8,230
Views
200
CrossRef citations to date
0
Altmetric
Reviews

Scheduling in production, supply chain and Industry 4.0 systems by optimal control: fundamentals, state-of-the-art and applications

ORCID Icon, ORCID Icon, ORCID Icon &
Pages 411-432 | Received 03 Nov 2017, Accepted 08 Feb 2018, Published online: 01 Mar 2018

References

  • Afanasiev, V. N. , V. B. Kolmanovskii , and V. R. Nosov . 1996. Mathematical Theory of Control Systems Design. Dordrecht: Kluwer.10.1007/978-94-017-2203-2
  • Albright, S. C. , and R. S. Collins . 1977. “A Bayesian Approach to the Optimal Control of Continuous Industrial Processes.” International Journal of Production Research 15 (1): 37–45.10.1080/00207547708943102
  • Athaus, M. , and P. L. Falb . 1966. Optimal Control: An Introduction to the Theory and Its Applications. New York : McGraw-Hill.
  • Bedini, R. , and P. Toni . 1980. “The Planning of a Manufacturing System: A Dynamic Model.” International Journal of Production Research 18 (2): 189–199.10.1080/00207548008919660
  • Bellmann, R. 1972. Adaptive Control Processes: A Guided Tour. Princeton, NJ: Princeton University Press.
  • Blazewicz, J. , K. Ecker , E. Pesch , G. Schmidt , and J. Weglarz . 2001. Scheduling Computer and Manufacturing Processes. 2nd ed. Berlin: Springer Verlag.10.1007/978-3-662-04363-9
  • Borisovsky, P. , A. Dolgui , and A. Eremeev . 2009. “Genetic Algorithms for a Supply Management Problem: MIP-Recombination vs Greedy Decoder.” European Journal of Operational Research 195 (3): 770–779.10.1016/j.ejor.2007.06.060
  • Bożek, A. , and M. Wysocki . 2015. “Flexible Job Shop with Continuous Material Flow.” International Journal of Production Research 53 (4): 1273–1290.
  • Bryson, A. E. , and Y.-C. Ho . 1975. Applied Optimal Control. Washington, DC: Hemisphere.
  • Chang, P. C. , M. H. Chen , M. K. Tiwari , and A. S. Iquebal . 2013. “Block-Based Evolutionary Algorithm for Flow-Shop Scheduling Problem.” Applied Soft Computing 13 (12): 4536–4547.10.1016/j.asoc.2013.07.018
  • Chernousko, F. L. , and A. A. Lyubushin . 1982. “Method of Successive Approximations for Solution of Optimal Control Problems.” Optimal Control Applications and Methods 3 (2): 101–114.
  • Choi, T.-M. , W.-K. Yeung , and T. C. E. Cheng . 2013. “Scheduling and Co-Ordination of Multi-Suppliers Single-Warehouse-Operator Single-Manufacturer Supply Chains with Variable Production Rates and Storage Costs.” International Journal of Production Research 51 (9): 2593–2601.10.1080/00207543.2012.737949
  • Ciro, G. K. , F. Dugardin , F. Yalaoui , and R. Kelly . 2016. “Open Shop Scheduling Problem with a Multi-Skills Resource Constraint: A Genetic Algorithm and an Ant Colony Optimisation Approach.” International Journal of Production Research 54 (16): 4854–4881.10.1080/00207543.2015.1126371
  • Dejonckheere, J. , S. M. Disney , M. R. Lambrecht , and D. R. Towill . 2004. “The Impact of Information Enrichment on the Bullwhip Effect in Supply Chains: A Control Engineering Perspective.” European Journal of Operational Research 153 (3): 727–750.10.1016/S0377-2217(02)00808-1
  • Dolgui, A. , and J.-M. Proth . 2010. Supply Chains Engineering: Useful Methods and Techniques. Heidelberg: Springer.
  • Dolgui, A. , D. Ivanov , and B. Sokolov . 2018. “Ripple Effect in the Supply Chain: An Analysis and Recent Literature.” International Journal of Production Research 56 (1–2): 1–17. Advance online publication.
