Coordination mechanisms with mathematical programming models for decentralized decision-making, a literature review

[EN] The increase in the complexity of supply chains requires greater efforts to align the activities of all its members in order to improve the creation of value of their products or services offered to customers. In general, the information is asymmetric; each member has its own objective and limitations that may be in conflict with other members. Operations managements face the challenge of coordinating activities in such a way that the supply chain as a whole remains competitive, while each member improves by cooperating. This document aims to offer a systematic review of the collaborative planning in the last decade on the mechanisms of coordination in mathematical programming models that allow us to position existing concepts and identify areas where more research is needed.Rius-Sorolla, G.; Maheut, J.; Estelles Miguel, S.; García Sabater, JP. (2020). Coordination mechanisms with mathematical programming models for decentralized decision-making, a literature review. Central European Journal of Operations Research. 28(1):61-104. https://doi.org/10.1007/s10100-018-0594-zS61104281Acar Y, Atadeniz SN (2015) Comparison of integrated and local planning approaches for the supply network of a globally-dispersed enterprise. Int J Prod Econ 167:204–219. https://doi.org/10.1016/j.ijpe.2015.05.028Agnetis A, Hall NG, Pacciarelli D (2006) Supply chain scheduling: sequence coordination. Discrete Appl Math 154(15):2044–2063. https://doi.org/10.1016/j.dam.2005.04.019Agnetis A, Aloulou MA, Fu LL (2016) Production and interplant batch delivery scheduling: Dominance and cooperation. Int J Prod Econ 182:38–49. https://doi.org/10.1016/j.ijpe.2016.08.007Albrecht M (2010) Supply chain coordination mechanisms Lecture notes in economics and mathematical systems, vol 628. Springer, Berlin. https://doi.org/10.1007/978-3-642-02833-5Albrecht M, Stadtler H (2015) Coordinating decentralized linear programs by exchange of primal information. Eur J Oper Res 247(3):788–796. https://doi.org/10.1016/j.ejor.2015.06.045Arkan A, Hejazi SR (2012) Coordinating orders in a two echelon supply chain with controllable lead time and ordering cost using the credit period. Comput Ind Eng 62(1):56–69. https://doi.org/10.1016/j.cie.2011.08.016Arshinder, Kanda A, Deshmukh SG (2008) Supply chain coordination: perspectives, empirical studies and research directions. Int J Prod Econ 115(2):316–335. https://doi.org/10.1016/j.ijpe.2008.05.011Attanasio A, Ghiani G, Grandinetti L, Guerriero F (2006) Auction algorithms for decentralized parallel machine scheduling. Parallel Comput 32(9):701–709. https://doi.org/10.1016/j.parco.2006.03.002Badole CM, Jain R, Rathore APS, Nepal B (2012) Research and opportunities in supply chain modeling: a review. Int J Supply Chain Manag 1(3):63–86Bajgiran OS, Zanjani MK, Nourelfath M (2016) The value of integrated tactical planning optimization in the lumber supply chain. Int J Prod Econ 171:22–33. https://doi.org/10.1016/j.ijpe.2015.10.021Behnamian J (2014) Multi-cut Benders decomposition approach to collaborative scheduling. Int J Comput Integr Manuf 28(11):1–11. https://doi.org/10.1080/0951192X.2014.961963Ben-Daya M, Darwish M, Ertogral K (2008) The joint economic lot sizing problem: review and extensions. Eur J Oper Res 185(2):726–742. https://doi.org/10.1016/j.ejor.2006.12.026Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238–252. https://doi.org/10.1007/BF01386316Bhatnagar R, Chandra P, Goyal SK (1993) Models for multi-plant coordination. Eur J Oper Res 67(2):141–160. https://doi.org/10.1016/0377-2217(93)90058-UBuer T, Homberger JJ, Gehring H (2013) A collaborative ant colony metaheuristic for distributed multi-level uncapacitated lot-sizing. Int J Prod Res 51(17):5253–5270. https://doi.org/10.1080/00207543.2013.802822Buer T, Ziebuhr M, Kopfer H (2015) A coordination mechanism for a collaborative lot-sizing problem with rivaling agents. In: Mattfeld D, Spengler T, Brinkmann J, Grunewald M (eds) Logistics management. Springer, Cham. https://doi.org/10.1007/978-3-319-13177-1_26Buxmann P, Ahsen A Von, Díaz LM (2008) Economic evaluation of cooperation scenarios in supply chains. J Enterp Inf Manag 21(3):247–262. https://doi.org/10.1108/17410390810866628Chakraborty A, Chatterjee AK (2015) A surcharge pricing scheme for supply chain coordination under JIT environment. Eur J Oper Res 253(1):14–24. https://doi.org/10.1016/j.ejor.2016.02.001Chen IJ, Paulraj A, Lado AA (2004) Strategic purchasing, supply management, and firm performance. J Oper Manag 22(5):505–523. https://doi.org/10.1016/j.jom.2004.06.002Cheng JH (2011) Inter-organizational relationships and information sharing in supply chains. Int J Inf Manag 31(4):374–384. https://doi.org/10.1016/j.ijinfomgt.2010.09.004Cheng R, Forbes JF, San Yip W, Fraser Forbes J, Yip WS (2008) Dantzig–Wolfe decomposition and plant-wide MPC coordination. Comput Chem Eng 32(7):1507–1522. https://doi.org/10.1016/j.compchemeng.2007.07.003Cooper MC, Lambert DM, Pagh JD (1997) Supply chain management: more than a new name for logistics. Int J Logist Manag 8(1):1–14. https://doi.org/10.1108/09574099710805556Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8(1):101–111. https://doi.org/10.1287/opre.8.1.101Dash RK, Vytelingum P, Rogers A, David E, Jennings NR (2007) Market-based task allocation mechanisms for limited-capacity suppliers. IEEE Trans Syst Man Cybern Part A Syst Hum 