A probabilistic bi-level linear multi-objective programming problem to supply chain planning
Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible...
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| Vydáno v: | Applied mathematics and computation Ročník 188; číslo 1; s. 786 - 800 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York, NY
Elsevier Inc
01.05.2007
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels.
In most of the real life problems in mathematical programming, the parameters are considered as random variables. The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called “stochastic programming”.
Supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers.
Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using “multi-level programming” principles.
In this paper, we consider a “probabilistic bi-level linear multi-objective programming problem” and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not. This probabilistic model is first converted into an equivalent deterministic model in each level, to which fuzzy programming technique is applied to solve the multi-objective nonlinear programming problem to obtain a compromise solution. |
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| AbstractList | Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels.
In most of the real life problems in mathematical programming, the parameters are considered as random variables. The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called “stochastic programming”.
Supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers.
Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using “multi-level programming” principles.
In this paper, we consider a “probabilistic bi-level linear multi-objective programming problem” and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not. This probabilistic model is first converted into an equivalent deterministic model in each level, to which fuzzy programming technique is applied to solve the multi-objective nonlinear programming problem to obtain a compromise solution. |
| Author | Aryanezhad, M.B. Sadjadi, S.J. Roghanian, E. |
| Author_xml | – sequence: 1 givenname: E. surname: Roghanian fullname: Roghanian, E. email: E-roghanian@iustarak.ac.ir – sequence: 2 givenname: S.J. surname: Sadjadi fullname: Sadjadi, S.J. email: Sjsadjadi@iust.ac.ir – sequence: 3 givenname: M.B. surname: Aryanezhad fullname: Aryanezhad, M.B. email: Mirarya@iust.ac.ir |
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| Cites_doi | 10.1016/0377-2217(86)90160-8 10.1016/S0098-1354(00)00496-8 10.1287/mnsc.6.1.73 10.1016/0038-0121(78)90023-X 10.1287/mnsc.17.4.B141 10.1111/j.1540-5915.1981.tb00102.x 10.1021/ie960901+ 10.1016/S0098-1354(00)00617-7 10.1021/ie0100030 10.1021/ie9909284 10.1016/j.compchemeng.2003.09.021 10.1016/0165-0114(81)90019-1 10.1016/S0096-3003(03)00628-3 10.1016/0165-0114(78)90031-3 10.1287/opre.16.3.576 10.1111/j.1540-5915.1980.tb01142.x 10.1016/S0098-1354(00)00469-5 10.1287/opre.24.6.1078 10.1021/ie000668m 10.1016/0377-2217(82)90129-1 10.1016/S0165-0114(98)00070-0 10.1016/S0098-1354(00)00495-6 |
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| Keywords | Supply chain management Multi-level multi-objective decision-making Bi-level programming Multi-objective decision-making Fuzzy decision-approach Stochastic programming Decision making Optimization method Linear programming Probability distribution Scheduling Nonlinear problems Non linear programming Extremum problem Numerical analysis Applied mathematics Distribution function Probabilistic model Fuzzy decision- approach Random variable Programming theory Mathematical programming |