  • Eilon, S. 1961. “Two Inventory Control Models.” International Journal of Production Research 1 (1): 48–55.10.1080/00207546108943073
  • Feng, Y. Y. , and H. Yan . 2000. “Optimal Production Control in a Discrete Manufacturing System with Unreliable Machines and Random Demands.” IEEE Transactions on Automatic Control 45: 2280–2296.10.1109/9.895564
  • Gershwin, S. B. 1994. Manufacturing Systems Engineering. Englewood Cliffs, NJ: PTR Prentice Hall.
  • Giglio, D. 2015. “Optimal Control Strategies for Single-Machine Family Scheduling with Sequence-Dependent Batch Setup and Controllable Processing times.” Journal of Scheduling 18 (5): 525–543.10.1007/s10951-015-0440-2
  • Harjunkoski, I. , C. T. Maravelias , P. Bongers , P. M. Castro , S. Engell , I. E. Grossmann , J. Hooker , C. Méndez , G. Sand , and J. Wassick . 2014. “Scope for Industrial Applications of Production Scheduling Models and Solution Methods.” Computers and Chemical Engineering 62: 161–193.10.1016/j.compchemeng.2013.12.001
  • Hartl, R. F. , and S. P. Sethi . 1984. “Optimal Control Problems with Differential Inclusions: Sufficiency Conditions and an Application to a Production Inventory Model.” Optimal Control Applications and Methods 5: 289–307.10.1002/(ISSN)1099-1514
  • Hartl, R. F. , S. P. Sethi , and R. G. Vickson . 1995. “A Survey of the Maximum Principles for Optimal Control Problems with State Constraints.” SIAM Review 37 (2): 181–218.10.1137/1037043
  • Hultquispt, F. 1988. Numerical Methods for Engineers and Computer Scientists. Menlo Park: Benjamin-Cummings Pub Co.
  • Hwang, C. L. , L. T. Fan , and L. E. Erickson . 1967. “Optimum Production Planning by the Maximum Principle.” Management Science 13 (9): 751–755.10.1287/mnsc.13.9.751
  • Hwang, C. L. , L. T. Fan , F. A. Tillman , and R. Sharma . 1969. “Optimal Production Planning and Inventory Control.” International Journal of Production Research 8 (1): 75–83.
  • Ivanov, D. 2018. Structural Dynamics and Resilience in Supply Chain Risk Management. New York : Springer.10.1007/978-3-319-69305-7
  • Ivanov, D. , and B. Sokolov . 2010. Adaptive Supply Chain Management. London: Springer.10.1007/978-1-84882-952-7
  • Ivanov, D. , and B. Sokolov . 2012. “Dynamic Supply Chain Scheduling.” Journal of Scheduling 15 (2): 201–216.10.1007/s10951-010-0189-6
  • Ivanov, D. , and B. Sokolov . 2013a. “Dynamic Coordinated Scheduling in the Supply Chain under a Process Modernization.” International Journal of Production Research. 51 (9): 2680–2697.10.1080/00207543.2012.737950
  • Ivanov, D. , and B. Sokolov . 2013b. “Control and System-Theoretic Identification of the Supply Chain Dynamics Domain for Planning, Analysis, and Adaptation of Performance under Uncertainty.” European Journal of Operational Research 224 (2): 313–323.10.1016/j.ejor.2012.08.021
  • Ivanov, D. , B. Sokolov , and A. Dolgui . 2012. “Applicability of Optimal Control Theory to Adaptive Supply Chain Planning and Scheduling.” Annual Reviews in Control 36: 73–84.10.1016/j.arcontrol.2012.03.006
  • Ivanov, D. , B. Sokolov , and A. Dolgui . 2014. “Multi-Stage Supply Chain Scheduling with Non-Preemptive Continuous Operations and Execution Control.” International Journal of Production Research 52 (13): 4059–4077.10.1080/00207543.2013.793429
  • Ivanov, D. , A. Dolgui , B. Sokolov , and F. Werner . 2016a. “Schedule Robustness Analysis with the Help of Attainable Sets in Continuous Flow Problem under Capacity Disruptions.” International Journal of Production Research 54 (11): 3397–3413.10.1080/00207543.2015.1129467
  • Ivanov, D. , A. Dolgui , and B. Sokolov . 2016b. “Robust Dynamic Schedule Coordination Control in the Supply Chain.” Computers and Industrial Engineering 94 (1): 18–31.10.1016/j.cie.2016.01.009
  • Ivanov, D. , B. Sokolov , A. Dolgui , F. Werner , and M. Ivanova . 2016c. “A Dynamic Model and an Algorithm for Short-Term Supply Chain Scheduling in the Smart Factory Industry 4.0.” International Journal of Production Research 54 (2): 386–402.10.1080/00207543.2014.999958
  • Ivanov, D. , A. Dolgui , B. Sokolov , and M. Ivanova . 2017a. “Optimal Control Representation of the Mathematical Programming Model for Supply Chain Dynamic Reconfiguration.”   IFAC Papers Online 50–1, 20th IFAC World Congress, Toulouse, July 9–14, 4994–4999.