37(3):391–405. https://doi.org/10.1109/TSMCA.2007.893474Dudek G, Stadtler H (2005) Negotiation-based collaborative planning between supply chains partners. Eur J Operat Res 163(3):668–687. https://doi.org/10.1016/j.ejor.2004.01.014Dudek G, Stadtler H (2007) Negotiation-based collaborative planning in divergent two-tier supply chains. Int J Prod Res 45(2):465–484Ertogral K, David Wu S (2000) Auction-theoretic coordination of production planning in the supply chain. IIE Trans 32:931–940. https://doi.org/10.1080/07408170008967451Eslikizi S, Ziebuhr M, Kopfer H, Buer T (2015) Shapley-based side payments and simulated annealing for distributed lot-sizing. IFAC-PapersOnLine 48(3):1592–1597. https://doi.org/10.1016/j.ifacol.2015.06.313Fan M, Stallaert J, Whinston AB (2003) Decentralized mechanism design for supply chain organizations using an auction market. Inf Syst Res 14(1):1–22. https://doi.org/10.1287/isre.14.1.1.14763Feng Y, D’Amours S, Beauregard R (2008) The value of sales and operations planning in oriented strand board industry with make-to-order manufacturing system: cross functional integration under deterministic demand and spot market recourse. Int J Prod Econ 115(1):189–209. https://doi.org/10.1016/j.ijpe.2008.06.002Fisher ML (1985) An applications oriented guide to Lagrangian relaxation. Interfaces 15(2):10–21. https://doi.org/10.1287/inte.15.2.10Fisher ML (2004) The Lagrangian relaxation method for solving integer programming problems. Manag Sci 50(12 Supplement):1861–1871. https://doi.org/10.1287/mnsc.1040.0263Frazzon E, Makuschewits T, Scholz-Reiter B, Novaes AGN (2010) Assessing the integrated scheduling of manufacturing and transportation systems along global supply chains. In: World conference on transport research, LisbonGaudreault J, Forget P, Frayret JMJ, Rousseau A, Lemieux S, D’Amours S (2010) Distributed operations planning in the softwood lumber supply chain: models and coordination. Int J Ind Eng Theory Appl Pract 17(3):168–189Gunnerud V, Foss B (2010) Oil production optimization—a piecewise linear model, solved with two decomposition strategies. Comput Chem Eng 34(11):1803–1812. https://doi.org/10.1016/j.compchemeng.2009.10.019Harb H, Paprott JN, Matthes P, Schütz T, Streblow R, Mueller D (2015) Decentralized scheduling strategy of heating systems for balancing the residual load. Build Environ 86:132–140. https://doi.org/10.1016/j.buildenv.2014.12.015Held M, Karp RM (1970) The traveling-salesman problem and minimum spanning trees. Oper Res 18(6):1138–1162. https://doi.org/10.1287/opre.18.6.1138Held M, Karp RM (1971) The traveling-salesman problem and minimum spanning trees: part II. Math Program 1(1):6–25. https://doi.org/10.1007/BF01584070Homberger J (2010) Decentralized multi-level uncapacitated lot-sizing by automated negotiation. 4OR 8(2):155–180. https://doi.org/10.1007/s10288-009-0104-1Homberger J (2011) A generic coordination mechanism for lot-sizing in supply chains. Electron Commer Res 11(2):123–149. https://doi.org/10.1007/s10660-010-9053-1Homberger J, Gehring H (2010) A pheromone-based negotiation mechanism for lot-sizing in supply chains. In: 2010 43rd Hawaii international conference on system sciences. IEEE, pp 1–10. https://doi.org/10.1109/hicss.2010.26Homberger J, Gehring H (2011) An ant colony optimization-based negotiation approach for lot-sizing in supply chains. Int J Inf Process Manag 2(3):86–99. https://doi.org/10.4156/ijipm.vol2.issue3.10Homberger J, Gehring H, Buer T (2015) Integrating side payments into collaborative planning for the distributed multi-level unconstrained lot sizing problem. In: Bui TX, Sprague RH (eds) 2015 48th Hawaii international conference on system sciences, vol 2015. IEEE, pp 1068–1077. https://doi.org/10.1109/hicss.2015.131Huang GQ, Lau JSK, Mak KL (2003) The impacts of sharing production information on supply chain dynamics: a review of the literature. Int J Prod Res 41(7):1483–1517. https://doi.org/10.1080/0020754031000069625Jeong I-J (2012) A centralized/decentralized design of a full return contract for a risk-free manufacturer and a risk-neutral retailer under partial information sharing. Int J Prod Econ 136(1):110–115. https://doi.org/10.1016/j.ijpe.2011.09.019Jeong IJ, Leon VJ (2002) Decision-making and cooperative interaction via coupling agents in organizationally distributed systems. IIE Trans (Inst Ind Eng) 34(9):789–802. https://doi.org/10.1023/A:1015548705266Jeong IJ, Yim SB (2009) A job shop distributed scheduling based on Lagrangian relaxation to minimise total completion time. Int J Prod Res 47(24):6783–6805. https://doi.org/10.1080/00207540701824217Jia ZZ, Deschamps JC, Dupas R (2016) A negotiation protocol to improve planning coordination in transport-driven supply chains. J Manuf Syst 38:13–26. https://doi.org/10.1016/j.jmsy.2015.10.003Jung H, Chen FF, Jeong B (2008) Decentralized supply chain planning framework for third party logistics partnership. Comput Ind Eng 55(2):348–364. https://doi.org/10.1016/j.cie.2007.12.017Katok E, Pavlov V (2013) Fairness in supply chain contracts: a laboratory study. J Oper Manag 31(3):129–137. https://doi.org/10.1016/j.jom.2013.01.001Kelly JD, Zyngier D (2008) Hierarchical decomposition heuristic for scheduling: coordinated reasoning for decentralized and distributed decision-making problems. Comput Chem Eng 32(11):2684–2705. https://doi.org/10.1016/j.compchemeng.2007.08.007Kong J, Rönnqvist M (2014) Coordination between strategic forest management and tactical logistic and production planning in the forestry supply chain. Int Trans Oper Res 