An optimization-based decision support is proposed for trade-off analysis between makespan, a measure of service and energy consumption, a measure of sustainability in a two machine flowshop scheduling problem. A MIP model is developed and a MOGA to find Pareto fronts to support informed decision making by operations managers

Aktas, E

Mansouri, A

English

Brunel University Research Archive

MotivationProblem DefinitionMethodologyResultsSummaryReferencesTowards green scheduling: A decision supportfor trade-off analysis between makespan andenergy consumptionAfshin Mansouri 1 Emel Aktas 1 Umut Besikci 21Brunel Business School, Brunel University London, UK2Faculty of Engineering and Natural Sciences, Sabanci University, Turkey43rd DSI Annual Meeting 2012November 17-20, San Francisco, CAMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesOutline1 Motivation2 Problem Definition3 Methodology4 Results5 SummaryMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesSustainability Concerns in ManufacturingChallengesIncreasing energy costScarcity of energy, resources, and materialManufacturing sector:The third largest sector in the UK economyOver 11% of the national economyMore than 8% of total UK employmentTransition to a low-carbon economyEnergy considerations for resource efficient manufacturingOne third of world energy is consumed by manufacturingsector36% of global CO2 emissions by manufacturing sector(OECD-IEA 2007)Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesManufacturing: A Global DriverManufacturing’s global contribution (Mellows-Facer & Maer 2012)Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesCommitment of Developed EconomiesThe Kyoto Protocol target for 37 industrialized countriesand the European community for reducing GreenhouseGas (GHG) emissions by 5% against 1990 levels over thefive-year period 2008-2012.Carbon Reduction Commitment scheme aims to reduceCO2 emissions from the target organisations in UK by atleast 4 million tonnes per year by 2020.(www.carbontrust.com)Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesAn Immediate NeedCarbon footprint reduction has high priority for a major UKbiscuit manufacturer with core markets in Europe in linewith their strategy to minimize impact on the environmentBaking profile can influence up to 25% of total energyKey decision variablesLine process rates which may be driven by pack sizeChangeovers (ie milk to plain chocolate) pause the process(the time requirement depends on the sequence)Baking profileMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesCharacteristics of the ProblemMultiple productsDifferent running speedsConflicting criteria: Cmax (orMakespan) and Total EnergyConsumption (TEC)Two machine sequencedependent permutation flowshop(F2|STsd |Cmax , TEC)Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesSummary of the LiteratureYu (2010) defined Green Scheduling as “modernscheduling which considers resource consumption andenvironmental effect”Survey on scheduling problems with setup times / costs(Allahverdi et al. 2008)Minimizing Total Energy Consumption and TotalCompletion Time (Yildirim & Mouzon 2011)Energy consumption characteristics driven by task flow inmachining (He et al. 2012)Energy consumption model and energy optimization inmanufacturing (Dietmair & Verl 2009)Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesFour Interrelated GapsGap 1: Automatic access to data andanalysis (Mani et al. 2012)Gap 2: Modelling carbon footprint (Jayalet al. 2010, Neto et al. 2010, Dekker et al.2011, Tsoulfas & Pappis 2008)Gap 3: Optimization techniques(Maniet al. 2012, Sbihi & Eglese 2007)Gap 4: Decision support toolsMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesMulti-Objective Optimization (MOO)Min {f1(x˜), . . . , fm(x˜)};st: x˜ ∈ {Feasible Set}Dominance Relationx˜ dominates y˜ (x˜  y˜ ) iff:fi(x˜) ≤ fi(y˜); ∀ i ∈ {1, . . . ,m};∃ i ∈ {1, . . . ,m} | fi(x˜) < fi(y˜).Pareto FrontierNon-dominated solutions constitute the Pareto frontier in theobjective space.