272 research outputs found
Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control
This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model
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.; GarcÃa 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, DÃaz 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, GarcÃa-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 bibliografÃa (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, DÃaz-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
Decomposition techniques for large scale stochastic linear programs
Stochastic linear programming is an effective and often used technique for incorporating uncertainties about future events into decision making processes. Stochastic linear programs tend to be significantly larger than other types of linear programs and generally require sophisticated decomposition solution procedures. Detailed algorithms based uponDantzig-Wolfe and L-Shaped decomposition are developed and implemented. These algorithms allow for solutions to within an arbitrary tolerance on the gap between the lower and upper bounds on a problem\u27s objective function value. Special procedures and implementation strategies are presented that enable many multi-period stochastic linear programs to be solved with two-stage, instead of nested, decomposition techniques. Consequently, abroad class of large scale problems, with tens of millions of constraints and variables, can be solved on a personal computer. Myopic decomposition algorithms based upon a shortsighted view of the future are also developed. Although unable to guarantee an arbitrary solution tolerance, myopic decomposition algorithms may yield very good solutions in a fraction of the time required by Dantzig-Wolfe/L-Shaped decomposition based algorithms.In addition, derivations are given for statistics, based upon Mahalanobis squared distances,that can be used to provide measures for a random sample\u27s effectiveness in approximating a parent distribution. Results and analyses are provided for the applications of the decomposition procedures and sample effectiveness measures to a multi-period market investment model
A Polyhedral Approximation Framework for Convex and Robust Distributed Optimization
In this paper we consider a general problem set-up for a wide class of convex
and robust distributed optimization problems in peer-to-peer networks. In this
set-up convex constraint sets are distributed to the network processors who
have to compute the optimizer of a linear cost function subject to the
constraints. We propose a novel fully distributed algorithm, named
cutting-plane consensus, to solve the problem, based on an outer polyhedral
approximation of the constraint sets. Processors running the algorithm compute
and exchange linear approximations of their locally feasible sets.
Independently of the number of processors in the network, each processor stores
only a small number of linear constraints, making the algorithm scalable to
large networks. The cutting-plane consensus algorithm is presented and analyzed
for the general framework. Specifically, we prove that all processors running
the algorithm agree on an optimizer of the global problem, and that the
algorithm is tolerant to node and link failures as long as network connectivity
is preserved. Then, the cutting plane consensus algorithm is specified to three
different classes of distributed optimization problems, namely (i) inequality
constrained problems, (ii) robust optimization problems, and (iii) almost
separable optimization problems with separable objective functions and coupling
constraints. For each one of these problem classes we solve a concrete problem
that can be expressed in that framework and present computational results. That
is, we show how to solve: position estimation in wireless sensor networks, a
distributed robust linear program and, a distributed microgrid control problem.Comment: submitted to IEEE Transactions on Automatic Contro
Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic
Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time
Column-generation and interior point methods applied to the long-term electric power-planning problem
Aquesta tesi s'adreça al problema de planificació de la generació elèctrica a llarg termini per a una companyia especÃfica (SGC) que participa en un mercat liberalitzat organitzat en un pool. Els objectius de la tesi són: modelitzar aquest problema, i desenvolupar i implementar tècniques apropiades i eficients que el resolguin. Un planificació òptima a llarg termini és important, per exemple, per a la confecció de pressupostos, o per a la gestió de compres/consum de combustibles. Una altra aplicació és la de guiar la planificació a curt termini perquè aquesta tingui en compte decisions preses sota una òptica de llarg termini. La nostra proposta per a fer la planificació de la generació és optimitzar la generació esperada de cada unitat (o la unió de diverses unitats de caracterÃstiques semblants) del pool per a cada interval en que dividim el llarg termini. El model bà sic per la planificació de la generació a llarg termini (LTGP) maximitza el benefici de totes les unitats del pool. La constricció més important és la satisfacció de la demanda, ja que el sistema està sempre balancejat. Utilitzem la formulació de Bloom i Gallant, la qual modela la cà rrega a través d'una monòtona de cà rrega per cada interval i requereix un número exponencial de constriccions lineals de desigualtat, anomenades LMCs. Altres constriccions (lineals) incloses en el model són: garantia de potència, lÃmits en la disponibilitat de combustibles, emissions mà ximes de CO2 o una quota de mercat mÃnima per a la SGC. Una extensió d'aquest model és la planificació conjunta de l'assignació de manteniments de les unitats tèrmiques d'una