21(5):703–735. https://doi.org/10.1111/itor.12089Kovács A, Egri P, Kis T, Váncza J (2013) Inventory control in supply chains: alternative approaches to a two-stage lot-sizing problem. Int J Prod Econ 143(2):385–394. https://doi.org/10.1016/j.ijpe.2012.01.001Kumar BK, Nagaraju D, Narayanan S (2016) Supply chain coordination models: a literature review. Indian J Sci Technol. https://doi.org/10.17485/ijst/2016/v9i38/86938Kutanoglu E, David Wu S (1999) On combinatorial auction and Lagrangean relaxation for distributed resource scheduling. IIE Trans 31(9):813–826. https://doi.org/10.1080/07408179908969883Lau HC, Zhao ZJ, Ge SS, Lee TH (2011) Allocating resources in multiagent flowshops with adaptive auctions. IEEE Trans Autom Sci Eng 8(4):732–743. https://doi.org/10.1109/TASE.2011.2160536Lee DJ, Jeong IJ (2010) A distributed coordination for a single warehouse-multiple retailer problem under private information. Int J Prod Econ 125(1):190–199. https://doi.org/10.1016/j.ijpe.2010.02.001Lehoux N, D’Amours S, Frein Y, Langevin A, Penz B (2010a) Collaboration for a two-echelon supply chain in the pulp and paper industry: the use of incentives to increase profit. J Oper Res Soc 62(4):581–592. https://doi.org/10.1057/jors.2009.167Lehoux N, D’Amours S, Langevin A (2010b) A win–win collaboration approach for a two-echelon supply chain: a case study in the pulp and paper industry. Eur J Ind Eng 4(4):493. https://doi.org/10.1504/EJIE.2010.035656Lehoux N, D’Amours S, Langevin A (2014) Inter-firm collaborations and supply chain coordination: review of key elements and case study. Prod Plan Control 25(10):858–872. https://doi.org/10.1080/09537287.2013.771413Li X, Wang Q (2007) Coordination mechanisms of supply chain systems. Eur J Oper Res 179(1):1–16. https://doi.org/10.1016/j.ejor.2006.06.023Lu SYP, Lau HYK, Yiu CKF (2012) A hybrid solution to collaborative decision-making in a decentralized supply-chain. J Eng Technol Manag 29(1):95–111. https://doi.org/10.1016/j.jengtecman.2011.09.008Mahdiraji HA, Zavadskas EK, Hajiagha SHR (2015) Game theoretic approach for coordinating unlimited multi echelon supply chains. Transform Bus Econ 14(2):133–151Maheut J, Besga JM, Uribetxebarria J, Garcia-Sabater JP (2014a) A decision support system for modelling and implementing the supply network configuration and operations scheduling problem in the machine tool industry. Prod Plan Control 25(8):679–697. https://doi.org/10.1080/09537287.2013.798087Maheut J, Garcia-Sabater JP, Garcia-Sabater JJ, Marin-Garcia J (2014b) Coordination mechanism for MILP models to plan operations within an advanced planning and scheduling system in a motor company: a case study. In: Prado-Prado JC, García-Arca J (eds) Annals of industrial engineering 2012. Springer, London, pp 245–253. https://doi.org/10.1007/978-1-4471-5349-8_29Manrodt KB, Vitasek K (2004) Global process standardization: a case study. J Bus Logist 25(1):1–23. https://doi.org/10.1002/j.2158-1592.2004.tb00168.xMarin-Garcia JA, Ramirez Bayarri L, Atares Huerta L (2015) Protocol: comparing advantages and disadvantages of rating scales, behavior observation scales and paired comparison scales for behavior assessment of competencies in workers. A systematic literature review. Work Pap Oper Manag 6(2):49. https://doi.org/10.4995/wpom.v6i2.4032Mason AN, Villalobos JR (2015) Coordination of perishable crop production using auction mechanisms. Agric Syst 138:18–30. https://doi.org/10.1016/j.agsy.2015.04.008McAfee RP, McMillan J (1987) Auctions and bidding. J Econ Lit 25(2):699–738Medina-Lopez C, Marin-Garcia JA, Alfalla-Luque R (2010) Una propuesta metodológica para la realización de búsquedas sistemáticas de bibliografía (A methodological proposal for the systematic literature review). Work Pap Oper Manag. https://doi.org/10.4995/wpom.v1i2.786Mouret S, Grossmann IE, Pestiaux P (2011) A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling. Comput Chem Eng 35(12):2750–2766. https://doi.org/10.1016/j.compchemeng.2011.03.026Mula J, Peidro D, Díaz-Madroñero M, Vicens E (2010) Mathematical programming models for supply chain production and transport planning. Eur J Oper Res 204(3):377–390. https://doi.org/10.1016/j.ejor.2009.09.008Nie L, Xu X, Zhan D (2008) Collaborative planning in supply chains by lagrangian relaxation and genetic algorithms. Int J Inf Technol Decis Mak 7(1):183–197. https://doi.org/10.1142/s0219622008002879Nishi T, Shinozaki R, Konishi M (2008) An augmented Lagrangian approach for distributed supply chain planning for multiple companies. IEEE Trans Autom Sci Eng 5(2):259–274. https://doi.org/10.1109/TASE.2007.894727Ouelhadj D, Petrovic S (2009) A survey of dynamic scheduling in manufacturing systems. J Sched 12(4):417–431. https://doi.org/10.1007/s10951-008-0090-8Pibernik R, Sucky E (2007) An approach to inter-domain master planning in supply chains. Int J Prod Econ 108(1–2):200–212. https://doi.org/10.1016/j.ijpe.2006.12.010Pittman SD, Bare BB, Briggs DG (2007) Hierarchical production planning in forestry using price-directed decomposition. Can J For 37(10):2010–2021. https://doi.org/10.1139/X07-026Polyak BT (1969) Minimization of unsmooth functionals. USSR Comput Math Math Phys 9(3):14–29. https://doi.org/10.1016/0041-5553(69)90061-5Pukkala T, Heinonen T, Kurttila M (2009) An application of a reduced cost approach to spatial forest planning. For Sci 55(1):13–22Qu T, Nie DX, Chen X, Chen XD, Dai QY, Huang GQ (2015) Optimal configuration of cluster supply chains with augmented Lagrange coordination. Comput Ind Eng 