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A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment

Year 2016, Volume: 16 Özel Sayı, 85 - 92, 01.11.2016

Abstract

Modeling of the competitive decision making process between two players which have opposite objectives is defined as “Network Interdiction Problem” in the literature. In this study, procurement process in which two competitive firms procure liquid good from the same set of the suppliers is handled. This process is designed as a network interdiction problem for competition environment in which one of the firms tries to procure goods with minimum cost, the other one tries to maximize the procurement cost of the competitor with owned interdiction budget, as well. In this problem transforming the structure of supply chain into minimum cost flow network, a bi-level mathematical model is proposed

References

  • Akgün, İ., Tansel, B.Ç. ve Wood, R.K. (2011) “The Multi-Terminal Maximum-Flow Network-Interdiction Problem” European Journal of Operational Research, 211(2), 241-251.
  • Ball, M.O., Golden, B.L. ve Vohra, R.V. (1989) “Finding the Most Vital Arcs in a Network” Operations Research Letters, 8(2), 73-76.
  • Bayrak, H. ve Matthew D. Bailey, M.D. (2008) “Shortest Path Network Interdiction with Asymmetric Information” Networks, 52(3), 133-140.
  • Borrero, J.S., Prokopyev, O.A. ve Sauré, D. (2016) “Sequential Shortest Path Interdiction with Incomplete Information” Decision Analysis, 13(1), 68-98.
  • Corley, H. ve Chang, H. (1974) “Finding the n Most Vital Nodes in a Flow Network” Manage Science, 21, 362-364.
  • Corley, H. ve David, Y.S. (1982) “Most Vital Links and Nodes in Weighted Networks” Operations Research Letters, 1(4), 157-160.
  • Cormican, K.J., Morton, D.P. ve Wood, R.K. (1998) “Stochastic Network Interdiction” Operations Research, 46(2), 184-197.
  • Fulkerson, D.R. ve Harding, G.C. (1977) “Maximiz- ing the Minimum Source-Sink Path Subject to a Budget Constraint” Mathematical Programming, 13(1), 116-118.
  • Golden, B. (1978) “A Problem in Network Interdic- tion” Naval Research Logistics Quarterly, 25(4), 711-713.
  • Granata, D., Steeger, G. ve Rebennack, S. (2013) “Network Interdiction via a Critical Disruption Path: Branch-and-Price Algorithms” Computers & Operations Research, 40(11), 2689-2702.
  • Gutfraind, A., Hagberg, A.A., Izraelevitz, D. ve Pan, F. (2010) “Interdiction of a Markovian Evader” Paper presented at the INFORMS Computing Society Confer- ence.
  • Israeli, E. ve Wood, R.K. (2002) “Shortest‐Path Net- work Interdiction” Networks, 40(2), 97-111.
  • Janjarassuk, U. ve Nakrachata-Amon, T. (2016) “A Simulated Annealing Algorithm to the Stochastic Network Interdiction Problem” Paper presented at the IEEE In- ternational Conference on Industrial Engineering and Engineering Management.
  • Keshavarzi, R. ve Fathabadi, H.S. (2015) “Multi-Commodity Multi-Source-Sinks Network Flow Interdiction Problem with Several Interdictors” Journal of Engineering and Applied Sciences, 10(6), 118-122.
  • Khachiyan, L., Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Rudolf, G. ve Zhao, J. (2007) “On Short Paths Interdiction Problems: Total and Node-Wise Lim- ited Interdiction” Theory of Computing Systems, 43(2), 204-233.
  • Lim, C. ve Smith, J.C. (2007) “Algorithms for Dis- crete And Continuous Multicommodity Flow Network Interdiction Problems” IIE Transactions, 39(1), 15-26.
  • Lubore, S., Ratliff, H. ve Sicilia, G.T. (1971) “Deter- mining the Most Vital Link in a Flow Network” Naval Research Logistics Quarterly, 18(4), 497-502.
  • Malik, K., Mittal, A.K. ve Gupta, S.K. (1989) “The k Most Vital Arcs in the Shortest Path Problem” Operations Research Letters, 8(4), 223-227.
  • McMasters, A.W. ve Mustin, T.M. (1970) “Optimal Interdiction of a Supply Network” Naval Research Logis- tics Quarterly, 17(3), 261-268.
  • Nardelli, E., Proietti, G. ve Widmayer, P. (2003) “Finding the Most Vital Node of a Shortest Path” Theo- retical Computer Science, 296(1), 167-177.
  • Prince, M., Smith, J.C. ve Geunes, J. (2013a). “A Three-Stage Procurement Optimization Problem under Uncertainty” Naval Research Logistics (NRL), 60(5), 395- 412.
  • Prince, M., Geunes, J. ve Smith, J.C. (2013b) “Pro- curement Allocation Planning with Multiple Suppliers under Competition” International Journal of Production Research, 51(23-24), 6900-6922.
  • Ratliff, H.D., Sicilia, G.T. ve Lubore, S.H. (1975) “Finding the Most Vital Links in Flow Networks” Man- agement Science, 21(5), 531-539.
  • Royset, J.O. ve Wood, R.K. (2007) “Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem” INFORMS Journal on Computing, 19(2), 175- 184.
  • Stackelberg, v.H. (1952) “The Theory of the Market Economy” London, UK: William Hodge & Co.
  • Washburn, A. ve Wood, K. (1995) “Two-Person Zero-Sum Games for Network Interdiction” Operations Research, 43(2), 243-251.
  • Wollmer, R. (1963) “Some Methods for Determining the Most Vital Link in a Railway Network” Santa Monica, California: Rand Corporation.
  • Wollmer, R. (1964) “Removing Arcs from a Network” Operations Research, 12(6), 934-940.
  • Wood, R.K. (1993) “Deterministic Network Interdic- tion” Mathematical and Computer Modelling, 17(2), 1-18.
  • Yates, J. ve Sanjeevi, S. (2013) “A Length-Based, Multiple-Resource Formulation for Shortest Path Net- work Interdiction Problems in the Transportation Sector” International Journal of Critical Infrastructure Protection, 6(2), 107-119.

