The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Sumit Kunnumkal - One of the best experts on this subject based on the ideXlab platform.
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technical note a note on relaxations of the choice network revenue management Dynamic Program
Operations Research, 2016Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:In recent years, several approximation methods have been proposed for the choice network revenue management problem. These approximation methods are proposed because the Dynamic Programming formulation of the choice network revenue management problem is intractable even for moderately sized instances. In this paper, we consider three approximation methods that obtain upper bounds on the value function, namely, the choice deterministic linear Program (CDLP), the affine approximation (AF), and the piecewise-linear approximation (PL). It is known that the piecewise-linear approximation bound is tighter than the affine bound, which in turn is tighter than CDLP. In this paper, we prove bounds on how much the affine and piecewise-linear approximations can tighten CDLP. We show (i) the gap between the AF and CDLP bounds is at most a factor of 1+1/(mini{ri1}), where ri1>0 are the resource capacities, and (ii) the gap between the piecewise-linear and CDLP bounds is within a factor of 2. Moreover, we show that thes...
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On a piecewise-linear approximation for network revenue management
Mathematics of Operations Research, 2016Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:The network revenue management (RM) problem arises in airline, hotel, media, and other industries where the sale products use multiple resources. It can be formulated as a stochastic Dynamic Program, but the Dynamic Program is computationally intractable because of an exponentially large state space, and a number of heuristics have been proposed to approximate its value function. In this paper we show that the piecewise-linear approximation to the network RM Dynamic Program is tractable; specifically we show that the separation problem of the approximation can be solved as a relatively compact linear Program. Moreover, the resulting compact formulation of the approximate Dynamic Program turns out to be exactly equivalent to the Lagrangian relaxation of the Dynamic Program, an earlier heuristic method proposed for the same problem. We perform a numerical comparison of solving the problem by generating separating cuts or as our compact linear Program. We discuss extensions to versions of the network RM prob...
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Technical Note—A Note on Relaxations of the Choice Network Revenue Management Dynamic Program
Operations Research, 2016Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:In recent years, several approximation methods have been proposed for the choice network revenue management problem. These approximation methods are proposed because the Dynamic Programming formulation of the choice network revenue management problem is intractable even for moderately sized instances. In this paper, we consider three approximation methods that obtain upper bounds on the value function, namely, the choice deterministic linear Program (CDLP), the affine approximation (AF), and the piecewise-linear approximation (PL). It is known that the piecewise-linear approximation bound is tighter than the affine bound, which in turn is tighter than CDLP. In this paper, we prove bounds on how much the affine and piecewise-linear approximations can tighten CDLP. We show (i) the gap between the AF and CDLP bounds is at most a factor of 1+1/(mini{ri1}), where ri1>0 are the resource capacities, and (ii) the gap between the piecewise-linear and CDLP bounds is within a factor of 2. Moreover, we show that thes...
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Randomization Approaches for Network Revenue Management with Customer Choice Behavior
Production and Operations Management, 2013Co-Authors: Sumit KunnumkalAbstract:In this study, we present new approximation methods for the network revenue management problem with customer choice behavior. Our methods are sampling-based and so can handle fairly general customer choice models. The starting point for our methods is a Dynamic Program that allows randomization. An attractive feature of this Dynamic Program is that the size of its action space is linear in the number of itineraries, as opposed to exponential. It turns out that this Dynamic Program has a structure that is similar to the Dynamic Program for the network revenue management problem under the so called independent demand setting. Our approximation methods exploit this similarity and build on ideas developed for the independent demand setting. We present two approximation methods. The first one is based on relaxing the flight leg capacity constraints using Lagrange multipliers, whereas the second method involves solving a perfect hindsight relaxation problem. We show that both methods yield upper bounds on the optimal expected total revenue. Computational experiments demonstrate the tractability of our methods and indicate that they can generate tighter upper bounds and higher expected revenues when compared with the standard deterministic linear Program that appears in the literature.