84(SI):43–55. https://doi.org/10.1016/j.cie.2014.12.026Reiss F, Buer T (2014) A coordination mechanism for capacitated lot-sizing in non-hierarchical n-tier supply chains. In: 2014 IEEE symposium on computational intelligence in production and logistics systems (Cipls), pp 9–15. https://doi.org/10.1109/cipls.2014.7007155Rius-Sorolla G, Maheut J, Estelles-Miguel S, Garcia-Sabater JP (2017) Protocol: systematic literature review on coordination mechanisms for the mathematical programming models in production planning with decentralized decision making. Work Pap Oper Manag 8(2):22. https://doi.org/10.4995/wpom.v8i2.7858Sahin F, Robinson EPP (2002) Flow coordination and information sharing in supply chains: review, implications, and directions for future research. Decis Sci 33(4):505–535. https://doi.org/10.1111/j.1540-5915.2002.tb01654.xSilva CA, Sousa JMC, Runkler TA, Sá da Costa J (2009) Distributed supply chain management using ant colony optimization. Eur J Oper Res 199(2):349–358. https://doi.org/10.1016/j.ejor.2008.11.021Simatupang T, Sridharan R (2006) The collaboration index: a measure for supply chain collaboration. Int J Phys Distrib Logist Manag 35:44–62. https://doi.org/10.1108/09600030510577421Singh G, Ernst A (2011) Resource constraint scheduling with a fractional shared resource. Oper Res Lett 39(5):363–368. https://doi.org/10.1016/j.orl.2011.06.003Singh G, O’Keefe CM (2016) Decentralised scheduling with confidentiality protection. Oper Res Lett 44(4):514–519. https://doi.org/10.1016/j.orl.2016.05.004Sokoler LE, Standardi L, Edlund K, Poulsen NK, Madsen H, Jørgensen JB (2014) A Dantzig–Wolfe decomposition algorithm for linear economic model predictive control of dynamically decoupled subsystems. J Process Control 24(8):1225–1236. https://doi.org/10.1016/j.jprocont.2014.05.013Sridharan R, Simatupang TM (2009) Managerial views of supply chain collaboration. Gadjah Mada Int J Bus 11(2):253–273Stadtler H (2007) A framework for collaborative planning and state-of-the-art. OR Spectr 31(1):5–30. https://doi.org/10.1007/s00291-007-0104-5Stadtler H, Kilger C (2008) Supply chain management and advanced planning. In: Stadtler H, Kilger C (eds) Supply chain management and advanced planning. Concepts, models, software, and case studies. Springer, BerlinStank TP, Goldsby TJ, Vickery SK (1999) Effect of service supplier performance on satisfaction and loyalty of store managers in the fast food industry. J Oper Manag 17(4):429–447. https://doi.org/10.1016/S0272-6963(98)00052-7Taghipour A, Frayret JM (2013) An algorithm to improve operations planning in decentralized supply chains. In: 2013 international conference on advanced logistics and transport, ICALT 2013, pp 100–103. https://doi.org/10.1109/icadlt.2013.6568442Tang SH, Rahimi I, Karimi H (2016a) Objectives, products and demand requirements in integrated supply chain network design: a review. Int J Ind Syst Eng 23(2):181. https://doi.org/10.1504/IJISE.2016.076399Tang J, Zeng C, Pan Z (2016b) Auction-based cooperation mechanism to parts scheduling for flexible job shop with inter-cells. Appl Soft Comput 49:590–602. https://doi.org/10.1016/j.asoc.2016.08.046Thomas A, Singh G, Krishnamoorthy M, Venkateswaran J (2013) Distributed optimisation method for multi-resource constrained scheduling in coal supply chains. Int J Prod Res 51(9):2740–2759. https://doi.org/10.1080/00207543.2012.737955Thomas A, Venkateswaran J, Singh G, Krishnamoorthy M (2014) A resource constrained scheduling problem with multiple independent producers and a single linking constraint: a coal supply chain example. Eur J Oper Res 236(3):946–956. https://doi.org/10.1016/j.ejor.2013.10.006Thomas A, Krishnamoorthy M, Singh G, Venkateswaran J (2015) Coordination in a multiple producers–distributor supply chain and the value of information. Int J Prod Econ 167:63–73. https://doi.org/10.1016/j.ijpe.2015.05.020VICS (2004) Collaborative planning, forecasting and replenishment. Retrieved January 21, 2017, from https://www.gs1us.org/Vitasek K (2016) Strategic sourcing business models. Strateg Outsour Int J 9(2):126–138. https://doi.org/10.1108/SO-02-2016-0003Walther G, Schmid E, Spengler TS (2008) Negotiation-based coordination in product recovery networks. Int J Prod Econ 111(2):334–350. https://doi.org/10.1016/j.ijpe.2006.12.069Wang L, Pfohl HC, Berbner U, Keck AK (2016) Supply chain collaboration or conflict? Information sharing and supply chain performance in the automotive industry. In: Clausen U, Friedrich H, Thaller C, Geiger C (eds) Commercial transport. Springer, Cham, pp 303–318. https://doi.org/10.1007/978-3-319-21266-1Wenzel S, Paulen R, Krämer S, Beisheim B, Engell S (2016a) Shared resource allocation in an integrated petrochemical site by price-based coordination using quadratic approximation. In: 2016 European control conference, ECC 2016, pp 1045–1050. https://doi.org/10.1109/ecc.2016.7810427Wenzel S, Paulen R, Stojanovski G, Kraemer S, Beisheim B, Engell S (2016b) Optimal resource allocation in industrial complexes by distributed optimization and dynamic pricing. At-Automatisierungstechnik 64(6):428–442. https://doi.org/10.1515/auto-2016-0003Whang S (1995) Coordination in operat

Optimality condition decomposition approach to distributed model predictive control