Rekabet Ortamında Akışkan Mal Satın Alma Süreci için İki Seviyeli Matematiksel Model Önerisi

Year 2016, Volume: 16 Özel Sayı, 85 - 92, 01.11.2016

Abstract

Literatürde zıt amaçları olan iki taraf arasındaki rekabetçi karar verme sürecinin modellenmesi “Şebeke Engelleme Problemi” olarak ifade edilmektedir. Bu çalışmada aynı tedarikçi kümesini kullanan rekabetçi iki firmanın akışkan mal satın alma süreci ele alınmıştır. Bu süreç, firmalardan birinin minimum maliyetle mal tedarik etmeye çalıştığı, diğerinin ise sahip olduğu engelleme bütçesi ile rakibinin minimum satın alma maliyetini en büyüklemeye çalıştığı bir rekabet ortamı için şebeke engelleme problemi şeklinde tasarlanmıştır. Bu problemdeki tedarik zinciri yapısı minimum maliyetli akış şebekesine dönüştürülerek, iki seviyeli (bi-level) matematiksel bir model önerilmiştir

References

  • Akgün, İ., Tansel, B.Ç. ve Wood, R.K. (2011) “The Multi-Terminal Maximum-Flow Network-Interdiction Problem” European Journal of Operational Research, 211(2), 241-251.
  • Ball, M.O., Golden, B.L. ve Vohra, R.V. (1989) “Finding the Most Vital Arcs in a Network” Operations Research Letters, 8(2), 73-76.
  • Bayrak, H. ve Matthew D. Bailey, M.D. (2008) “Shortest Path Network Interdiction with Asymmetric Information” Networks, 52(3), 133-140.
  • Borrero, J.S., Prokopyev, O.A. ve Sauré, D. (2016) “Sequential Shortest Path Interdiction with Incomplete Information” Decision Analysis, 13(1), 68-98.
  • Corley, H. ve Chang, H. (1974) “Finding the n Most Vital Nodes in a Flow Network” Manage Science, 21, 362-364.
  • Corley, H. ve David, Y.S. (1982) “Most Vital Links and Nodes in Weighted Networks” Operations Research Letters, 1(4), 157-160.
  • Cormican, K.J., Morton, D.P. ve Wood, R.K. (1998) “Stochastic Network Interdiction” Operations Research, 46(2), 184-197.
  • Fulkerson, D.R. ve Harding, G.C. (1977) “Maximiz- ing the Minimum Source-Sink Path Subject to a Budget Constraint” Mathematical Programming, 13(1), 116-118.
  • Golden, B. (1978) “A Problem in Network Interdic- tion” Naval Research Logistics Quarterly, 25(4), 711-713.
  • Granata, D., Steeger, G. ve Rebennack, S. (2013) “Network Interdiction via a Critical Disruption Path: Branch-and-Price Algorithms” Computers & Operations Research, 40(11), 2689-2702.
  • Gutfraind, A., Hagberg, A.A., Izraelevitz, D. ve Pan, F. (2010) “Interdiction of a Markovian Evader” Paper presented at the INFORMS Computing Society Confer- ence.
  • Israeli, E. ve Wood, R.K. (2002) “Shortest‐Path Net- work Interdiction” Networks, 40(2), 97-111.
  • Janjarassuk, U. ve Nakrachata-Amon, T. (2016) “A Simulated Annealing Algorithm to the Stochastic Network Interdiction Problem” Paper presented at the IEEE In- ternational Conference on Industrial Engineering and Engineering Management.
  • Keshavarzi, R. ve Fathabadi, H.S. (2015) “Multi-Commodity Multi-Source-Sinks Network Flow Interdiction Problem with Several Interdictors” Journal of Engineering and Applied Sciences, 10(6), 118-122.
  • Khachiyan, L., Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Rudolf, G. ve Zhao, J. (2007) “On Short Paths Interdiction Problems: Total and Node-Wise Lim- ited Interdiction” Theory of Computing Systems, 43(2), 204-233.
  • Lim, C. ve Smith, J.C. (2007) “Algorithms for Dis- crete And Continuous Multicommodity Flow Network Interdiction Problems” IIE Transactions, 39(1), 15-26.
  • Lubore, S., Ratliff, H. ve Sicilia, G.T. (1971) “Deter- mining the Most Vital Link in a Flow Network” Naval Research Logistics Quarterly, 18(4), 497-502.
