Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results
Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator gro...
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| Autor*in: |
Ruokokoski, Mirko [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of combinatorial optimization - Springer US, 1997, 29(2013), 4 vom: 08. Mai, Seite 750-780 |
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| Übergeordnetes Werk: |
volume:29 ; year:2013 ; number:4 ; day:08 ; month:05 ; pages:750-780 |
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10.1007/s10878-013-9620-1 |
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| 520 | |a Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. | ||
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| 700 | 1 | |a Pardalos, Panos M. |4 aut | |
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10.1007/s10878-013-9620-1 doi (DE-627)OLC2044618451 (DE-He213)s10878-013-9620-1-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Ruokokoski, Mirko verfasserin aut Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. Elevator dispatching problem Routing Polyhedral results Valid inequalities Ehtamo, Harri aut Pardalos, Panos M. aut Enthalten in Journal of combinatorial optimization Springer US, 1997 29(2013), 4 vom: 08. Mai, Seite 750-780 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:29 year:2013 number:4 day:08 month:05 pages:750-780 https://doi.org/10.1007/s10878-013-9620-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 AR 29 2013 4 08 05 750-780 |
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10.1007/s10878-013-9620-1 doi (DE-627)OLC2044618451 (DE-He213)s10878-013-9620-1-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Ruokokoski, Mirko verfasserin aut Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. Elevator dispatching problem Routing Polyhedral results Valid inequalities Ehtamo, Harri aut Pardalos, Panos M. aut Enthalten in Journal of combinatorial optimization Springer US, 1997 29(2013), 4 vom: 08. Mai, Seite 750-780 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:29 year:2013 number:4 day:08 month:05 pages:750-780 https://doi.org/10.1007/s10878-013-9620-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 AR 29 2013 4 08 05 750-780 |
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10.1007/s10878-013-9620-1 doi (DE-627)OLC2044618451 (DE-He213)s10878-013-9620-1-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Ruokokoski, Mirko verfasserin aut Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. Elevator dispatching problem Routing Polyhedral results Valid inequalities Ehtamo, Harri aut Pardalos, Panos M. aut Enthalten in Journal of combinatorial optimization Springer US, 1997 29(2013), 4 vom: 08. Mai, Seite 750-780 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:29 year:2013 number:4 day:08 month:05 pages:750-780 https://doi.org/10.1007/s10878-013-9620-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 AR 29 2013 4 08 05 750-780 |
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10.1007/s10878-013-9620-1 doi (DE-627)OLC2044618451 (DE-He213)s10878-013-9620-1-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Ruokokoski, Mirko verfasserin aut Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. Elevator dispatching problem Routing Polyhedral results Valid inequalities Ehtamo, Harri aut Pardalos, Panos M. aut Enthalten in Journal of combinatorial optimization Springer US, 1997 29(2013), 4 vom: 08. Mai, Seite 750-780 (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:29 year:2013 number:4 day:08 month:05 pages:750-780 https://doi.org/10.1007/s10878-013-9620-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_24 GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 AR 29 2013 4 08 05 750-780 |
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Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. © Springer Science+Business Media New York 2013 |
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Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. © Springer Science+Business Media New York 2013 |
| abstract_unstemmed |
Abstract In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing. © Springer Science+Business Media New York 2013 |
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Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results |
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Ehtamo, Harri Pardalos, Panos M. |
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