International audienceThis paper presents a new methodology for distributed model predictive control of large-scale systems. The methodology involves two distinct stages, i.e., the decomposition of large-scale systems into subsystems and the design of subsystem controllers. Two procedures are used: in the first stage, the structure of the Karush-Kuhn-Tucker matrix resulting from the necessary optimality conditions is exploited to yield a decomposition of the large-scale system into several subsystems. In the second stage, a particular technique, the so-called optimality condition decomposition makes it possible to synthesize distributed coordinated subcontrollers thus achieving an optimal distributed control of the large-scale system. The convergence of the proposed approach is stated

A distributed predictive control approach for periodic flow-based networks: application to drinking water systems

This paper proposes a distributed model predictive control approach designed to work in a cooperative manner for controlling flow-based networks showing periodic behaviours. Under this distributed approach, local controllers cooperate in order to enhance the performance of the whole flow network avoiding the use of a coordination layer. Alternatively, controllers use both the monolithic model of the network and the given global cost function to optimise the control inputs of the local controllers but taking into account the effect of their decisions over the remainder subsystems conforming the entire network. In this sense, a global (all-to-all) communication strategy is considered. Although the Pareto optimality cannot be reached due to the existence of non-sparse coupling constraints, the asymptotic convergence to a Nash equilibrium is guaranteed. The resultant strategy is tested and its effectiveness is shown when applied to a large-scale complex flow-based network: the Barcelona drinking water supply system.Peer ReviewedPostprint (author's final draft

Distributed Model Predictive Control Based on Dynamic Games

Model predictive control (MPC) is widely recognized as a high performance, yet practical,control technology. This model-based control strategy solves at each sample a discrete-timeoptimal control problem over a finite horizon, producing a control input sequence. Anattractive attribute of MPC technology is its ability to systematically account for systemconstraints. The theory of MPC for linear systems is well developed; all aspects suchas stability, robustness,feasibility and optimality have been extensively discussed in theliterature (see, e.g., (Bemporad & Morari, 1999; Kouvaritakis & Cannon, 2001; Maciejowski, 2002; Mayne et al., 2000)). The effectiveness of MPC depends on model accuracy and the availability of fast computational resources. These requirements limit the application base for MPC. Even though, applications abound in process industries (Camacho & Bordons, 2004), manufacturing (Braun et al., 2003), supply chains (Perea-Lopez et al., 2003), among others, are becoming more widespread.Two common paradigms for solving system-wide MPC calculations are centralised anddecentralised strategies. Centralised strategies may arise from the desire to operate thesystem in an optimal fashion, whereas decentralised MPC control structures can result fromthe incremental roll-out of the system development. An effective centralised MPC can bedifficult, if not impossible to implement in large-scale systems (Kumar & Daoutidis, 2002;Lu, 2003). In decentralised strategies, the system-wide MPC problem is decomposed intosubproblems by taking advantage of the system structure, and then, these subproblemsare solved independently. In general, decentralised schemes approximate the interactionsbetween subsystems and treat inputs in other subsystems as external disturbances. Thisassumption leads to a poor systemperformance (Sandell Jr et al., 1978; ?iljak, 1996). Therefore, there is a need for a cross-functional integration between the decentralised controllers, in which a coordination level performs steady-state target calculation for decentralised controller (Aguilera & Marchetti, 1998; Aske et al., 2008; Cheng et al., 2007; 2008; Zhu & Henson, 2002).Several distributed MPC formulations are available in the literature. A distributed MPCframework was proposed by Dumbar and Murray (Dunbar & Murray, 2006) for the classof systems that have independent subsystem dynamic but link through their cost functionsand constraints. Then, Dumbar (Dunbar, 2007) proposed an extension of this framework thathandles systemswith weakly interacting dynamics. Stability is guaranteed through the use ofa consistency constraint that forces the predicted and assumed input trajectories to be close toeach other. The resulting performance is different from centralised implementations in mostof cases. Distributed MPC algorithms for unconstrained and LTI systems were proposed in(Camponogara et al., 2002; Jia & Krogh, 2001; Vaccarini et al., 2009; Zhang & Li, 2007). In (Jia & Krogh, 2001) and (Camponogara et al., 2002) the evolution of the states of each subsystem is assumed to be only influenced by the states of interacting subsystems and local inputs, while these restrictions were removed in (Jia & Krogh, 2002; Vaccarini et al., 2009; Zhang & Li, 2007). This choice of modelling restricts the system where the algorithm can be applied, because inmany cases the evolution of states is also influenced by the inputs of interconnected subsystems. More critically for these frameworks is the fact that subsystems-based MPCs only know the cost functions and constraints of their subsystem. However, stability and optimality as well as the effect of communication failures has not been established.The distributed model predictive control problem from