  • Malik, K., Mittal, A.K. ve Gupta, S.K. (1989) “The k Most Vital Arcs in the Shortest Path Problem” Operations Research Letters, 8(4), 223-227.
  • McMasters, A.W. ve Mustin, T.M. (1970) “Optimal Interdiction of a Supply Network” Naval Research Logis- tics Quarterly, 17(3), 261-268.
  • Nardelli, E., Proietti, G. ve Widmayer, P. (2003) “Finding the Most Vital Node of a Shortest Path” Theo- retical Computer Science, 296(1), 167-177.
  • Prince, M., Smith, J.C. ve Geunes, J. (2013a). “A Three-Stage Procurement Optimization Problem under Uncertainty” Naval Research Logistics (NRL), 60(5), 395- 412.
  • Prince, M., Geunes, J. ve Smith, J.C. (2013b) “Pro- curement Allocation Planning with Multiple Suppliers under Competition” International Journal of Production Research, 51(23-24), 6900-6922.
  • Ratliff, H.D., Sicilia, G.T. ve Lubore, S.H. (1975) “Finding the Most Vital Links in Flow Networks” Man- agement Science, 21(5), 531-539.
  • Royset, J.O. ve Wood, R.K. (2007) “Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem” INFORMS Journal on Computing, 19(2), 175- 184.
  • Stackelberg, v.H. (1952) “The Theory of the Market Economy” London, UK: William Hodge & Co.
  • Washburn, A. ve Wood, K. (1995) “Two-Person Zero-Sum Games for Network Interdiction” Operations Research, 43(2), 243-251.
  • Wollmer, R. (1963) “Some Methods for Determining the Most Vital Link in a Railway Network” Santa Monica, California: Rand Corporation.
  • Wollmer, R. (1964) “Removing Arcs from a Network” Operations Research, 12(6), 934-940.
  • Wood, R.K. (1993) “Deterministic Network Interdic- tion” Mathematical and Computer Modelling, 17(2), 1-18.
  • Yates, J. ve Sanjeevi, S. (2013) “A Length-Based, Multiple-Resource Formulation for Shortest Path Net- work Interdiction Problems in the Transportation Sector” International Journal of Critical Infrastructure Protection, 6(2), 107-119.
There are 30 citations in total.

Details

Other ID JA36MR32BB
Journal Section Research Article
Authors

Gökhan Özçelik This is me

Cevriye Temel Gencer This is me

Publication Date November 1, 2016
Published in Issue Year 2016 Volume: 16 Özel Sayı

Cite

APA Özçelik, G., & Gencer, C. T. (2016). A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment. Ege Academic Review, 16(5), 85-92.
AMA Özçelik G, Gencer CT. A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment. ear. November 2016;16(5):85-92.
Chicago Özçelik, Gökhan, and Cevriye Temel Gencer. “A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment”. Ege Academic Review 16, no. 5 (November 2016): 85-92.
EndNote Özçelik G, Gencer CT (November 1, 2016) A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment. Ege Academic Review 16 5 85–92.
IEEE G. Özçelik and C. T. Gencer, “A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment”, ear, vol. 16, no. 5, pp. 85–92, 2016.
ISNAD Özçelik, Gökhan - Gencer, Cevriye Temel. “A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment”. Ege Academic Review 16/5 (November 2016), 85-92.
JAMA Özçelik G, Gencer CT. A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment. ear. 2016;16:85–92.
MLA Özçelik, Gökhan and Cevriye Temel Gencer. “A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment”. Ege Academic Review, vol. 16, no. 5, 2016, pp. 85-92.
Vancouver Özçelik G, Gencer CT. A Bi-Level Mathematical Model Proposal for Procurement Process of Liquid Good in Competitive Environment. ear. 2016;16(5):85-92.