The Experts below are selected from a list of 166257 Experts worldwide ranked by ideXlab platform
Denis Lebedev - One of the best experts on this subject based on the ideXlab platform.
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a Dynamic Programming framework for optimal delivery time slot pricing
European Journal of Operational Research, 2021Co-Authors: Denis Lebedev, Paul J Goulart, Kostas MargellosAbstract:Abstract We study the Dynamic Programming approach to revenue management in the context of attended home delivery. We draw on results from Dynamic Programming theory for Markov decision problems to show that the underlying Bellman operator has a unique fixed point. We then provide a closed-form expression for the resulting fixed point and show that it admits a natural interpretation. Moreover, we also show that – under certain technical assumptions – the value function, which has a discrete domain and a continuous codomain, admits a continuous extension, which is a finite-valued, concave function of its state variables, at every time step. Furthermore, we derive results on the monotonicity of prices with respect to the number of orders placed in our setting. These results open the road for achieving scalable implementations of the proposed formulation, as it allows making informed choices of basis functions in an approximate Dynamic Programming context. We illustrate our findings on a low-dimensional and an industry-sized numerical example using real-world data, for which we derive an approximately optimal pricing policy based on our theoretical results.
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convexity and feedback in approximate Dynamic Programming for delivery time slot pricing
IEEE Transactions on Control Systems and Technology, 2021Co-Authors: Denis Lebedev, Kostas Margellos, P GoulartAbstract:We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a Dynamic Programming formulation that is intractable for realistic problem sizes due to the socalled “curse of dimensionality”. Therefore, we study three approximate Dynamic Programming algorithms both from a control-theoretical perspective and numerically. Our analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests indicate that one of these algorithms, namely gradient-bounded Dynamic Programming, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates.
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approximate Dynamic Programming for delivery time slot pricing a sensitivity analysis
arXiv: Optimization and Control, 2020Co-Authors: Denis Lebedev, Kostas Margellos, Paul J GoulartAbstract:We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a Dynamic Programming formulation that is intractable for realistic problem sizes due to the so-called "curse of dimensionality". Therefore, we study three approximate Dynamic Programming algorithms both from a control-theoretical perspective and in a parametric numerical case study. Our numerical analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests show that one of these algorithms, namely gradient-bounded Dynamic Programming, dominates the others with respect to computation time and profit-generation capabilities of the delivery slot pricing policies that it generates. Finally, we show that uncertainty in the estimates of the model parameters further increases the profit-generation dominance of this approach.
Kostas Margellos - One of the best experts on this subject based on the ideXlab platform.
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a Dynamic Programming framework for optimal delivery time slot pricing
European Journal of Operational Research, 2021Co-Authors: Denis Lebedev, Paul J Goulart, Kostas MargellosAbstract:Abstract We study the Dynamic Programming approach to revenue management in the context of attended home delivery. We draw on results from Dynamic Programming theory for Markov decision problems to show that the underlying Bellman operator has a unique fixed point. We then provide a closed-form expression for the resulting fixed point and show that it admits a natural interpretation. Moreover, we also show that – under certain technical assumptions – the value function, which has a discrete domain and a continuous codomain, admits a continuous extension, which is a finite-valued, concave function of its state variables, at every time step. Furthermore, we derive results on the monotonicity of prices with respect to the number of orders placed in our setting. These results open the road for achieving scalable implementations of the proposed formulation, as it allows making informed choices of basis functions in an approximate Dynamic Programming context. We illustrate our findings on a low-dimensional and an industry-sized numerical example using real-world data, for which we derive an approximately optimal pricing policy based on our theoretical results.
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convexity and feedback in approximate Dynamic Programming for delivery time slot pricing
IEEE Transactions on Control Systems and Technology, 2021Co-Authors: Denis Lebedev, Kostas Margellos, P GoulartAbstract:We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a Dynamic Programming formulation that is intractable for realistic problem sizes due to the socalled “curse of dimensionality”. Therefore, we study three approximate Dynamic Programming algorithms both from a control-theoretical perspective and numerically. Our analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests indicate that one of these algorithms, namely gradient-bounded Dynamic Programming, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates.