a game theory perspective for LTIsystems with general dynamical couplings, and the presence of convex coupled constraintsis addressed. The original centralised optimisation problem is transformed in a dynamicgame of a number of local optimisation problems, which are solved using the relevantdecision variables of each subsystem and exchanging information in order to coordinatetheir decisions. The relevance of proposed distributed control scheme is to reduce thecomputational burden and avoid the organizational obstacles associated with centralisedimplementations, while retains its properties (stability, optimality, feasibility). In this context,the type of coordination that can be achieved is determined by the connectivity and capacity of the communication network as well as the information available of system?s cost function and constraints. In this work we will assume that the connectivity of the communication network is sufficient for the subsystems to obtain information of all variables that appear in their local problems. We will show that when system?s cost function and constraints are known by all distributed controllers, the solution of the iterative process converge to the centralised MPC solution. This means that properties (stability, optimality, feasibility) of the solution obtained using the distributed implementation are the same ones of the solution obtained using the centralised implementation. Finally, the effects of communication failures on the system?s properties (convergence, stability and performance) are studied. We will show the effect of the system partition and communication on convergence and stability, and we will find a upper bound of the system performance.Fil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Sanchez, Guido Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Murillo, Marina Hebe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Protocolo:revisión sistemática de literatura sobre los mecanismos de coordinación en los modelos de programación matemática para la toma de decisiones descentralizadas

[EN] The article presents the research protocol for a systematic literature review on the coordination mechanisms in the mathematical programming for decentralized decision making on the planning and scheduling, intra or inter companies from 2006 to 2016.[ES] El artículo presenta el protocolo de investigación para la realización de una revisión sistemática sobre los mecanismos de coordinación en los modelos de programación matemá- tica, para la toma de decisiones descentralizadas sobre la planificación y la programación de la producción, entre plantas de la misma empresa o entre plantas de diferentes empresas, en el periodo de 2006 a 2016.Rius-Sorolla, G.; Maheut, J.; Estelles-Miguel, S.; Garcia-Sabater, JP. (2017). Protocol: Systematic Literature Review on coordination mechanisms for the mathematical programming models in production planning with decentralized decision making. Working Papers on Operations Management. 8(2):22-43. https://doi.org/10.4995/wpom.v8i2.7858SWORD224382Lehoux, N., D’Amours, S., Frein, Y., Langevin, A., & Penz, B. (2011). Collaboration for a two-echelon supply chain in the pulp and paper industry: the use of incentives to increase profit. Journal of the Operational Research Society, 62(4), 581-592. doi:10.1057/jors.2009.167Lehoux, N., D’Amours, S., & Langevin, A. (2010). A win-win collaboration approach for a two-echelon supply chain: a case study in the pulp and paper industry. European J. of Industrial Engineering, 4(4), 493. doi:10.1504/ejie.2010.035656Li, X., & Wang, Q. (2007). Coordination mechanisms of supply chain systems. European Journal of Operational Research, 179(1), 1-16. doi:10.1016/j.ejor.2006.06.023Lu, S. Y. P., Lau, H. Y. K., & Yiu, C. K. F. (2012). A hybrid solution to collaborative decision-making in a decentralized supply-chain. Journal of Engineering and Technology Management, 29(1), 95-111. doi:10.1016/j.jengtecman.2011.09.008Malone, T. W., & Crowston, K. (1994). The interdisciplinary study of coordination. ACM Computing Surveys, 26(1), 87-119. doi:10.1145/174666.174668Mason, A. N., & Villalobos, J. R. (2015). Coordination of perishable crop production using auction mechanisms. Agricultural Systems, 138, 18-30. doi:10.1016/j.agsy.2015.04.008Mejias-Sacaluga, A., & Prado-Prado, J. C. (2003). Implementing buyer-supplier partnerships in retailing channels through continuous improvement. International Journal of Services Technology and Management, 4(2), 181. doi:10.1504/ijstm.2003.002578Mouret, S., Grossmann, I. E., & Pestiaux, P. (2011). A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling. Computers & Chemical Engineering, 35(12), 2750-2766. doi:10.1016/j.compchemeng.2011.03.026Mula, J., Peidro, D., Díaz-Madroñero, M., & Vicens, E. (2010). Mathematical programming models for supply chain production and transport planning. European Journal of Operational Research, 204(3), 377-390. doi:10.1016/j.ejor.2009.09.008NIE, L., XU, X., & ZHAN, D. (2008). COLLABORATIVE PLANNING IN SUPPLY CHAINS BY LAGRANGIAN RELAXATION AND GENETIC ALGORITHMS. International Journal of Information Technology & Decision Making, 07(01), 183-197. doi:10.1142/s0219622008002879Nishi, T., Shinozaki, R., & Konishi, M. (2008). An Augmented Lagrangian Approach for Distributed Supply Chain Planning for Multiple Companies. IEEE Transactions on Automation Science and Engineering, 5(2), 259-274. doi:10.1109/tase.2007.894727Peset, F., Ferrer-Sapena, A., Villamón, M., González, L.-M., Toca-Herrera, J.