From precedence constraint posting to partial order schedules: A CSP approach to Robust Scheduling

  • Authors:

  • Nicola Policella;Amedeo Cesta;Angelo Oddi;Stephen F. Smith

  • Affiliations:

  • ISTC-CNR - Institute for Cognitive Science and Technology, National Research Council of Italy, Italy. E-mails: {name.surname}@istc.cnr.it;ISTC-CNR - Institute for Cognitive Science and Technology, National Research Council of Italy, Italy. E-mails: {name.surname}@istc.cnr.it;ISTC-CNR - Institute for Cognitive Science and Technology, National Research Council of Italy, Italy. E-mails: {name.surname}@istc.cnr.it;The Robotics Institute, Carnegie Mellon University, USA. E-mail: sfs@cs.cmu.edu

  • Venue:
  • AI Communications - Constraint Programming for Planning and Scheduling
  • Year:
  • 2007

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Abstract

Constraint-based approaches to scheduling have typicallyformulated the problem as one of finding a consistent assignment ofstart times for each goal activity. In contrast, we are pursuing anapproach that operates with a problem formulation more akin toleast-commitment frameworks, where the objective is to postsufficient additional precedence constraints between pairs ofactivities contending for the same resources to ensure feasibilitywith respect to time and resource constraints. One noteworthycharacteristic of this Precedence Constraint Posting (PCP)approach, is that solutions generated in this way generallyencapsulate a set of feasible schedules (i.e., a solution containsthe sets of activity start times that remain consistent with postedsequencing constraints). Such solutions can offer advantages whenthere is temporal uncertainty associated with executingactivities.In this paper, we consider the problem of generating temporallyflexible schedules that possess good robustness properties. Wefirst introduce the concept of a Partial Order Schedule (POS), atype of temporally flexible schedule in which each embeddedtemporal solution is also guaranteed to be resource feasible, as atarget class of solutions that exploit flexibility in a robust way.We then present and analyze two PCP-based methods for generatingPOSs. The first method uses a pure least commitment approach, wherethe set of all possible time-feasible schedules is successivelywinnowed into a smaller resource-feasible set. The second methodalternatively utilizes a focused analysis of one possible solution,and first generates a single, resource-feasible, fixed-timesschedule. This point solution is then transformed into a POS in asecond post-processing phase. Somewhat surprisingly, this secondmethod is found to be a quite effective means of generating robustschedules.