Skip to main content
Erschienen in: Soft Computing 4/2020

05.04.2019 | Focus

Bi-level programming problem in the supply chain and its solution algorithm

verfasst von: Haiyan Luo, Linzhong Liu, Xun Yang

Erschienen in: Soft Computing | Ausgabe 4/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where the upper level of a hierarchy may have his objective function and decision space partly determined by other levels. In addition, each planner’s control instruments may allow him to influence the policies at other levels and thereby to improve his own objective function. As a tool, bi-level programming is applied for modeling decentralized decisions in which two decision makers make decisions successively. In this paper, we specifically address bi-level decision-making problems with budget constraint as an attractive feature in the context of enterprise-wide supply chain. We first describe the typical bi-level linear programming problem (BLLPP) and its optimal solution to the penalty function problem, and then, a cooperative decision-making problem in supply chain is modeled as BLLPP. A particle swarm optimization-based computational algorithm is designed to solve the problem, and the numerical example is presented to illustrate the proposed framework.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Anandalingam G, White D (1990) A solution method for the linear static Stackelberg problem using penalty functions. IEEE Trans Autom Control 35:1170–1173MathSciNetMATH Anandalingam G, White D (1990) A solution method for the linear static Stackelberg problem using penalty functions. IEEE Trans Autom Control 35:1170–1173MathSciNetMATH
Zurück zum Zitat Bard J (1984) An investigation of the linear three level programming problem. IEEE Trans Syst Man Cybern 14:711–717MathSciNetMATH Bard J (1984) An investigation of the linear three level programming problem. IEEE Trans Syst Man Cybern 14:711–717MathSciNetMATH
Zurück zum Zitat Bard J (1998) Practical bi-level optimization: algorithms and applications. Kluwer Academic Publishers, BostonMATH Bard J (1998) Practical bi-level optimization: algorithms and applications. Kluwer Academic Publishers, BostonMATH
Zurück zum Zitat Bard J, Falk J (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9:77–100MathSciNet Bard J, Falk J (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9:77–100MathSciNet
Zurück zum Zitat Bard J, Moore J (1990) A branch and bound algorithm for the bi-level programming problem. SIAM J Sci Stat Comput 11:281–292MATH Bard J, Moore J (1990) A branch and bound algorithm for the bi-level programming problem. SIAM J Sci Stat Comput 11:281–292MATH
Zurück zum Zitat Baumol W, Fabian T (1964) Decomposition, pricing for decentralization and external economies. Manag Sci 11:1–32 Baumol W, Fabian T (1964) Decomposition, pricing for decentralization and external economies. Manag Sci 11:1–32
Zurück zum Zitat Ben-Ayed O, Blair C (1990) Computational difficulties of bi-level linear programming. Oper Res 38:556–560MathSciNetMATH Ben-Ayed O, Blair C (1990) Computational difficulties of bi-level linear programming. Oper Res 38:556–560MathSciNetMATH
Zurück zum Zitat Bernstein F, Federgruen A (2003) Pricing and replenishment strategies in a distribution system with competing retailers. Oper Res 51(3):409–426MATH Bernstein F, Federgruen A (2003) Pricing and replenishment strategies in a distribution system with competing retailers. Oper Res 51(3):409–426MATH
Zurück zum Zitat Boyaci Gallego (2002) Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers. Int J Prod Econ 77(2):95–111 Boyaci Gallego (2002) Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers. Int J Prod Econ 77(2):95–111
Zurück zum Zitat Brandenburger AM, Stuart HW (1996) Value-based business strategy. J Econ Manag Strat 5(1):5–24 Brandenburger AM, Stuart HW (1996) Value-based business strategy. J Econ Manag Strat 5(1):5–24
