# Flexibility and decoupling in the simple temporal problem

IJCAI, pp. 2422-2428, 2013.

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Abstract:

In this paper we concentrate on finding a suitable metric to determine the flexibility of a Simple Temporal Problem (STP). After reviewing some flexibility metrics that have been proposed, we conclude that these metrics fail to capture the correlation between events specified in the STP, resulting in an overestimation of the available fle...More

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Introduction

- Scheduling problems occur in many diverse application domains such as transportation, process industry, health and education.
- Instead of offering a fixed schedule as a solution, one would like to compute an interval schedule, that is, an assignment of time intervals to variables, such that for every event t one can freely choose a specific time point in its interval
- Such an interval for event t indicates the flexibility the authors have w.r.t. starting t.
- The sum of such flexibilities indicates the flexibility of the interval schedule and could be used to measure its quality in this respect

Highlights

- Scheduling problems occur in many diverse application domains such as transportation, process industry, health and education
- We show that in case of Simple Temporal Problem this flexibility metric can be computed in polynomial time and offers the possibility to adapt existing schedules in O(1) time
- In this paper we have discussed an efficient method to determine the flexibility of a schedule for an Simple Temporal Network
- The advantage of the flexibility metric we propose is twofold: First of all, this metric takes into account the correlations between time events unlike previous methods that have been proposed in the literature
- Our metric does not suffer from overestimations of the flexibility in an Simple Temporal Network
- Using this improved flexibility metric allows us to disprove a rather widespread belief in the research community, i.e., that temporal decoupling of an Simple Temporal Network necessarily results in reduced flexibility: We showed that once the flexibility of an Simple Temporal Network is determined, it can be used to decide upon a temporal decoupling that does not affect the flexibility of the system

Conclusion

- The authors' metric does not suffer from overestimations of the flexibility in an STN
- Using this improved flexibility metric allows them to disprove a rather widespread belief in the research community, i.e., that temporal decoupling of an STN necessarily results in reduced flexibility: The authors showed that once the flexibility of an STN is determined, it can be used to decide upon a temporal decoupling that does not affect the flexibility of the system.
- The authors could propose more fair distributions of flexibility and evaluate their performance by comparing it to the maximally obtainable flexibility as the authors have proposed in the paper to establish the price of fairness

Summary

## Introduction:

Scheduling problems occur in many diverse application domains such as transportation, process industry, health and education.- Instead of offering a fixed schedule as a solution, one would like to compute an interval schedule, that is, an assignment of time intervals to variables, such that for every event t one can freely choose a specific time point in its interval
- Such an interval for event t indicates the flexibility the authors have w.r.t. starting t.
- The sum of such flexibilities indicates the flexibility of the interval schedule and could be used to measure its quality in this respect
## Conclusion:

The authors' metric does not suffer from overestimations of the flexibility in an STN- Using this improved flexibility metric allows them to disprove a rather widespread belief in the research community, i.e., that temporal decoupling of an STN necessarily results in reduced flexibility: The authors showed that once the flexibility of an STN is determined, it can be used to decide upon a temporal decoupling that does not affect the flexibility of the system.
- The authors could propose more fair distributions of flexibility and evaluate their performance by comparing it to the maximally obtainable flexibility as the authors have proposed in the paper to establish the price of fairness

Reference

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- [Boerkoel, 2012] J.C. Boerkoel. Distributed Approaches for Solving Constraint-based Multiagent Scheduling Problems. PhD thesis, University of Michigan, 2012.
- [Brambilla, 2010] A. Brambilla. Artificial Intelligence in Space Systems: Coordination Through Problem Decoupling in Multi Agent Planning for Space Systems. Lambert Academic Publishing, 2010.
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- [Planken et al., 2010] L. Planken, M. de Weerdt, and C. Witteveen. Optimal temporal decoupling in multiagent systems. In Proceedings AAMAS, 2010.
- [Policella et al., 2007] N. Policella, A. Cesta, A. Oddi, and S.F. Smith. From precedence constraint posting to partial order schedules: A CSP approach to robust scheduling. AI Communications, 20:163–180, 2007.

Best Paper

Best Paper of IJCAI, 2013

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