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| References | Contini (bib5) 1978; 16 Gjerdrum, Shah, Papageorgiou (bib24) 2001; 40 Zimmermann (bib16) 1978; 1 McDonald, Karimi (bib22) 1997; 36 Sullivan, Fitzsimmoms (bib14) 1978; 12 Gupta, Maranas (bib20) 2000; 39 Osman, Abo-Sinna, Amer (bib29) 2004; 153 Sinha, Hulsurkar, Biswal (bib30) 2000; 109 Sakawa (bib31) 1993 Colson, Marcotte, Savard (bib2) 2005 M.E. Flores, D.E. Rivera, V. Smith-Daniels, Supply chain management using model predictive control, in: AIChE Annual Meeting, Los Angeles, 2000. T. Backx, O. Bosgra, W. Marquardt, Towards intentional dynamics in supply chain conscious process operation, in: Proceedings of the Third International Conference on Foundations of Computer-aided Process Operations, 1998. Leberling (bib8) 1981; 6 Stancu-Minasian, Wets (bib13) 1976; 24 Bose, Pekny (bib27) 2000; 24 Charnes, Cooper (bib4) 1959; 6 Narasimhan (bib10) 1980; 11 Hanan (bib6) 1981; 12 Tsiakis, Shah, Pantelides (bib19) 2001; 40 Zhou, Cheng, Hua (bib25) 2000; 24 Emam (bib1) 2005 Kolbin (bib7) 1977 Abdelaziz, Aouni, El Fayedh (bib11) 2005 Gupta, Maranas, McDonald (bib21) 2000; 24 Leclercq (bib9) 1982; 10 Teghem, Dufrance, Thauvoye, Kunch (bib15) 1986; 26 Perea-Lopez, Grossmann, Ydstie, Tahmassebi (bib26) 2000; 24 Bellman, Zadeh (bib3) 1970; 17 Ryu, Dua, Pistikopoulos (bib17) 2004; 28 Lee, Padmanabhan, Whang (bib23) 1997; 38 Sengupta (bib12) 1972 Sakawa (10.1016/j.amc.2006.10.032_bib31) 1993 Stancu-Minasian (10.1016/j.amc.2006.10.032_bib13) 1976; 24 Tsiakis (10.1016/j.amc.2006.10.032_bib19) 2001; 40 Sinha (10.1016/j.amc.2006.10.032_bib30) 2000; 109 Emam (10.1016/j.amc.2006.10.032_bib1) 2005 Colson (10.1016/j.amc.2006.10.032_bib2) 2005 Leclercq (10.1016/j.amc.2006.10.032_bib9) 1982; 10 Kolbin (10.1016/j.amc.2006.10.032_bib7) 1977 Sullivan (10.1016/j.amc.2006.10.032_bib14) 1978; 12 Hanan (10.1016/j.amc.2006.10.032_bib6) 1981; 12 Zhou (10.1016/j.amc.2006.10.032_bib25) 2000; 24 Sengupta (10.1016/j.amc.2006.10.032_bib12) 1972 Lee (10.1016/j.amc.2006.10.032_bib23) 1997; 38 10.1016/j.amc.2006.10.032_bib28 Osman (10.1016/j.amc.2006.10.032_bib29) 2004; 153 Teghem (10.1016/j.amc.2006.10.032_bib15) 1986; 26 Perea-Lopez (10.1016/j.amc.2006.10.032_bib26) 2000; 24 Abdelaziz (10.1016/j.amc.2006.10.032_bib11) 2005 Leberling (10.1016/j.amc.2006.10.032_bib8) 1981; 6 Gupta (10.1016/j.amc.2006.10.032_bib21) 2000; 24 Bellman (10.1016/j.amc.2006.10.032_bib3) 1970; 17 Narasimhan (10.1016/j.amc.2006.10.032_bib10) 1980; 11 Ryu (10.1016/j.amc.2006.10.032_bib17) 2004; 28 Zimmermann (10.1016/j.amc.2006.10.032_bib16) 1978; 1 Charnes (10.1016/j.amc.2006.10.032_bib4) 1959; 6 Gjerdrum (10.1016/j.amc.2006.10.032_bib24) 2001; 40 Contini (10.1016/j.amc.2006.10.032_bib5) 1978; 16 Bose (10.1016/j.amc.2006.10.032_bib27) 2000; 24 McDonald (10.1016/j.amc.2006.10.032_bib22) 1997; 36 Gupta (10.1016/j.amc.2006.10.032_bib20) 2000; 39 10.1016/j.amc.2006.10.032_bib18 |
| References_xml | – volume: 153 start-page: 239 year: 2004 end-page: 252 ident: bib29 article-title: A multi-level non-linear multi-objective decision-making under fuzziness publication-title: Appl. Math. Comput. – volume: 10 start-page: 33 year: 1982 end-page: 41 ident: bib9 article-title: Stochastic programming: an interactive multi-criteria approach publication-title: Eur. J. Oper. Res. – year: 1993 ident: bib31 article-title: Fuzzy Sets and Interactive Multi-Objective Optimization – volume: 6 start-page: 105 year: 1981 end-page: 118 ident: bib8 article-title: On finding compromise solution in multi-criteria problems using