Zurück zum Zitat Calvete H, Gale C, Mateo P (2008) A new approach for solving linear bilevel problems using genetic algorithms. Eur J Oper Res 188:14–28MathSciNetMATH Calvete H, Gale C, Mateo P (2008) A new approach for solving linear bilevel problems using genetic algorithms. Eur J Oper Res 188:14–28MathSciNetMATH
Zurück zum Zitat Calvete H, Gale C, Dempe S, Lohse S (2012) Bi-level problems over polyhedra with extreme point optimal solutions. J Global Optim 53:573–586MathSciNetMATH Calvete H, Gale C, Dempe S, Lohse S (2012) Bi-level problems over polyhedra with extreme point optimal solutions. J Global Optim 53:573–586MathSciNetMATH
Zurück zum Zitat Carrasqueira P, Alves M, Antunes C (2017) Bi-level particle swarm optimization and evolutionary algorithm approaches for residential demand response with different user profiles. Inf Sci 418–419:405–420 Carrasqueira P, Alves M, Antunes C (2017) Bi-level particle swarm optimization and evolutionary algorithm approaches for residential demand response with different user profiles. Inf Sci 418–419:405–420
Zurück zum Zitat Chirgui Z (2005) The economies of the smart card industry: towards coopetitive strategies. Econ Innov N Technol 14(6):455–477 Chirgui Z (2005) The economies of the smart card industry: towards coopetitive strategies. Econ Innov N Technol 14(6):455–477
Zurück zum Zitat Choi S (1991) Price competition in a channel structure with a common retailer. Market Sci 10(4):271–296MathSciNet Choi S (1991) Price competition in a channel structure with a common retailer. Market Sci 10(4):271–296MathSciNet
Zurück zum Zitat Clerc M, Kennedy J (2002) The particle swarm–explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6:58–73 Clerc M, Kennedy J (2002) The particle swarm–explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6:58–73
Zurück zum Zitat Coello Coello C (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41:113–127MATH Coello Coello C (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41:113–127MATH
Zurück zum Zitat Coello Coello C, Christiansen A (1997) A simple genetic algorithm for the design of reinforced concrete beams. Eng Comput 13:185–196 Coello Coello C, Christiansen A (1997) A simple genetic algorithm for the design of reinforced concrete beams. Eng Comput 13:185–196
Zurück zum Zitat Cruz J (1978) Leader-follower strategies for multilevel systems. IEEE Trans Autom Control 23:244–255MathSciNetMATH Cruz J (1978) Leader-follower strategies for multilevel systems. IEEE Trans Autom Control 23:244–255MathSciNetMATH
Zurück zum Zitat Dantzig G, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8:101–111MATH Dantzig G, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8:101–111MATH
Zurück zum Zitat Das T, Teng B (2000) Instabilities of strategic alliances: an internal tensions perspective. Organ Sci 11(1):77–101 Das T, Teng B (2000) Instabilities of strategic alliances: an internal tensions perspective. Organ Sci 11(1):77–101
Zurück zum Zitat Dasgupta D, Michalewicz Z (1997) Evolutionary algorithms in engineering applications, 1st edn. Springer, BerlinMATH Dasgupta D, Michalewicz Z (1997) Evolutionary algorithms in engineering applications, 1st edn. Springer, BerlinMATH
Zurück zum Zitat Davood M, Seyed H, Ashkan H (2016) A game theoretic analysis in capacity-constrained supplier-selection and cooperation by considering the total supply chain inventory costs. Int J Prod Econ 181:87–97 Davood M, Seyed H, Ashkan H (2016) A game theoretic analysis in capacity-constrained supplier-selection and cooperation by considering the total supply chain inventory costs. Int J Prod Econ 181:87–97