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesPareto Frontier and Trade-off AnalysisMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesMOO in a Decision Support FrameworkMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesBicriteria MILP ModelMin Cmax and TECs.t.Timing Constraints;Balance Constraints (for binary variables);Binary and non-negativity constraints.ComplexityFlowshop scheduling with sequence-dependent setups tominimize Cmax is a special case of TSP and therefore NP-hard.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesBicriteria MILP ModelMin Cmax and TECs.t.Timing Constraints;Balance Constraints (for binary variables);Binary and non-negativity constraints.ComplexityFlowshop scheduling with sequence-dependent setups tominimize Cmax is a special case of TSP and therefore NP-hard.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesInitiation and EvolutionTwo Dimensional Chromosome StructureJob string: J1 J2 ... JnSpeed on Machine 1 y11` y12` ... y1n`Speed on Machine 2 y21` y22` ... y2n`Random initial populationNon-dominated sorting (Deb 2009) to calculate fitnessvaluesElitist strategy to preserve non-dominated solutionsGenetic operatorsOrder cross-over Michalewicz (1998) for recombinationFour Mutation Strategies: Inversion, Insertion, Swap andAlterationMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesParameter SettingBenchmarking MOGA with CPLEX in small problems, thefollowing parameter set found to be effective:Population size = 4× nMaximum execution time = 5× n secondsCrossover rate = 0.7Mutation Strategies:Insertion rate = 0.08Inversion rate = 0.10Swap rate = 0.02Alteration rate = 0.10Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesLower BoundsLB on Cmax : for a no-setup single-speed version of theoriginal problem wherein jobs are processed at the highestspeed (v1) after the shortest possible setups.LB on TEC: for a no-setup single-speed version of problemP in which jobs are processed at the lowest speedfollowing the shortest possible setups.The straight connecting the above two LBs is a lowerbound for the Pareto frontier.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesSample Comparison in a Small ProblemPerformanceMOGA: 35s, 4.06% distant with LB; CPLEX: 2610s, 3.41% distant with LBMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesComparisons in Large ProblemsJobs CPU Time (s)∗ Distance with LB (%)MOGA Random Search10 50 16.64 63.1420 100 22.51 62.5730 150 31.47 70.0740 200 43.70 72.6850 250 39.48 73.5860 300 42.84 72.9170 350 51.74 73.7280 400 45.39 71.64* On a Pentium 2.67GHz with 4GB RAMMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesSummaryContributionsExtending the literature on Green SchedulingMathematical modelling of Total Energy Consumption, asustainability metric alongside Makespan, a measure ofserviceDefining lower bounds on energy and MakespanDeveloping MOGA to facilitate trade-off analysis in largeproblemsFuture WorkImproving performance of MOGAPossible tightening of the Lower BoundsEmbedding MOGA in DSS framework for trade-off analysisTackling other problems for reducing carbon footprint inmanufacturing supply chainsMansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesThanks for your attention!Questions or Comments?Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesReferences IAllahverdi, A., Ng, C., Cheng, T. & Kovalyov, M. Y. (2008), ‘A survey of schedulingproblems with setup times or costs’, European Journal of Operational Research187(3), 985 – 1032.URL: http://www.sciencedirect.com/science/article/pii/S0377221706008174Coello, C., Lamont, G. & Van Veldhuisen, D. (2007), Evolutionary Algorithms for SolvingMulti-Objective Problems, Genetic and Evolutionary Computation Series, Springer.URL: http://books.google.co.uk/books?id=rXIuAMw3lGACDeb, K. (2009), Multi-Objective Optimization Using Evolutionary Algorithms,Wiley-Interscience series in systems and optimization, John Wiley & Sons.URL: http://books.google.co.uk/books?id=U0dnPwAACAAJDekker, R., Bloemhof, J. & Mallidis, I. (2011), ‘Operations research for greenlogistics–an overview of aspects, issues, contributions and challenges’, EuropeanJournal of Operational Research .Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesReferences IIDeva Prasad, S., Krishnaiah Chetty, O. & Rajendran, C. (2006), ‘A genetic algorithmicapproach to multi-objective scheduling in a kanban-controlled flowshop withintermediate buffer and transport constraints’, The International Journal ofAdvanced Manufacturing Technology 29(5), 564–576.Dietmair, A. & Verl, A. (2009), ‘A generic energy consumption model for decisionmaking and energy efficiency optimisation in manufacturing’, International Journalof Sustainable Engineering 2(2), 123–133.He, Y., Liu, B., Zhang, X., Gao, H. & Liu, X. (2012), ‘A modeling method oftask-oriented energy consumption for machining manufacturing system’, Journal ofCleaner Production 23(1), 167 – 174.URL: http://www.sciencedirect.com/science/article/pii/S0959652611004197Jayal, A., Badurdeen, F., Dillon, O. & Jawahir, I. (2010), ‘Sustainable manufacturing:Modeling and optimization challenges at the product, process and system levels’,CIRP Journal of manufacturing science and technology 2(3), 144–152.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesReferences IIIMani, M., Madan, J., Lee, J. H., Lyons, K. & Gupta, S. K. (2012), Characterizingsustainability for manufacturing performance management, in ‘Proceedings of theASME 2012 International Design Engineering Technical Conferences & Computersand Information in Engineering Conference (IDETC / CIE 2012)’, Chicago, IL, USA,pp. 1–10.Mellows-Facer, A. & Maer, L. (2012), International comparisons of manufacturingoutput, Technical report, Parliment UK.Michalewicz, Z. (1998), Genetic Algorithms + Data Structures = Evolution Programs,Artificial intelligence, Springer.URL: http://books.google.co.uk/books?id=vlhLAobsK68CNeto, J., Walther, G., Bloemhof, J., Van Nunen, J. & Spengler, T. (2010), ‘Fromclosed-loop to sustainable supply chains: the weee case’, International Journal ofProduction Research 48(15), 4463–4481.OECD-IEA (2007), Tracking industrial energy efficiency and co2 emissions., Technicalreport, International Energy Agency.http://www.iea.org/Textbase/npsum/tracking2007SUM.pdf date accessed:13/11/2012.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesReferences IVPasupathy, T., Rajendran, C. & Suresh, R. (2006), ‘A multi-objective genetic algorithmfor scheduling in flow shops to minimize the makespan and total flow time of jobs’,The International Journal of Advanced Manufacturing Technology 27(7), 804–815.Ponnambalam, S., Jagannathan, H., Kataria, M. & Gadicherla, A. (2004), ‘A tsp-gamulti-objective algorithm for flow-shop scheduling’, The International Journal ofAdvanced Manufacturing Technology 23(11), 909–915.Sbihi, A. & Eglese, R. (2007), ‘Combinatorial optimization and green logistics’, 4OR: AQuarterly Journal of Operations Research 5(2), 99–116.T’kindt, V. & Billaut, J. (2006), Multicriteria scheduling: theory, models and algorithms,Springer.Tsoulfas, G. & Pappis, C. (2008), ‘A model for supply chains environmentalperformance analysis and decision making’, Journal of Cleaner Production16(15), 1647–1657.Yildirim, M. B. & Mouzon, G. (2011), ‘Single-machine sustainable production planningto minimize total energy consumption and total completion time using a multipleobjective genetic algorithm’, Engineering Management, IEEE Transactions onPP(99), 1 –13.Mansouri, Aktas, Besikci Decision Support for Green SchedulingMotivationProblem DefinitionMethodologyResultsSummaryReferencesReferences VYu, J. J. (2010), ‘Green scheduling and its solution’, Advanced Materials Research139, 1415–1418.Mansouri, Aktas, Besikci Decision Support for Green Scheduling

Green scheduling and its solution’,

Towards green scheduling: A decision support for trade-off analysis between makespan and energy consumption

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Towards green scheduling: A decision support for trade-off analysis between makespan and energy consumption

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