  • Ivanov, D. , A. Dolgui , and B. Sokolov . 2017b. “A Dynamic Approach to Multi-Stage Job Shop Scheduling in an Industry 4.0-Based Flexible Assembly System.” In Advances in Production Management Systems. the Path to Intelligent, Collaborative and Sustainable Manufacturing, edited by H. Lödding , R. Riedel , K.-D. Thoben , D. Kiritsis , and G. von Cieminski . Proceedings of IFIP WG 5.7 International Conference, APMS 2017, Hamburg, Germany, Part I, September 3–7, 475–482.
  • Ivanov, D. , A. Dolgui , and B. Sokolov . 2018. “Scheduling of Recovery Actions in the Supply Chain with Resilience Analysis Considerations.” International Journal of Production Research. doi:10.1080/00207543.2017.1401747.
  • Jiang, J. , and S. P. Sethi . 1991. “A State Aggregation Approach to Manufacturing Systems Having Machine States with Weak and Strong Interactions.” Operations Research 39: 970–978.10.1287/opre.39.6.970
  • Jungwattanakit, J. , M. Reodecha , P. Chaovalitwongse , and F. Werner . 2009. “A Comparison of Scheduling Algorithms for Flexible Flow Shop Problems with Unrelated Parallel Machines, Setup times, and Dual Criteria.” Computers and Operations Research 36 (2): 358–378.10.1016/j.cor.2007.10.004
  • Kalinin, V. N. , and B. V. Sokolov . 1985. “Optimal Planning of the Process of Interaction of Moving Operating Objects.” International Journal of Difference Equations 21 (5): 502–506.
  • Kalinin, V. N. , and B. V. Sokolov . 1987. “A Dynamic Model and an Optimal Scheduling Algorithm for Activities with Bans of Interrupts.” Automation and Remote Control 48 (1–2): 88–94.
  • Khmelnitsky, E. , K. Kogan , and O. Maimon . 1997. “Maximum Principle-Based Methods for Production Scheduling with Partially Sequence-Dependent Setups.” International Journal of Production Research 35 (10): 2701–2712.10.1080/002075497194390
  • Khmelnitsky, E. , E. Presman , and S. P. Sethi . 2011. “Optimal Production Control of a Failure-Prone Machine.” Annals of Operations Research 182: 67–86.10.1007/s10479-009-0668-3
  • Kimemia, J., and S. B. Gershwin. 1985. Flow Optimization in Flexible Manufacturing Systems. International Journal of Production Research 23 (1): 81–96.
  • Kimemia, J. G. , and Stanley B. Gershwin . 1983. “An Algorithm for the Computer Control of a Flexible Manufacturing System.” IIE Transactions 15: 353–362.10.1080/05695558308974659
  • Kogan, K. , and E. Khmelnitsky . 1996. “An Optimal Control Model for Continuous Time Production and Setup Scheduling.” International Journal of Production Research 34 (3): 715–725.10.1080/00207549608904930
  • Kogan, K. , and E. Khmelnitsky . 2000. Scheduling: Control-Based Theory and Polynomial-Time Algorithms. Dordrecht: Kluwer.10.1007/978-1-4615-4675-7
  • Krylov, I. A. , and F. L. Chernousko . 1972. “An Algorithm for the Method of Successive Approximations in Optimal Control Problems.” USSR Computational Mathematics and Mathematical Physics 12 (1): 14–34.