the min-operator publication-title: Fuzzy Sets Syst. – volume: 12 start-page: 215 year: 1978 end-page: 220 ident: bib14 article-title: A goal programming model for readiness and optimal deployment of resources publication-title: Socio-Economic Planning Sci. – reference: T. Backx, O. Bosgra, W. Marquardt, Towards intentional dynamics in supply chain conscious process operation, in: Proceedings of the Third International Conference on Foundations of Computer-aided Process Operations, 1998. – volume: 28 start-page: 1121 year: 2004 end-page: 1129 ident: bib17 article-title: A bilevel programming framework for enterprise-wide process networks under uncertainty publication-title: Comput. Chem. Eng. – volume: 36 start-page: 2691 year: 1997 end-page: 2700 ident: bib22 article-title: Planning and scheduling of parallel semicontinuous processes. Part 1. Production planning publication-title: Ind. Eng. Chem. Res. – volume: 109 start-page: 91 year: 2000 end-page: 96 ident: bib30 article-title: Fuzzy programming approach to multi-objective stochastic programming problems when publication-title: Fuzzy Sets Syst. – reference: M.E. Flores, D.E. Rivera, V. Smith-Daniels, Supply chain management using model predictive control, in: AIChE Annual Meeting, Los Angeles, 2000. – year: 2005 ident: bib2 publication-title: Bilevel Programming: A Survey – volume: 6 start-page: 73 year: 1959 end-page: 79 ident: bib4 article-title: Chance constrained programming publication-title: Manage. Sci. – year: 1977 ident: bib7 article-title: Stochastic Programming – volume: 24 start-page: 2613 year: 2000 end-page: 2621 ident: bib21 article-title: Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management publication-title: Comput. Chem. Eng. – volume: 38 start-page: 93 year: 1997 end-page: 102 ident: bib23 article-title: The bullwhip effect in supply-chains publication-title: Sloan Manage. Rev. – volume: 24 start-page: 1143 year: 2000 end-page: 1149 ident: bib26 article-title: Dynamic modeling and classical control theory for supply chain management publication-title: Comput. Chem. Eng. – volume: 40 start-page: 3585 year: 2001 end-page: 3604 ident: bib19 article-title: Design of multiechelon supply chain networks under demand uncertainty publication-title: Ind. Eng. Chem. Res. – volume: 12 start-page: 522 year: 1981 end-page: 531 ident: bib6 article-title: On fuzzy goal programming publication-title: Decision Sci. – year: 1972 ident: bib12 article-title: Stochastic Programming: Methods and Applications – volume: 39 start-page: 3799 year: 2000 end-page: 3813 ident: bib20 article-title: A two-stage modeling and solution framework for multisite midterm planning under uncertainty publication-title: Ind. Eng. Chem. Res. – start-page: 4 year: 2005 end-page: 6 ident: bib11 article-title: Multi-objective stochastic programming for portfolio selection publication-title: Eur. J. Oper. Res. – volume: 24 start-page: 329 year: 2000 end-page: 335 ident: bib27 article-title: A model predictive framework for planning and scheduling problem: a case study of consumer goods supply chain publication-title: Comput. Chem. Eng. – volume: 16 start-page: 576 year: 1978 end-page: 586 ident: bib5 article-title: A stochastic approach to goal programming publication-title: Oper. Res. – volume: 24 start-page: 1078 year: 1976 end-page: 1119 ident: bib13 article-title: A research bibliography in stochastic programming 1955–1975 publication-title: Oper. Res. – volume: 1 start-page: 45 year: 1978 end-page: 55 ident: bib16 article-title: Fuzzy programming and linear programming with several objective functions publication-title: Fuzzy Sets Syst. – volume: 26 start-page: 5 year: 1986 end-page: 82 ident: bib15 article-title: Strange: an interactive method for multi-objective linear programming under uncertainty publication-title: Eur. J. Oper. Res. – volume: 24 start-page: 1151 year: 2000 end-page: 1158 ident: bib25 article-title: Supply chain optimization of continuous process industries with sustainability considerations publication-title: Comput. Chem. Eng. – volume: 17 start-page: 141 year: 1970 end-page: 164 ident: bib3 article-title: Decision making in a fuzzy environment publication-title: Manage. Sci. – volume: 40 start-page: 1650 year: 2001 end-page: 1660 ident: bib24 article-title: Transfer prices for multienterprise supply chain optimization publication-title: Ind. Eng. Chem. Res. – year: 2005 ident: bib1 article-title: A fuzzy approach for bi-level integer non-linear programming problem publication-title: Appl. Math. Comput. – volume: 11 start-page: 325 year: 1980 end-page: 336 ident: bib10 article-title: Goal programming in a fuzzy environment publication-title: Decision Sci. – volume: 26 start-page: 5 year: 1986 ident: 10.1016/j.amc.2006.10.032_bib15 article-title: Strange: an interactive method for multi-objective linear programming under uncertainty publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(86)90160-8 – volume: 24 start-page: 1151 year: 2000 ident: 10.1016/j.amc.2006.10.032_bib25 article-title: Supply chain optimization of continuous process industries with sustainability considerations publication-title: Comput. Chem. Eng. doi: 10.1016/S0098-1354(00)00496-8 – volume: 6 start-page: 73 year: 1959 ident: 10.1016/j.amc.2006.10.032_bib4 article-title: Chance constrained programming publication-title: Manage. Sci. doi: 10.1287/mnsc.6.1.73 – volume: 12 start-page: 215 year: 1978 ident: 10.1016/j.amc.2006.10.032_bib14 article-title: A goal programming model for readiness and optimal deployment of resources publication-title: Socio-Economic Planning Sci. doi: 10.1016/0038-0121(78)90023-X – volume: 17 start-page: 141 year: 1970 ident: 10.1016/j.amc.2006.10.032_bib3 article-title: Decision making in a fuzzy environment publication-title: Manage. Sci. doi: 10.1287/mnsc.17.4.B141 – start-page: 4 year: 2005 ident: 10.1016/j.amc.2006.10.032_bib11 article-title: Multi-objective stochastic programming for portfolio selection publication-title: Eur. J. Oper. Res. – volume: 12 start-page: 522 year: 1981 ident: 10.1016/j.amc.2006.10.032_bib6 article-title: On fuzzy goal programming publication-title: Decision Sci. doi: 10.1111/j.1540-5915.1981.tb00102.x – ident: 10.1016/j.amc.2006.10.032_bib18 – volume: 36 start-page: 2691 year: 1997 ident: 10.1016/j.amc.2006.10.032_bib22 article-title: Planning and scheduling of parallel semicontinuous processes. Part 1. Production planning publication-title: Ind. Eng. Chem. Res. doi: 10.1021/ie960901+ – volume: 24 start-page: 2613 year: 2000 ident: 10.1016/j.amc.2006.10.032_bib21 article-title: Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management publication-title: Comput. Chem. Eng. doi: 10.1016/S0098-1354(00)00617-7 – year: 1972 ident: 10.1016/j.amc.2006.10.032_bib12 – year: 1977 ident: 10.1016/j.amc.2006.10.032_bib7 – volume: 40 start-page: 3585 year: 2001 ident: 10.1016/j.amc.2006.10.032_bib19 article-title: Design of multiechelon supply chain networks under demand uncertainty publication-title: Ind. Eng. Chem. Res. doi: 10.1021/ie0100030 – volume: 39 start-page: 3799 year: 2000 ident: 10.1016/j.amc.2006.10.032_bib20 article-title: A two-stage modeling and solution framework for multisite midterm planning