To optimize revenue, service firms must integrate within their pricing policies the rational reac... more To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper, we consider a streamlined version of this situation where a firm's decision variables involve both prices and investments. We model this situation as a joint design and pricing problem that we formulate as a mixed-integer bilevel program, and whose properties are investigated. In particular, we take advantage of a feature of the model that allows the development of an algorithmic framework based on Lagrangean relaxation. This approach is entirely novel, and numerical results show that it is capable of solving problems of significant sizes.
"Revenue optimization in energy networks involving self-scheduled demand and a smart grid" Forthc... more "Revenue optimization in energy networks involving self-scheduled demand and a smart grid" Forthcoming, Computers and Operations Research 134 (2021) 2. M. Zimmermann, E. Frejinger and P. Marcotte "A strategic Markovian traffic equilibrium model for capacitated networks" Transportation Science 5 (2021) 574-591 3. T. Dan, A. Lodi and P. Marcotte "An exact algorithmic framework for a class of mixed-integer programs with equilibrium constraints"
Journal of Optimization Theory and Applications, 1997
We study links between the linear bilevel and linear mixed 0-1 programming problems. A new reform... more We study links between the linear bilevel and linear mixed 0-1 programming problems. A new reformulation of the linear mixed 0-1 programming problem into a linear bilevel programming one, which does not require the introduction of a large finite constant, is presented. We show that solving a linear mixed 0-1 problem by a classical branchand-bound algorithm is equivalent in a strong sense to solving its bilevel reformulation by a bilevel branch-and-bound algorithm. The mixed 0-1 algorithm is embedded in the bilevel algorithm through the aforementioned reformulation; i.e., when applied to any mixed 0-1 instance and its bilevel reformulation, they generate sequences of subproblems which are identical via the reformulation.
In this work, we address the problem of maximizing the revenue raised from tolls set on a multico... more In this work, we address the problem of maximizing the revenue raised from tolls set on a multicommodity transportation network, taking into account that users are assigned to cheapest paths, and that demand is a linearly decreasing function of total path cost (initial cost of carrying the products plus toll). We propose for its numerical solution three mixed quadratic formulations, either in arc or path flow space. Similar to what was achieved in the fixed demand case, we analyze the structure and properties of the problem, including its theoretical complexity. On the computational side, we analyze the sensitivity of central processing unit time with respect to two key parameters, namely, demand elasticity and percentage of toll arcs.
International Journal of Environment and Pollution, 1999
... Note that the total waste q[src,t] generated at each source and time period is exogenously de... more ... Note that the total waste q[src,t] generated at each source and time period is exogenously defined. It is given to the model. An interesting option to consider would be to introduce price sensitivity of total waste generation in order to test waste reduction policies. ...
Proceedings IEEE International Conference on Software Maintenance - 1999 (ICSM'99). 'Software Maintenance for Business Change' (Cat. No.99CB36360), 1999
... This notion was first mentioned in 13, 17 . Let CFG = VCFG; ECFG be a Control Flow Graph for ... more ... This notion was first mentioned in 13, 17 . Let CFG = VCFG; ECFG be a Control Flow Graph for a given program, where each node in VCFG corresponds to a statement in the analyzed program and each edge in ECFG corresponds to a flow of control between state-ments. ...
Transportation Research Part B: Methodological, 2013
We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbé et ... more We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbé et al. (1998). In the first stage, the leader sets tariffs on a subset of arcs of a transportation network, with the aim of maximizing profits while, at the lower level, flows are assigned to cheapest paths of a multicommodity transportation network. In the second stage, the situation repeats itself under the constraint that tariffs should not differ too widely from those set at the first stage, a condition that frequently arises in practice. We analyze properties of the model, provide numerical illustrations, and open avenues for further research into this area.