  • Lauff, V. , and F. Werner . 2004. “On the Complexity and Some Properties of Multi-Stage Scheduling Problems with Earliness and Tardiness Penalties.” Computers and Operations Research 31: 317–345.10.1016/S0305-0548(02)00194-6
  • Lee, E. B. , and L. Markus . 1967. Foundations of Optimal Control Theory. New York : Wiley.
  • Lou, S. X. C. , and G. Van Ryzin . 1989. “Optimal Control Rules for Scheduling Job Shops.” Annals of Operations Research 17 (1): 233–248.10.1007/BF02096607
  • Lou, S. , S. P. Sethi , and Q. Zhang . 1994. “Optimal Feedback Production Planning in a Stochastic Two Machine Flowshop.” European Journal of Operational Research, Special Issue on Stochastic Control Theory and Operational Research 73: 331–345.10.1016/0377-2217(94)90269-0
  • Lyubushin, A. A. 1979. “Modifications and Convergence of Successive Approximations for Optimal Control Problems.” USSR Computational Mathematics and Mathematical Physics 19 (6): 1414–1421.
  • Maimon, O. , Eugene Khmelnitsky , and K. Kogan . 1998. Optimal Flow Control in Manufacturing Systems. Heidelberg: Springer.
  • Moiseev, N. N. 1974. Element of the Optimal Systems Theory. Moscow: Nauka (in Russian).
  • Okhtilev, M Yu , B. V. Sokolov , and R. M. Yusupov . 2006. Intellectual Technologies for Monitoring and Control of Structure-Dynamics of Complex Technical Objects. Moscow: Nauka.
  • Ortega, M. , and L. Lin . 2004. “Control Theory Applications to the Production-Inventory Problem: A Review.” International Journal of Production Research. 42: 2303–2322.10.1080/00207540410001666260
  • Pinedo, M. 2008. Scheduling: Theory, Algorithms, and Systems. New York : Springer.
  • Pinha, D. , R. Ahluwalia , and A. Carvalho . 2015. “Parallel Mode Schedule Generation Scheme.” 15th IFAC Symposium on Information Control Problems in Manufacturing INCOM 2015, Ottawa.
  • Pontryagin, L. S. , V. G. Boltyanskiy , R. V. Gamkrelidze , and E. F. Mishchenko . 1964. The Mathematical Theory of Optimal Processes. Oxford: Pergamon Press.
  • Powell, W. B. , and Z. L. Chen . 1997. “An Optimal Control Formulation of Large-Scale Multiclass Machine Scheduling Problems.” In Network Optimization. Lecture Notes in Economics and Mathematical Systems, edited by  P. M. Pardalos, D. W. Hearn, and W. W. Hager, Vol. 450. Berlin, Heidelberg: Springer.
  • Pratap, S. , M. Kumar , D. Saxena , and M. K. Tiwari . 2016. “Integrated Scheduling of Rake and Stockyard Management with Ship Berthing: A Block Based Evolutionary Algorithm.” International Journal of Production Research 54 (14): 4182–4204.10.1080/00207543.2015.1111535
  • Presman, E. S. P. , and S. P. Sethi . 1997.Optimal Feedback Production Planning in a Stochastic N-Machine Flowshop with Limited Buffers. Automatica 33: 1899–1903.10.1016/S0005-1098(97)00096-4
  • Presman, E. , S. P. Sethi , and Q. Zhang . 1995. “Optimal Feedback Production Planning in a Stochastic N-Machine Flowshop.” Automatica 31: 1325–1332.10.1016/0005-1098(95)00040-4
  • Presman, E. , S. P. Sethi , H. Zhang , and A. Bisi . 2000. ““Optimality in Two-Machine Flowshop with Limited Buffer.” Annals of Operations Research 98: 333–351.
  • Samaratunga, C. , S. P. Sethi , and X. Y. Zhou . 1997. “Computational Evaluation of Hierarchical Production Control Policies for Stochastic Manufacturing Systems.” Operations Research 45: 258–274.