Zurück zum Zitat Deb K, Sinha A (2010) An efficient and accurate solution methodology for bi-level multi-objective programming problems using a hybrid evolutionary-local-search algorithm. Evol Comput 18:403–449 Deb K, Sinha A (2010) An efficient and accurate solution methodology for bi-level multi-objective programming problems using a hybrid evolutionary-local-search algorithm. Evol Comput 18:403–449
Zurück zum Zitat Dempe S, Zemkoho A (2012) On the Karush-Kuhn-Tucker reformulation of the bi-level optimization problem. Nonlinear Anal: Theory, Methods Appl 75:1202–1218MATH Dempe S, Zemkoho A (2012) On the Karush-Kuhn-Tucker reformulation of the bi-level optimization problem. Nonlinear Anal: Theory, Methods Appl 75:1202–1218MATH
Zurück zum Zitat Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micromachine and human science, 1995 (MHS’95). IEEE Nagoya, Japan: IEEE, pp 39–43 Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micromachine and human science, 1995 (MHS’95). IEEE Nagoya, Japan: IEEE, pp 39–43
Zurück zum Zitat Esmaeili M, Aryanezhad MB, Zeephongsekul P (2009) A game theory approach in seller-buyer supply chain. Eur J Oper Res 195:442–448MathSciNetMATH Esmaeili M, Aryanezhad MB, Zeephongsekul P (2009) A game theory approach in seller-buyer supply chain. Eur J Oper Res 195:442–448MathSciNetMATH
Zurück zum Zitat Gendreau M, Marcotte P, Savard G (1996) A hybrid tabu-ascent algorithm for the linear bi-level programming problem. J Global Optim 8:217–233MathSciNetMATH Gendreau M, Marcotte P, Savard G (1996) A hybrid tabu-ascent algorithm for the linear bi-level programming problem. J Global Optim 8:217–233MathSciNetMATH
Zurück zum Zitat Granot D, Sosic GA (2003) Three-stage model for a decentralized distribution system of retailers. Oper Res 51(5):771–784MathSciNetMATH Granot D, Sosic GA (2003) Three-stage model for a decentralized distribution system of retailers. Oper Res 51(5):771–784MathSciNetMATH
Zurück zum Zitat Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bi-level programming. SIAM J Sci Stat Comput 13:1194–1217MATH Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bi-level programming. SIAM J Sci Stat Comput 13:1194–1217MATH
Zurück zum Zitat He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20:89–99 He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20:89–99
Zurück zum Zitat Hejazi S, Memariani A, Jahanshahloo G, Sepehri M (2002) Linear bi-level programming solution by genetic algorithm. Comput Oper Res 29:1913–1925MathSciNetMATH Hejazi S, Memariani A, Jahanshahloo G, Sepehri M (2002) Linear bi-level programming solution by genetic algorithm. Comput Oper Res 29:1913–1925MathSciNetMATH
Zurück zum Zitat Heppner F, Grenander U (1990) A stochastic non-linear model for bird flocking. In: Krasner S (ed) The Ubiquity of Chaos Washington, D.C.: American Association for the Advancement of Science, 1st edn. American Association for the Advancement of Science, Washington, D.C., pp 233–238 Heppner F, Grenander U (1990) A stochastic non-linear model for bird flocking. In: Krasner S (ed) The Ubiquity of Chaos Washington, D.C.: American Association for the Advancement of Science, 1st edn. American Association for the Advancement of Science, Washington, D.C., pp 233–238
Zurück zum Zitat Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks. Perth, Australia: Piscataway, NJ, USA: IEEE, pp 1942–1948 Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks. Perth, Australia: Piscataway, NJ, USA: IEEE, pp 1942–1948
Zurück zum Zitat Kim K, Hwang H (1989) Simultaneous improvement of supplier’s profit and buyer’s cost by utilizing quantity discounts. J Oper Res Soc 40:255–256MATH Kim K, Hwang H (1989) Simultaneous improvement of supplier’s profit and buyer’s cost by utilizing quantity discounts. J Oper Res Soc 40:255–256MATH
Zurück zum Zitat Kohli R, Park H (1989) A cooperative game theory model of quantity discounts. Manag Sci 35:693–707MATH Kohli R, Park H (1989) A cooperative game theory model of quantity discounts. Manag Sci 35:693–707MATH
