react after a disruption happened and try to revert to a feasible schedule. Traditionally, reactive approaches have focused on obtaining a good schedule with respect to the original objective function or a schedule that deviates as little as possible from the baseline schedule. In this paper, we present various approaches, exact as well as heuristic, for optimizing the latter objective and thus encouraging schedule stability. Furthermore, in contrast to traditional rescheduling algorithms, we present a new heuristic that also takes future uncertainty into account when repairing the schedule. We consider a variant of the resource- constrained project scheduling problem in which the uncertainty is modeled by means of unexpected resource breakdowns. The results of an extensive computational experiment are given to compare the performance of the proposed strategies.Schedule stability; Stability; Algorithms; Heuristic; Uncertainty; Project scheduling; Scheduling; Performance; Strategy; Order; Project management; Management; Time;

Learning Scheduling Algorithms for Data Processing Clusters

Efficiently scheduling data processing jobs on distributed compute clusters requires complex algorithms. Current systems, however, use simple generalized heuristics and ignore workload characteristics, since developing and tuning a scheduling policy for each workload is infeasible. In this paper, we show that modern machine learning techniques can generate highly-efficient policies automatically. Decima uses reinforcement learning (RL) and neural networks to learn workload-specific scheduling algorithms without any human instruction beyond a high-level objective such as minimizing average job completion time. Off-the-shelf RL techniques, however, cannot handle the complexity and scale of the scheduling problem. To build Decima, we had to develop new representations for jobs' dependency graphs, design scalable RL models, and invent RL training methods for dealing with continuous stochastic job arrivals. Our prototype integration with Spark on a 25-node cluster shows that Decima improves the average job completion time over hand-tuned scheduling heuristics by at least 21%, achieving up to 2x improvement during periods of high cluster load

SELFISHMIGRATE: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online \emph{non-clairvoyant} setting. In this problem, a set of jobs $J$ arrive over time to be scheduled on a set of $M$ machines. Each job $j$ has processing length $p_j$, weight $w_j$, and is processed at a rate of $\ell_{ij}$ when scheduled on machine $i$. The online scheduler knows the values of $w_j$ and $\ell_{ij}$ upon arrival of the job, but is not aware of the quantity $p_j$. We present the {\em first} online algorithm that is {\em scalable} ((1+\eps)-speed $O(\frac{1}{\epsilon^2})$-competitive for any constant \eps > 0) for the total weighted flow-time objective. No non-trivial results were known for this setting, except for the most basic case of identical machines. Our result resolves a major open problem in online scheduling theory. Moreover, we also show that no job needs more than a logarithmic number of migrations. We further extend our result and give a scalable algorithm for the objective of minimizing total weighted flow-time plus energy cost for the case of unrelated machines and obtain a scalable algorithm. The key algorithmic idea is to let jobs migrate selfishly until they converge to an equilibrium. Towards this end, we define a game where each job's utility which is closely tied to the instantaneous increase in the objective the job is responsible for, and each machine declares a policy that assigns priorities to jobs based on when they migrate to it, and the execution speeds. This has a spirit similar to coordination mechanisms that attempt to achieve near optimum welfare in the presence of selfish agents (jobs). To the best our knowledge, this is the first work that demonstrates the usefulness of ideas from coordination mechanisms and Nash equilibria for designing and analyzing online algorithms

Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities.

Research concerning project planning under uncertainty has primarily focused on the stochastic resource-constrained project scheduling problem (stochastic RCPSP), an extension of the basic CPSP, in which the assumption of deterministic activity durations is dropped. In this paper, we introduce a new variant of the RCPSP for which the uncertainty is modeled by means of resource availabilities that are subject to unforeseen breakdowns. Our objective is to build a robust schedule that meets the project due date and minimizes the schedule instability cost, defined as the expected weighted sum of the absolute deviations between the planned and actually realized activity starting times during project execution. We describe how stochastic resource breakdowns can be modeled, which reaction is recommended when are source infeasibility occurs due to a breakdown and how one can protect the initial schedule from the adverse effects of potential breakdowns.