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approximate Dynamic Programming for delivery time slot pricing a sensitivity analysis
arXiv: Optimization and Control, 2020Co-Authors: Denis Lebedev, Kostas Margellos, Paul J GoulartAbstract:We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a Dynamic Programming formulation that is intractable for realistic problem sizes due to the so-called "curse of dimensionality". Therefore, we study three approximate Dynamic Programming algorithms both from a control-theoretical perspective and in a parametric numerical case study. Our numerical analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests show that one of these algorithms, namely gradient-bounded Dynamic Programming, dominates the others with respect to computation time and profit-generation capabilities of the delivery slot pricing policies that it generates. Finally, we show that uncertainty in the estimates of the model parameters further increases the profit-generation dominance of this approach.
Andres Ramos - One of the best experts on this subject based on the ideXlab platform.
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stochastic dual Dynamic Programming applied to nonconvex hydrothermal models
European Journal of Operational Research, 2012Co-Authors: Santiago Cerisola, Jesus M Latorre, Andres RamosAbstract:Abstract In this paper we apply stochastic dual Dynamic Programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive Programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual Dynamic Programming algorithm. A realistic large-scale case study is presented.
P Goulart - One of the best experts on this subject based on the ideXlab platform.
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convexity and feedback in approximate Dynamic Programming for delivery time slot pricing
IEEE Transactions on Control Systems and Technology, 2021Co-Authors: Denis Lebedev, Kostas Margellos, P GoulartAbstract:We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a Dynamic Programming formulation that is intractable for realistic problem sizes due to the socalled “curse of dimensionality”. Therefore, we study three approximate Dynamic Programming algorithms both from a control-theoretical perspective and numerically. Our analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests indicate that one of these algorithms, namely gradient-bounded Dynamic Programming, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates.
Paul J Goulart - One of the best experts on this subject based on the ideXlab platform.
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a Dynamic Programming framework for optimal delivery time slot pricing
European Journal of Operational Research, 2021Co-Authors: Denis Lebedev, Paul J Goulart, Kostas MargellosAbstract:Abstract We study the Dynamic Programming approach to revenue management in the context of attended home delivery. We draw on results from Dynamic Programming theory for Markov decision problems to show that the underlying Bellman operator has a unique fixed point. We then provide a closed-form expression for the resulting fixed point and show that it admits a natural interpretation. Moreover, we also show that – under certain technical assumptions – the value function, which has a discrete domain and a continuous codomain, admits a continuous extension, which is a finite-valued, concave function of its state variables, at every time step. Furthermore, we derive results on the monotonicity of prices with respect to the number of orders placed in our setting. These results open the road for achieving scalable implementations of the proposed formulation, as it allows making informed choices of basis functions in an approximate Dynamic Programming context. We illustrate our findings on a low-dimensional and an industry-sized numerical example using real-world data, for which we derive an approximately optimal pricing policy based on our theoretical results.
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approximate Dynamic Programming for delivery time slot pricing a sensitivity analysis
arXiv: Optimization and Control, 2020Co-Authors: Denis Lebedev, Kostas Margellos, Paul J GoulartAbstract:We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a Dynamic Programming formulation that is intractable for realistic problem sizes due to the so-called "curse of dimensionality". Therefore, we study three approximate Dynamic Programming algorithms both from a control-theoretical perspective and in a parametric numerical case study. Our numerical analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests show that one of these algorithms, namely gradient-bounded Dynamic Programming, dominates the others with respect to computation time and profit-generation capabilities of the delivery slot pricing policies that it generates. Finally, we show that uncertainty in the estimates of the model parameters further increases the profit-generation dominance of this approach.