Zurück zum Zitat Kuo R, Han Y (2011) A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem—a case study on supply chain model. Appl Math Model 35:3905–3917MathSciNetMATH Kuo R, Han Y (2011) A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem—a case study on supply chain model. Appl Math Model 35:3905–3917MathSciNetMATH
Zurück zum Zitat Kuo R, Huang C (2009) Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Comput Math Appl 58:678–685MathSciNetMATH Kuo R, Huang C (2009) Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Comput Math Appl 58:678–685MathSciNetMATH
Zurück zum Zitat Kuo R, Lee Y, Zulvia F, Tien F (2015) Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm. Appl Math Comput 266:1013–1026MathSciNetMATH Kuo R, Lee Y, Zulvia F, Tien F (2015) Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm. Appl Math Comput 266:1013–1026MathSciNetMATH
Zurück zum Zitat Li S, Huang Z, Ashley A (1996) Improving buyer seller system cooperation through inventory control. Int J Prod Econ 43(1):312–323 Li S, Huang Z, Ashley A (1996) Improving buyer seller system cooperation through inventory control. Int J Prod Econ 43(1):312–323
Zurück zum Zitat Liu Q, Wei W, Yuan H, Zhan ZH, Li Y (2016) Topology selection for particle swarm optimization. Inf Sci 363:154–173 Liu Q, Wei W, Yuan H, Zhan ZH, Li Y (2016) Topology selection for particle swarm optimization. Inf Sci 363:154–173
Zurück zum Zitat Liu L, Luo H, Mu H, yang J, Li X (2018) A self-adaptive hybrid particle swarm optimization algorithm. Inf Sci, (submitted) Liu L, Luo H, Mu H, yang J, Li X (2018) A self-adaptive hybrid particle swarm optimization algorithm. Inf Sci, (submitted)
Zurück zum Zitat Luo Y (2007) Coopetition perspective of global competition. J World Bus 42(1):129–144 Luo Y (2007) Coopetition perspective of global competition. J World Bus 42(1):129–144
Zurück zum Zitat Lynn N, Ali M, Suganthan P (2018) Population topologies for particle swarm optimization and differential evolution. Swarm Evol Comput 39:24–35 Lynn N, Ali M, Suganthan P (2018) Population topologies for particle swarm optimization and differential evolution. Swarm Evol Comput 39:24–35
Zurück zum Zitat Marinakis Y, Marinaki M (2013) Particle swarm optimization with expanding neighborhood topology for the permutation flowshop scheduling problem. Soft Comput 17:1159–1173MATH Marinakis Y, Marinaki M (2013) Particle swarm optimization with expanding neighborhood topology for the permutation flowshop scheduling problem. Soft Comput 17:1159–1173MATH
Zurück zum Zitat Mathieu R, Pittard L, Anandalingam G (1994) Genetic algorithm based approach to bi-level linear programming. Oper Res 28:1–21MathSciNetMATH Mathieu R, Pittard L, Anandalingam G (1994) Genetic algorithm based approach to bi-level linear programming. Oper Res 28:1–21MathSciNetMATH
Zurück zum Zitat Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler, maybe better. IEEE Trans Evol Comput 8:204–210 Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: simpler, maybe better. IEEE Trans Evol Comput 8:204–210
Zurück zum Zitat Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 2:1087–1092 Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 2:1087–1092
Zurück zum Zitat Mladenovic N, Hansen P (1997) Variable neighborhood search. Computers. Oper Res 24:1097–1100MathSciNetMATH Mladenovic N, Hansen P (1997) Variable neighborhood search. Computers. Oper Res 24:1097–1100MathSciNetMATH
Zurück zum Zitat Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization—an overview. Swarm Intell 1:33–57 Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization—an overview. Swarm Intell 1:33–57
Zurück zum Zitat Roghanian E, Sadiadi S, Aryanezhad M (2007) A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl Math Comput 188:786–800MathSciNetMATH Roghanian E, Sadiadi S, Aryanezhad M (2007) A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl Math Comput 188:786–800MathSciNetMATH
