Scheduling NonPreemptible Jobs to Minimize Peak Demand
Abstract
:1. Introduction
 An optimal dynamic programming algorithm for discretetimescale instances that utilizes branchandbound techniques that is fixedparameter tractable.
 A polynomialtime randomized algorithm based on linear programming that provides an $O\left(\frac{logn}{loglogn}\right)$approximation, where n is the number of jobs, and is the first known approximation for PDM.
 An effective and simple heuristic algorithm that can be used in either an online or offline fashion.
2. Related Work
3. Algorithms
3.1. An Optimal Dynamic Programming Algorithm
3.1.1. Configuration Lists
3.1.2. Configuration Trees
3.1.3. Dynamic Programming
3.1.4. BranchandBound Approach
3.1.5. FixedParameter Tractability
3.2. An Approximation Algorithm
3.2.1. Integer Linear Programming Formulation
 J—Set of jobs.
 ${I}_{j}$—A finite set of valid execution intervals for job $j\in J$ (an interval $[{s}_{j},{s}_{j}+{l}_{j})$ is valid for job j if and only if ${a}_{j}\le {s}_{j}$ and ${s}_{j}+{l}_{j}\le {d}_{j}$).
 ${h}_{j}$—Height of job j.
 L—Set of all left hand time points of intervals in ${\bigcup}_{j}{I}_{j}$.
 ${H}^{max}\in \mathbb{R}$—Peak demand.
 ${x}_{i,j}\in \{0,1\}$—Indicates if interval $i\in {I}_{j}$ is scheduled.
3.2.2. A Randomized Rounding Algorithm
Algorithm 1 RoundLP 

3.2.3. Continuous Timescales
3.3. A Greedy Heuristic
Algorithm 2 MinFitOnline 

Algorithm 3 MinFitOffline 

4. Experimental Results
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
 Koutsopoulos, I.; Tassiulas, L. Optimal control policies for power demand scheduling in the smart grid. IEEE J. Sel. Areas Commun. 2012, 30, 1049–1060. [Google Scholar] [CrossRef]
 Fathi, M.; Bevrani, H. Adaptive Energy Consumption Scheduling for Connected Microgrids Under Demand Uncertainty. IEEE Trans. Power Deliv. 2013, 28, 1576–1583. [Google Scholar] [CrossRef]
 Yaw, S.; Mumey, B. An Exact Algorithm for Nonpreemptive Peak Demand Job Scheduling. In Combinatorial Optimization and Applications; Lecture Notes in Computer Science; Springer: Cham, Switzerland, 2014; Volume 8881, pp. 3–12. [Google Scholar]
 Logenthiran, T.; Srinivasan, D.; Shun, T.Z. Demand Side Management in Smart Grid Using Heuristic Optimization. IEEE Trans. Smart Grid 2012, 3, 1244–1252. [Google Scholar] [CrossRef]
 Huang, Q.; Li, X.; Zhao, J.; Wu, D.; Li, X.Y. Social Networking Reduces Peak Power Consumption in Smart Grid. IEEE Trans. Smart Grid 2015, 6, 1403–1413. [Google Scholar] [CrossRef]
 Tang, S.; Huang, Q.; Li, X.Y.; Wu, D. Smoothing the energy consumption: Peak demand reduction in smart grid. In Proceedings of the 2013 IEEE INFOCOM, Turin, Italy, 14–19 April 2013; pp. 1133–1141. [Google Scholar]
 Yaw, S.; Mumey, B.; Mcdonald, E.; Lemke, J. Peak demand scheduling in the Smart Grid. In Proceedings of the 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm), Venice, Italy, 3–6 November 2014; pp. 770–775. [Google Scholar]
 Roh, H.T.; Lee, J.W. Residential demand response scheduling with multiclass appliances in the smart grid. IEEE Trans. Smart Grid 2016, 7, 94–104. [Google Scholar] [CrossRef]
 Chuzhoy, J.; Guha, S.; Khanna, S.; Naor, J. Machine minimization for scheduling jobs with interval constraints. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, Rome, Italy, 17–19 October 2004; pp. 81–90. [Google Scholar]
 Cieliebak, M.; Erlebach, T.; Hennecke, F.; Weber, B.; Widmayer, P. Scheduling with release times and deadlines on a minimum number of machines. In Exploring New Frontiers of Theoretical Informatics; IFIP International Federation for Information Processing; Levy, J.J., Mayr, E., Mitchell, J., Eds.; Springer: New York, NY, USA, 2004; Volume 155, pp. 209–222. [Google Scholar]
 Ortmann, F.G.; Ntene, N.; van Vuuren, J.H. New and improved level heuristics for the rectangular strip packing and variablesized bin packing problems. Eur. J. Oper. Res. 2010, 203, 306–315. [Google Scholar] [CrossRef]
 Gu, X.; Chen, G.; Xu, Y. AverageCase Performance Analysis of a 2D Strip Packing Algorithm—NFDH. J. Comb. Optim. 2005, 9, 19–34. [Google Scholar] [CrossRef]
 Baker, B.S.; Schwarz, J.S. Shelf algorithms for twodimensional packing problems. SIAM J. Comput. 1983, 12, 508–525. [Google Scholar] [CrossRef]
 Raghavan, P.; Tompson, C.D. Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic Proofs. Combinatorica 1987, 7, 365–374. [Google Scholar] [CrossRef]
 Raghavan, P. Probabilistic construction of deterministic algorithms: Approximating packing integer programs. In Proceedings of the 27th Annual Symposium on Foundations of Computer Science, Toronto, ON, Canada, 27–29 October 1986; pp. 10–18. [Google Scholar]
 Kolter, J.Z.; Johnson, M.J. Redd: A public data set for energy disaggregation research. In Proceedings of the SustKDD Workshop on Data Mining Applications in Sustainability, San Diego, CA, USA, 21 August 2011. [Google Scholar]
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Yaw, S.; Mumey, B. Scheduling NonPreemptible Jobs to Minimize Peak Demand. Algorithms 2017, 10, 122. https://doi.org/10.3390/a10040122
Yaw S, Mumey B. Scheduling NonPreemptible Jobs to Minimize Peak Demand. Algorithms. 2017; 10(4):122. https://doi.org/10.3390/a10040122
Chicago/Turabian StyleYaw, Sean, and Brendan Mumey. 2017. "Scheduling NonPreemptible Jobs to Minimize Peak Demand" Algorithms 10, no. 4: 122. https://doi.org/10.3390/a10040122