The interaction between a utility company and electricity cogenerators is modeled via a game-theo... more The interaction between a utility company and electricity cogenerators is modeled via a game-theoretic, systems analysis approach, under the assumption of asymmetric pricing of electricity purchased or sold by the cogenerators. The pricing scheme is derived from the PURPA legislation prevailing in the US and is compared to an efficient operation of the global system. An adaptation of a successive
The interaction between a utility company and electricity cogenerators is modeled via a game-theo... more The interaction between a utility company and electricity cogenerators is modeled via a game-theoretic, systems analysis approach, under the assumption of asymmetric pricing of electricity purchased or sold by the cogenerators. The pricing scheme is derived from the PURPA legislation prevailing in the US and is compared to an efficient operation of the global system. An adaptation of a successive
HAL (Le Centre pour la Communication Scientifique Directe), 2000
We consider a bilevel programming formulation of a freight tariff-setting problem where the leade... more We consider a bilevel programming formulation of a freight tariff-setting problem where the leader consists in one among a group of competing carriers and the follower is a shipper. At the upper level, the leader’s revenue corresponds to the total tariffs levied, whereas the shipper minimizes its transportation cost, given the tariff schedule set by the leader. We propose for this problem a class of heuristic procedures whose relative efficiencies, on small problem instances, could be validated with respect to optimal solutions obtained from a mixed integer reformula-tion of the mathematical model. We also present numerical results on large instances that could not be solved to optimality by an exact method. This work is devoted to a tariff-setting problem involving two decision makers acting non-coopera-tively and in a sequential way. We focus our atten-tion on a freight transportation application. In this context, a shipper company (the follower) is set to ship a prescribed amount of goods from origin nodes to its customers at minimum cost. Supply at the
Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bileve... more Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP) problems. We exploit these equivalences to transpose the concept of mixed 0-1 Gomory cuts to BLP. The first phase of our new algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of randomly generated problems.
Abstract We propose a new approach to solve the multi-objective portfolio selection problem in th... more Abstract We propose a new approach to solve the multi-objective portfolio selection problem in the presence of skewness. The selection of efficient portfolios requires the optimiza- tion of different and conflicting criteria: maximizing expected return and skewness and minimizing risk. Hence, the portfolio selection can be formulated as a tri-objective pro- gramming,problem to solve the mean-variance-skewness efficient set. Rescaling on the unit variance space leads to a biobjective problem, but adds a nonlinear equality con- straint to the model. Through a change in variables, we reformulate it as a lower dimensional bound constrained biobjective problem. The recent algorithm BiMads
To optimize revenue, service firms must integrate within their pricing policies the rational reac... more To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper, we consider a streamlined version of this situation where a firm's decision variables involve both prices and investments. We model this situation as a joint design and pricing problem that we formulate as a mixed-integer bilevel program, and whose properties are investigated. In particular, we take advantage of a feature of the model that allows the development of an algorithmic framework based on Lagrangean relaxation. This approach is entirely novel, and numerical results show that it is capable of solving problems of significant sizes.
"Revenue optimization in energy networks involving self-scheduled demand and a smart grid" Forthc... more "Revenue optimization in energy networks involving self-scheduled demand and a smart grid" Forthcoming, Computers and Operations Research 134 (2021) 2. M. Zimmermann, E. Frejinger and P. Marcotte "A strategic Markovian traffic equilibrium model for capacitated networks" Transportation Science 5 (2021) 574-591 3. T. Dan, A. Lodi and P. Marcotte "An exact algorithmic framework for a class of mixed-integer programs with equilibrium constraints"
Journal of Optimization Theory and Applications, 1997
We study links between the linear bilevel and linear mixed 0-1 programming problems. A new reform... more We study links between the linear bilevel and linear mixed 0-1 programming problems. A new reformulation of the linear mixed 0-1 programming problem into a linear bilevel programming one, which does not require the introduction of a large finite constant, is presented. We show that solving a linear mixed 0-1 problem by a classical branchand-bound algorithm is equivalent in a strong sense to solving its bilevel reformulation by a bilevel branch-and-bound algorithm. The mixed 0-1 algorithm is embedded in the bilevel algorithm through the aforementioned reformulation; i.e., when applied to any mixed 0-1 instance and its bilevel reformulation, they generate sequences of subproblems which are identical via the reformulation.
In this work, we address the problem of maximizing the revenue raised from tolls set on a multico... more In this work, we address the problem of maximizing the revenue raised from tolls set on a multicommodity transportation network, taking into account that users are assigned to cheapest paths, and that demand is a linearly decreasing function of total path cost (initial cost of carrying the products plus toll). We propose for its numerical solution three mixed quadratic formulations, either in arc or path flow space. Similar to what was achieved in the fixed demand case, we analyze the structure and properties of the problem, including its theoretical complexity. On the computational side, we analyze the sensitivity of central processing unit time with respect to two key parameters, namely, demand elasticity and percentage of toll arcs.
