Constraint Programming for Scheduling

Our goal is to introduce the constraint programming (CP) approach within the context of scheduling. We start with an introduction to CP and its distinct technical vocabulary. We then present and illustrate a general algorithm for solving a CP problem with a simple scheduling example. Next, we review several published studies where CP has been used in scheduling problems so as to provide a feel for its applicability. We discuss the advantages of CP in modeling and solving certain types of scheduling problems. We then provide an illustration of the use of a commercial CP tool (OPL Studio) in modeling and designing a solution procedure for a classic problem in scheduling. We conclude with our speculations about the future of scheduling research using this approach

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 Constraint Programming Approach for Non-Preemptive Evacuation Scheduling

Large-scale controlled evacuations require emergency services to select evacuation routes, decide departure times, and mobilize resources to issue orders, all under strict time constraints. Existing algorithms almost always allow for preemptive evacuation schedules, which are less desirable in practice. This paper proposes, for the first time, a constraint-based scheduling model that optimizes the evacuation flow rate (number of vehicles sent at regular time intervals) and evacuation phasing of widely populated areas, while ensuring a nonpreemptive evacuation for each residential zone. Two optimization objectives are considered: (1) to maximize the number of evacuees reaching safety and (2) to minimize the overall duration of the evacuation. Preliminary results on a set of real-world instances show that the approach can produce, within a few seconds, a non-preemptive evacuation schedule which is either optimal or at most 6% away of the optimal preemptive solution.Comment: Submitted to the 21st International Conference on Principles and Practice of Constraint Programming (CP 2015). 15 pages + 1 reference pag

Clustering and scheduling maintenance tasks over time

We report results on a maintenance scheduling problem. The problem consists of allocating maintenance task instances to and scheduling the performances of a suitable number of maintenance packages. The number of maintenance packages is not fixed, nor is, in general, the dates or durations of their performances. A constraint programming (CP) model and solver for the problem is presented together with preliminary computational results

Robots in Retirement Homes: Applying Off-the-Shelf Planning and Scheduling to a Team of Assistive Robots

This paper investigates three different technologies for solving a planning and scheduling problem of deploying multiple robots in a retirement home environment to assist elderly residents. The models proposed make use of standard techniques and solvers developed in AI planning and scheduling, with two primary motivations. First, to find a planning and scheduling solution that we can deploy in our real-world application. Second, to evaluate planning and scheduling technology in terms of the ``model-and-solve'' functionality that forms a major research goal in both domain-independent planning and constraint programming. Seven variations of our application are studied using the following three technologies: PDDL-based planning, time-line planning and scheduling, and constraint-based scheduling. The variations address specific aspects of the problem that we believe can impact the performance of the technologies while also representing reasonable abstractions of the real world application. We evaluate the capabilities of each technology and conclude that a constraint-based scheduling approach, specifically a decomposition using constraint programming, provides the most promising results for our application. PDDL-based planning is able to find mostly low quality solutions while the timeline approach was unable to model the full problem without alterations to the solver code, thus moving away from the model-and-solve paradigm. It would be misleading to conclude that constraint programming is ``better'' than PDDL-based planning in a general sense, both because we have examined a single application and because the approaches make different assumptions about the knowledge one is allowed to embed in a model. Nonetheless, we believe our investigation is valuable for AI planning and scheduling researchers as it highlights these different modelling assumptions and provides insight into avenues for the application of AI planning and scheduling for similar robotics problems. In particular, as constraint programming has not been widely applied to robot planning and scheduling in the literature, our results suggest significant untapped potential in doing so.California Institute of Technology. Keck Institute for Space Studie

MILP formulations of cumulative constraints for railway scheduling - A comparative study

This paper introduces two Mixed Integer Linear Programming (MILP) models for railway traffic planning using a cumulative scheduling constraint and associated pre-processing filters. We compare standard solver performance for these models on three sets of problems from the railway domain and for two of them, where tasks have unitary resource consumption, we also compare them with two more conventional models. In the experiments, the solver performance of one of the cumulative models is clearly the best and is also shown to scale very well for a large scale practical railway scheduling problem