  • Sethi, S. P. 1978. “A Survey of Management Science Applications of the Deterministic Maximum Principle.” TIMS Studies in the Management Science 9: 33–68.
  • Sethi, S. P. 1984. “Applications of the Maximum Principle to Production and Inventory Problems.” Proceedings Third International Symposium on Inventories, Budapest, August 27–31, 753–756.
  • Sethi, S. P. , and G. L. Thompson . 2000. Optimal Control Theory: Applications to Management Science and Economics. 2nd ed. Berlin: Springer.
  • Sethi, S. P. , and Q. Zhang . 1994. Hierarchical Decision Making in Stochastic Manufacturing Systems, in Series Systems and Control: Foundations and Applications. Cambridge, MA: Birkhäuser Boston.
  • Sethi, S. P. , and X. Y. Zhou . 1996. “Optimal Feedback Controls in Deterministic Dynamic Two-Machine Flowshops.” Operations Research Letters 19: 225–235.10.1016/S0167-6377(96)00023-5
  • Sethi, S. P. , H. Yan , H. Zhang , and Q. Zhang . 2002. “Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey.” Manufacturing & Service Operations Management 4 (2): 133–170.10.1287/msom.4.2.133.281
  • Sharifnia, A. , M. Caramanis , and S. B. Gershwin . 1991. “Dynamic Setup Scheduling and Flow Control in Manufacturing Systems.” Discrete Event Dynamic Systems 1: 149–175.10.1007/BF01805561
  • Sokolov, B. V. , and R. M. Yusupov . 2002. “Complex Simulation of Automated Control System of Navigation Spacecraft Operation.” Journal of Automation and Information Science 34 (9–12): 19–30.
  • Soner, H. M. 1986. “Optimal Control with State-Space Constraint. II.” SIAM Journal on Control and Optimization 24: 1110–1122.10.1137/0324067
  • Song, D. P. 2012. Optimal Control and Optimization of Stochastic Supply Chain Systems. Heidelberg: Springer.
  • Sotskov, Y. N. , T.-C. Lai , and F. Werner . 2013. “Measures of Problem Uncertainty for Scheduling with Interval Processing times.” OR Spectrum 35 (3): 659–689.10.1007/s00291-012-0306-3
  • Spiegler, V. , M. Naim , and J. Wikner . 2012. “A Control Engineering Approach to the Assessment of Supply Chain Resilience.” International Journal of Production Research 50: 6162–6187.10.1080/00207543.2012.710764
  • Spiegler, V. , A. T. Potter , M. M. Naim , and D. R. Towill . 2016. “The Value of Nonlinear Control Theory in Investigating the Underlying Dynamics and Resilience of a Grocery Supply Chain.” International Journal of Production Research 54 (1): 265–286.10.1080/00207543.2015.1076945
  • Stecke, K. E., and J. J. Solberg . 1981. “Loading and Control Policies for a Flexible Manufacturing System.” International Journal of Production Research 19 (5): 481–490.
  • Tabak, D. , and B. C. Kuo . 1971. Optimal Control by Mathematical Programming. New York: Prentice Hall.
  • Wang, X. , S. M. Disney , and J. Wang . 2012. “Stability Analysis of Constrained Inventory Systems with Transportation Delay.” European Journal of Operational Research 223 (1): 86–95.10.1016/j.ejor.2012.06.014
  • Werner, F. , and Y. Sotskov , eds. 2014. Sequencing and Scheduling with Inaccurate Data. New York: Nova.
  • Yang, J. , H. Yan , and S. P. Sethi . 1999. “Optimal Production Planning in Pull Flow Lines with Multiple Products.” European Journal of Operational Research 119 (3): 582–604.10.1016/S0377-2217(98)00358-0
  • Ye, H. , and R. Liu . 2016. “A Multiphase Optimal Control Method for Multi-Train Control and Scheduling on Railway Lines.” Transportation Research Part B: Methodological 93 (Part A): 377–393.10.1016/j.trb.2016.08.002
  • Zimin, I. N. , and Yu P Ivanilov . 1971. “Solution of Network Planning Problems by Reducing Them to Optimal Control Problems.” USSR Computational Mathematics and Mathematical Physics 11 (3): 632–641.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.