-L., & Aleixandre-Benavent, R. (2013). Scientific literature analysis of Judo in Web of Science®. Archives of Budo, 9, 81-91. doi:10.12659/aob.883883Pibernik, R., & Sucky, E. (2007). An approach to inter-domain master planning in supply chains. International Journal of Production Economics, 108(1-2), 200-212. doi:10.1016/j.ijpe.2006.12.010Pukkala, T., Heinonen, T., & Kurttila, M. (2009). An application of a reduced cost approach to spatial forest planning. Forest Science, 55(1), 13–22. Retrieved from https://www.scopus.com/inward/record.uri?eid=2-s2.0-68349091651&partnerID=40&md5=e1130a5ca21dcad175d7db89c4bd05edSahin, F., & Robinson, E. P. (2002). Flow Coordination and Information Sharing in Supply Chains: Review, Implications, and Directions for Future Research. Decision Sciences, 33(4), 505-536. doi:10.1111/j.1540-5915.2002.tb01654.xSanei Bajgiran, O., Kazemi Zanjani, M., & Nourelfath, M. (2016). The value of integrated tactical planning optimization in the lumber supply chain. International Journal of Production Economics, 171, 22-33. doi:10.1016/j.ijpe.2015.10.021Silva, C. A., Sousa, J. M. C., Runkler, T. A., & Sá da Costa, J. M. G. (2009). Distributed supply chain management using ant colony optimization. European Journal of Operational Research, 199(2), 349-358. doi:10.1016/j.ejor.2008.11.021Simatupang, T. M., & Sridharan, R. (2005). The collaboration index: a measure for supply chain collaboration. International Journal of Physical Distribution & Logistics Management, 35(1), 44-62. doi:10.1108/09600030510577421Singh, G., & Ernst, A. T. (2011). Resource constraint scheduling with a fractional shared resource. Operations Research Letters. doi:10.1016/j.orl.2011.06.003Singh, G., & O’Keefe, C. M. (2016). Decentralised scheduling with confidentiality protection. Operations Research Letters, 44(4), 514-519. doi:10.1016/j.orl.2016.05.004Sokoler, L. E., Standardi, L., Edlund, K., Poulsen, N. K., Madsen, H., & Jørgensen, J. B. (2014). A Dantzig–Wolfe decomposition algorithm for linear economic model predictive control of dynamically decoupled subsystems. Journal of Process Control, 24(8), 1225-1236. doi:10.1016/j.jprocont.2014.05.013Stadtler, H. (2007). A framework for collaborative planning and state-of-the-art. OR Spectrum, 31(1), 5-30. doi:10.1007/s00291-007-0104-5Tang, J., Zeng, C., & Pan, Z. (2016). Auction-based cooperation mechanism to parts scheduling for flexible job shop with inter-cells. Applied Soft Computing, 49, 590-602. doi:10.1016/j.asoc.2016.08.046Tang, S. H., Rahimi, I., & Karimi, H. (2016). Objectives, products and demand requirements in integrated supply chain network design: a review. International Journal of Industrial and Systems Engineering, 23(2), 181. doi:10.1504/ijise.2016.076399Thomas, A., Krishnamoorthy, M., Singh, G., & Venkateswaran, J. (2015). Coordination in a multiple producers–distributor supply chain and the value of information. International Journal of Production Economics, 167, 63-73. doi:10.1016/j.ijpe.2015.05.020Thomas, A., Singh, G., Krishnamoorthy, M., & Venkateswaran, J. (2013). Distributed optimisation method for multi-resource constrained scheduling in coal supply chains. International Journal of Production Research, 51(9), 2740-2759. doi:10.1080/00207543.2012.737955Thomas, A., Venkateswaran, J., Singh, G., & Krishnamoorthy, M. (2014). A resource constrained scheduling problem with multiple independent producers and a single linking constraint: A coal supply chain example. European Journal of Operational Research, 236(3), 946-956. doi:10.1016/j.ejor.2013.10.006Walther, G., Schmid, E., & Spengler, T. S. (2008). Negotiation-based coordination in product recovery networks. International Journal of Production Economics, 111(2), 334-350. doi:10.1016/j.ijpe.2006.12.069Waltman, L., van Eck, N. J., & Noyons, E. C. M. (2010). A unified approach to mapping and clustering of bibliometric networks. Journal of Informetrics, 4(4), 629-635. doi:10.1016/j.joi.2010.07.002Wang, L., Pfohl, H.-C., Berbner, U., & Keck, A. K. (2015). Supply Chain Collaboration or Conflict? Information Sharing and Supply Chain Performance in the Automotive Industry. Lecture Notes in Logistics, 303-318. doi:10.1007/978-3-319-21266-1_20Zoghlami, N., Taghipour, A., Merlo, C., & Abed, M. (2016). Management of divergent production network using decentralised multi-level capacitated lot-sizing models. International Journal of Shipping and Transport Logistics, 8(5), 590. doi:10.1504/ijstl.2016.07868

Dynamic mutual adjustment search for supply chain operations planning coordination

RÉSUMÉ Les chaînes d’approvisionnement sont des systèmes complexes comprenant plusieurs organisations indépendantes avec des objectifs différents dans un environnement incertain et dynamique. Une question clé dans la gestion de chaîne d’approvisionnement (Supply Chain Management) est la coordination des décisions de planification des opérations. Les systèmes de planification de chaîne d’approvisionnement introduits dans la littérature peuvent être classés en deux systèmes de planification principaux: les systèmes de planification centralisés et les systèmes de planification décentralisés. Les systèmes centralisés peuvent théoriquement optimiser les performances de la chaîne d’approvisionnement bien que leur mise en œuvre nécessite un haut degré d’échange d’informations entre les partenaires de la chaîne d’approvisionnement. Cela conduit à des difficultés lorsque des partenaires indépendants ne veulent pas partager l’information. Afin de répondre à ces