under uncertainty publication-title: Ind. Eng. Chem. Res. doi: 10.1021/ie9909284 – year: 2005 ident: 10.1016/j.amc.2006.10.032_bib1 article-title: A fuzzy approach for bi-level integer non-linear programming problem publication-title: Appl. Math. Comput. – volume: 28 start-page: 1121 year: 2004 ident: 10.1016/j.amc.2006.10.032_bib17 article-title: A bilevel programming framework for enterprise-wide process networks under uncertainty publication-title: Comput. Chem. Eng. doi: 10.1016/j.compchemeng.2003.09.021 – volume: 6 start-page: 105 year: 1981 ident: 10.1016/j.amc.2006.10.032_bib8 article-title: On finding compromise solution in multi-criteria problems using the min-operator publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(81)90019-1 – volume: 153 start-page: 239 year: 2004 ident: 10.1016/j.amc.2006.10.032_bib29 article-title: A multi-level non-linear multi-objective decision-making under fuzziness publication-title: Appl. Math. Comput. doi: 10.1016/S0096-3003(03)00628-3 – volume: 1 start-page: 45 year: 1978 ident: 10.1016/j.amc.2006.10.032_bib16 article-title: Fuzzy programming and linear programming with several objective functions publication-title: Fuzzy Sets Syst. doi: 10.1016/0165-0114(78)90031-3 – volume: 16 start-page: 576 year: 1978 ident: 10.1016/j.amc.2006.10.032_bib5 article-title: A stochastic approach to goal programming publication-title: Oper. Res. doi: 10.1287/opre.16.3.576 – volume: 11 start-page: 325 year: 1980 ident: 10.1016/j.amc.2006.10.032_bib10 article-title: Goal programming in a fuzzy environment publication-title: Decision Sci. doi: 10.1111/j.1540-5915.1980.tb01142.x – volume: 24 start-page: 329 year: 2000 ident: 10.1016/j.amc.2006.10.032_bib27 article-title: A model predictive framework for planning and scheduling problem: a case study of consumer goods supply chain publication-title: Comput. Chem. Eng. doi: 10.1016/S0098-1354(00)00469-5 – volume: 24 start-page: 1078 year: 1976 ident: 10.1016/j.amc.2006.10.032_bib13 article-title: A research bibliography in stochastic programming 1955–1975 publication-title: Oper. Res. doi: 10.1287/opre.24.6.1078 – volume: 40 start-page: 1650 year: 2001 ident: 10.1016/j.amc.2006.10.032_bib24 article-title: Transfer prices for multienterprise supply chain optimization publication-title: Ind. Eng. Chem. Res. doi: 10.1021/ie000668m – year: 2005 ident: 10.1016/j.amc.2006.10.032_bib2 – year: 1993 ident: 10.1016/j.amc.2006.10.032_bib31 – volume: 10 start-page: 33 year: 1982 ident: 10.1016/j.amc.2006.10.032_bib9 article-title: Stochastic programming: an interactive multi-criteria approach publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(82)90129-1 – volume: 38 start-page: 93 year: 1997 ident: 10.1016/j.amc.2006.10.032_bib23 article-title: The bullwhip effect in supply-chains publication-title: Sloan Manage. Rev. – volume: 109 start-page: 91 year: 2000 ident: 10.1016/j.amc.2006.10.032_bib30 article-title: Fuzzy programming approach to multi-objective stochastic programming problems when bi’s follow joint normal distribution publication-title: Fuzzy Sets Syst. doi: 10.1016/S0165-0114(98)00070-0 – ident: 10.1016/j.amc.2006.10.032_bib28 – volume: 24 start-page: 1143 year: 2000 ident: 10.1016/j.amc.2006.10.032_bib26 article-title: Dynamic modeling and classical control theory for supply chain management publication-title: Comput. Chem. Eng. doi: 10.1016/S0098-1354(00)00495-6 |
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| Title | A probabilistic bi-level linear multi-objective programming problem to supply chain planning |
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