SGC amb la planificació de la generació. El model conjunt és un problema quadrà tic amb variables binà ries i contÃnues. Per resoldre aquest model es proposa un parell d'heurÃstiques i s'ha implementat un prototipus de branch and bound en AMPL.Aquesta tesi també proposa una manera per coordinar el model LTGP proposat amb una planificació a curt termini. Es desenvolupa un model de curt que inclou els resultats de llarg termini. Donat que el model de planificació a llarg termini s'ha de resoldre sovint (principalment per passar informació acurada al model de curt), les tècniques emprades per a resoldre'l han de donar resultats fiables en un espai de temps curt. Les tècniques aplicades han estat:· Donat que les constriccions de recobriment i les fites de no negativitat defineixen un polÃedre convex els vèrtexs del qual són fà cils de trobar el model es transforma i les variables esdevenen els coeficients convexos que defineixen un punt. Aquest nou problema es resolt amb l'algoritme de Murtagh i Saunders, que és un procediment òptim. Aquest algoritme s'aplica sota un esquema de generació de columnes donat que el número de vèrtexs del polÃedre és comparable al número de constriccions. L'avantatge d'aquest mètode és que els vèrtexs es van generant a mesura que es necessiten.· L'aplicació de mètodes directes és computacionalment costós donat el número exponencial de LMCs. De totes maneres, a l'òptim només un conjunt reduït de constriccions de recobriment seran actives. Hem desenvolupat una heurÃstica, anomenada heurÃstica GP, la qual genera un subconjunt de constriccions, entre les quals hi ha les LMCs que són actives a l'òptim. L'heurÃstica resol una seqüència de problemes quadrà tics, els quals incrementen el número de LMCs considerades a cada iteració. Els problemes es resolen amb mètodes de punt interior que s'inicialitzen amb tècniques de warm start per tal d'accelerar la convergència cap a la nova solució. Aquest procediment resulta ser molt més eficient que el de generació de columnes. La modelització i els casos de prova estan basats en dades d'un sistema de pool pur i de mercat com ha estat a Espanya fins el juliol de 2006.This thesis presents an approach to the long-term planning of power generation for a company (SGC) participating in a liberalized market organized as a pool. The goal of this thesis is two-fold: to model the problem and to develop and implement appropriate and efficient techniques for solving it.The optimization of the long-term generation planning is important for budgeting and planning fuel acquisitions, and to give a frame where to fit short-term generation planning.Our proposal for planning long-term generation is to optimize the expected generation of each unit (or the merger of several units of the same type) in the power pool over each interval into which the long-term horizon is split.The basic model for long-term generation planning (LTGP) maximizes the profit for all the units participating in the pool. The most important constraint is matching demand, since the market always clears. The Bloom and Gallant formulation is used, which models the load with a load-duration curve for each interval and requires an exponential number of linear inequality constraints, called herein LMCs. Other (linear) constraints included in the model are: minimum generation time, limits on the availability of fuel, maximum CO2 emission limits or the market share of the SGC. This thesis also proposes the way in which coordination between the LTGP model developed and a short-term plan should be considered and provides a model for short-term electrical power planning adapted to the LTGP proposed and which includes the long-term results.Another decision that needs to be taken from a long-term point of view is the joint scheduling of thermal unit maintenances with the generation planning of a particular SGC. The results of a prototype of a Branch and Bound implemented in AMPL are included in this thesis.Long-term planning needs to be considered before short-term planning and whenever the real situation deviates from the forecasted parameters, so the techniques implemented must be efficient so as to provide reliable solutions in a short time. Two methods for handling the LMCs are proposed and compared:● A decomposition technique exploits the fact that the LMCs plus the non-negativity bounds define a convex polyhedron for each interval whose vertices are easy to find. Thus, the problem is transformed and the variables become the coefficients of a convex combination of the vertices. The transformed problem is quadratic with linear constraints, making it suitable to be solved with the Murtagh & Saunders algorithm, which gives an optimal solution. A column-generation approach is used because the number of vertices of the polyhedron is comparable to the number of LMCs. The advantage of this method is that it does not require previous computation of all of the vertices, but rather computes them as the algorithm iterates.● The application of direct methods is computationally difficult because of the exponential number of inequality LMCs. However, only a reduced subset of LMCs will be active at the optimizer. A heuristic, named GP heuristic, has been devised which is able to find a reduced set of LMCs including those that are active at the optimizer. It solves a sequence of quadratic problems in which the set of LMCs considered is enlarged at each iteration. The quadratic problems are solved with an interior point method, and warm starts are employed to accelerate the solution of the successively enlarged quadratic problems. This procedure is more efficient than the column generation one.The modeling and tests of this thesis are based on the pure pool system and market data from the Spanish system up to July 2006
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