International Journal of Environment and Pollution, 1999
... Note that the total waste q[src,t] generated at each source and time period is exogenously de... more ... Note that the total waste q[src,t] generated at each source and time period is exogenously defined. It is given to the model. An interesting option to consider would be to introduce price sensitivity of total waste generation in order to test waste reduction policies. ...
Proceedings IEEE International Conference on Software Maintenance - 1999 (ICSM'99). 'Software Maintenance for Business Change' (Cat. No.99CB36360), 1999
... This notion was first mentioned in 13, 17 . Let CFG = VCFG; ECFG be a Control Flow Graph for ... more ... This notion was first mentioned in 13, 17 . Let CFG = VCFG; ECFG be a Control Flow Graph for a given program, where each node in VCFG corresponds to a statement in the analyzed program and each edge in ECFG corresponds to a flow of control between state-ments. ...
Transportation Research Part B: Methodological, 2013
We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbé et ... more We consider a two-stage stochastic extension of the bilevel pricing model introduced by Labbé et al. (1998). In the first stage, the leader sets tariffs on a subset of arcs of a transportation network, with the aim of maximizing profits while, at the lower level, flows are assigned to cheapest paths of a multicommodity transportation network. In the second stage, the situation repeats itself under the constraint that tariffs should not differ too widely from those set at the first stage, a condition that frequently arises in practice. We analyze properties of the model, provide numerical illustrations, and open avenues for further research into this area.
The interaction between a utility company and electricity cogenerators is modeled via a game-theo... more The interaction between a utility company and electricity cogenerators is modeled via a game-theoretic, systems analysis approach, under the assumption of asymmetric pricing of electricity purchased or sold by the cogenerators. The pricing scheme is derived from the PURPA legislation prevailing in the US and is compared to an efficient operation of the global system. An adaptation of a successive
The interaction between a utility company and electricity cogenerators is modeled via a game-theo... more The interaction between a utility company and electricity cogenerators is modeled via a game-theoretic, systems analysis approach, under the assumption of asymmetric pricing of electricity purchased or sold by the cogenerators. The pricing scheme is derived from the PURPA legislation prevailing in the US and is compared to an efficient operation of the global system. An adaptation of a successive
HAL (Le Centre pour la Communication Scientifique Directe), 2000
We consider a bilevel programming formulation of a freight tariff-setting problem where the leade... more We consider a bilevel programming formulation of a freight tariff-setting problem where the leader consists in one among a group of competing carriers and the follower is a shipper. At the upper level, the leader’s revenue corresponds to the total tariffs levied, whereas the shipper minimizes its transportation cost, given the tariff schedule set by the leader. We propose for this problem a class of heuristic procedures whose relative efficiencies, on small problem instances, could be validated with respect to optimal solutions obtained from a mixed integer reformula-tion of the mathematical model. We also present numerical results on large instances that could not be solved to optimality by an exact method. This work is devoted to a tariff-setting problem involving two decision makers acting non-coopera-tively and in a sequential way. We focus our atten-tion on a freight transportation application. In this context, a shipper company (the follower) is set to ship a prescribed amount of goods from origin nodes to its customers at minimum cost. Supply at the
Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bileve... more Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP) problems. We exploit these equivalences to transpose the concept of mixed 0-1 Gomory cuts to BLP. The first phase of our new algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of randomly generated problems.
Abstract We propose a new approach to solve the multi-objective portfolio selection problem in th... more Abstract We propose a new approach to solve the multi-objective portfolio selection problem in the presence of skewness. The selection of efficient portfolios requires the optimiza- tion of different and conflicting criteria: maximizing expected return and skewness and minimizing risk. Hence, the portfolio selection can be formulated as a tri-objective pro- gramming,problem to solve the mean-variance-skewness efficient set. Rescaling on the unit variance space leads to a biobjective problem, but adds a nonlinear equality con- straint to the model. Through a change in variables, we reformulate it as a lower dimensional bound constrained biobjective problem. The recent algorithm BiMads
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Papers by Gilles Savard