difficultés, les systèmes décentralisés de planification des opérations sont conçus dans lesquels chaque membre est une entité économique distincte qui prend ses décisions opérationnelles de manière indépendante, mais avec un niveau minimal d’échange d’information. Dans cette thèse, nous étudions dans un premier temps les méthodes de coordination des processus de planification des opérations dans les chaînes d’approvisionnement proposées dans la littérature. Ensuite, nous proposons un cadre de classification de ces méthodes basée sur la technologie mise en œuvre, et identifions des opportunités de recherches. Dans un deuxième temps, nous proposons une approche de coordination décentralisée qui consiste en un ajustement mutuel des décisions de planification basé sur la programmation mathématique et l’échange d’incitatifs financiers. Ce mécanisme, contrairement à un système centralisé traditionnel, implique deux entreprises, qui interagissent l’une avec l’autre afin d’améliorer leur performance. Dans le cadre de cette approche, seul un petit sous ensemble des solutions de coordination sont considérées, et l’expérimentation montre que cette approche de coordination a un potentiel d’amélioration du profit global tout en préservant l’équité en termes de partage des bénéfices de l’amélioration. Enfin, afin de proposer une méthode de coordination capable d’être utilisable dans le contexte dynamique des chaînes d’approvisionnement, cette thèse propose dans un premier temps une stratégie performante de négociation du fournisseur adaptée à l’approche de coordination proposée, ainsi qu’une stratégie de partage des revenus appliquée à un contexte d’horizon roulant. L’analyse de la performance de cette méthode particulière montre également que l’approche proposée produit une stratégie gagnante-gagnante pour les deux partenaires de la chaîne d’approvisionnement et améliore les résultats de planification.----------ABSTRACT Supply chains are complex systems, which include several independent organizations with different objectives, in dynamic uncertain environment. A key issue in supply chain management (SCM) is the coordination of supply chain operations planning decisions. Supply chain planning systems introduced in the literature can be classified into two main planning systems: centralized and decentralized planning systems. Centralized systems can theoretically optimize supply chain performance although its implementation requires a high degree of information exchange among supply chain partners. This leads to difficulties when independent partners do not want to share information. In order to address these difficulties, decentralized systems are designed for supply chains where each member is a separate economic entity that makes its operational decisions independently, yet with some minimal level of information sharing. In this thesis, we first review supply chain operations planning coordination methods from centralized to decentralized approaches proposed in the literature. Next, we propose a classification scheme of these approaches based on the technology used by the authors. Finally, we identify research opportunities. Second, we propose a decentralized operations planning coordination mechanism referred to as mutual adjustment search (MAS), which is based on a negotiation-like mutual adjustment of planning decisions with financial incentives and rooted in mathematical programming. This mechanism, unlike traditional centralized system, involves two independent enterprises linked by material and non-strategic information flows, which interact with each other in order to coordinate their operations planning, and to improve their individual and collective performance. In this approach, only a few coordination solutions (pairs of coordinated operations plans) are considered and computational analysis shows that this coordination mechanism has the potential to improve global profit, while maintaining fairness in terms of revenue sharing. Finally, in order to develop an approach capable of supporting the dynamic coordination of operations planning in a rolling horizon context, this thesis first proposes a negotiation strategy for the supplier, as well as a revenue sharing protocol. Computational analysis shows that the proposed approach produces a win-win strategy for two partners of supply chain and improves the results of upstream planning

Coordination strategy based on hard-heuristics and price-updating scheme for copper smelting process

Optimal scheduling of the copper smelting process is of great concern in the process industry due to the contradictory objectives of the process units and the presence of inter-dependencies between them. This in combination with commercial interests such as maximizing input concentrates to the Flash Smelting Furnace (FSF), continuous operation of the FSF, and production of the blister copper batches with a shorter batch time hinders the development of a scheduling algorithm based on linear optimization techniques. In this study, a hierarchical scheduling framework is developed that finds feasible schedules for the copper smelting process by solving process inter-dependencies using heuristics. For addressing the FSF inter-dependencies, this framework sees the FSF matte as a scarce resource, and the coordinator uses price-based heuristics for the optimal allocation of the matte to various Peirce-Smith converters. Two case studies are presented to demonstrate the effectiveness of the framework.publishedVersionPeer reviewe