Zurück zum Zitat Ryu J, Dua V, Efstratios N (2004) A bi-level programming framework for enterprise-wide process networks under uncertainty. Comput Chem Eng 28:1121–1129 Ryu J, Dua V, Efstratios N (2004) A bi-level programming framework for enterprise-wide process networks under uncertainty. Comput Chem Eng 28:1121–1129
Zurück zum Zitat Samma H, Lim C, Saleh J (2016) A new reinforcement learning-based metric particle swarm optimizer. Appl Soft Comput 43:276–297 Samma H, Lim C, Saleh J (2016) A new reinforcement learning-based metric particle swarm optimizer. Appl Soft Comput 43:276–297
Zurück zum Zitat Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE World congress on computational intelligence. Anchorage, AK, USA: Piscataway, NJ, USA: IEEE, pp 69–73 Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE World congress on computational intelligence. Anchorage, AK, USA: Piscataway, NJ, USA: IEEE, pp 69–73
Zurück zum Zitat Wan Z, Wang G, Sun B (2013) A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving nonlinear bi-level programming problems. Swarm Evol Comput 8:26–32 Wan Z, Wang G, Sun B (2013) A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving nonlinear bi-level programming problems. Swarm Evol Comput 8:26–32
Zurück zum Zitat Wang Q (2004) Coordinating independent buyers with integer-ratio time coordination and quantity discounts. Naval Res Log 51(3):316–331MathSciNetMATH Wang Q (2004) Coordinating independent buyers with integer-ratio time coordination and quantity discounts. Naval Res Log 51(3):316–331MathSciNetMATH
Zurück zum Zitat Wang L, Yang B, Orchard J (2016) Particle swarm optimization using dynamic tournament topology. Appl Soft Comput 48:584–596 Wang L, Yang B, Orchard J (2016) Particle swarm optimization using dynamic tournament topology. Appl Soft Comput 48:584–596
Zurück zum Zitat White D, Anandalingam G (1993) A penalty function approach for solving bi-level linear programs. J Global Optim 3:397–419MathSciNetMATH White D, Anandalingam G (1993) A penalty function approach for solving bi-level linear programs. J Global Optim 3:397–419MathSciNetMATH
Zurück zum Zitat Wu T, Shi L, Geunes J et al (2011) An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging. Eur J Oper Res 214:428–441MathSciNetMATH Wu T, Shi L, Geunes J et al (2011) An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging. Eur J Oper Res 214:428–441MathSciNetMATH
Zurück zum Zitat Yeh K, Whittaker C, Realff M, Lee J (2015) Two stage stochastic bi-level programming model of a pre-established timberlands supply chain with biorefinery investment interests. Comput Chem Eng 73:141–153 Yeh K, Whittaker C, Realff M, Lee J (2015) Two stage stochastic bi-level programming model of a pre-established timberlands supply chain with biorefinery investment interests. Comput Chem Eng 73:141–153
Zurück zum Zitat Yin Y (2000) Genetic algorithm based approach for bi-level programming models. J Transp Eng 126:115–120 Yin Y (2000) Genetic algorithm based approach for bi-level programming models. J Transp Eng 126:115–120
Zurück zum Zitat Yu G, Liang H, George Q (2006) Leader-follower game in vender-managed inventory system with limited production capacity considering wholesale and retail prices. Int J Log: Res Appl 9:335–350 Yu G, Liang H, George Q (2006) Leader-follower game in vender-managed inventory system with limited production capacity considering wholesale and retail prices. Int J Log: Res Appl 9:335–350
Metadaten
Titel
Bi-level programming problem in the supply chain and its solution algorithm
verfasst von
Haiyan Luo
Linzhong Liu
Xun Yang
Publikationsdatum
05.04.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 4/2020
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-019-03930-7

Weitere Artikel der Ausgabe 4/2020

Soft Computing 4/2020 Zur Ausgabe