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A new compact linear Programming formulation for choice network revenue management
2012Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:The choice network revenue management model incorporates customer purchase behavior as a function of the offered products, and is the appropriate model for airline and hotel network revenue management, Dynamic sales of bundles, and Dynamic assortment optimization. The optimization problem is a stochastic Dynamic Program and is intractable. A certainty equivalence relaxation of the Dynamic Program, called the choice deterministic linear Program (CDLP) is usually used to generate Dynamic controls. Recently, a compact linear Programming formulation of this linear Program was given for the multi-segment multinomial-logit (MNL) model of customer choice with non-overlapping consideration sets. Our objective is to obtain a tighter bound than this formulation while retaining the appealing properties of a compact linear Programming representation. To this end, it is natural to consider the affine relaxation of the Dynamic Program. We first show that the affine relaxation is NP-complete even for a single-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a new compact linear Program that approximates the Dynamic Programming value function better than CDLP, provably between the CDLP value and the affine relaxation, and often coming close to the latter in our numerical experiments. When the segment consideration sets overlap, we show that some strong equalities called product cuts developed for the CDLP remain valid for our new formulation. Finally we perform extensive numerical comparisons on the various bounds to evaluate their performance.
Kalyan T Talluri - One of the best experts on this subject based on the ideXlab platform.
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technical note a note on relaxations of the choice network revenue management Dynamic Program
Operations Research, 2016Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:In recent years, several approximation methods have been proposed for the choice network revenue management problem. These approximation methods are proposed because the Dynamic Programming formulation of the choice network revenue management problem is intractable even for moderately sized instances. In this paper, we consider three approximation methods that obtain upper bounds on the value function, namely, the choice deterministic linear Program (CDLP), the affine approximation (AF), and the piecewise-linear approximation (PL). It is known that the piecewise-linear approximation bound is tighter than the affine bound, which in turn is tighter than CDLP. In this paper, we prove bounds on how much the affine and piecewise-linear approximations can tighten CDLP. We show (i) the gap between the AF and CDLP bounds is at most a factor of 1+1/(mini{ri1}), where ri1>0 are the resource capacities, and (ii) the gap between the piecewise-linear and CDLP bounds is within a factor of 2. Moreover, we show that thes...
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On a piecewise-linear approximation for network revenue management
Mathematics of Operations Research, 2016Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:The network revenue management (RM) problem arises in airline, hotel, media, and other industries where the sale products use multiple resources. It can be formulated as a stochastic Dynamic Program, but the Dynamic Program is computationally intractable because of an exponentially large state space, and a number of heuristics have been proposed to approximate its value function. In this paper we show that the piecewise-linear approximation to the network RM Dynamic Program is tractable; specifically we show that the separation problem of the approximation can be solved as a relatively compact linear Program. Moreover, the resulting compact formulation of the approximate Dynamic Program turns out to be exactly equivalent to the Lagrangian relaxation of the Dynamic Program, an earlier heuristic method proposed for the same problem. We perform a numerical comparison of solving the problem by generating separating cuts or as our compact linear Program. We discuss extensions to versions of the network RM prob...
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Technical Note—A Note on Relaxations of the Choice Network Revenue Management Dynamic Program
Operations Research, 2016Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:In recent years, several approximation methods have been proposed for the choice network revenue management problem. These approximation methods are proposed because the Dynamic Programming formulation of the choice network revenue management problem is intractable even for moderately sized instances. In this paper, we consider three approximation methods that obtain upper bounds on the value function, namely, the choice deterministic linear Program (CDLP), the affine approximation (AF), and the piecewise-linear approximation (PL). It is known that the piecewise-linear approximation bound is tighter than the affine bound, which in turn is tighter than CDLP. In this paper, we prove bounds on how much the affine and piecewise-linear approximations can tighten CDLP. We show (i) the gap between the AF and CDLP bounds is at most a factor of 1+1/(mini{ri1}), where ri1>0 are the resource capacities, and (ii) the gap between the piecewise-linear and CDLP bounds is within a factor of 2. Moreover, we show that thes...
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New Formulations for Choice Network Revenue Management
INFORMS Journal on Computing, 2014Co-Authors: Kalyan T TalluriAbstract:Models incorporating more realistic models of customer behavior, as customers choosing from an offer set, have recently become popular in assortment optimization and revenue management. The Dynamic Program for these models is intractable and approximated by a deterministic linear Program called the choice deterministic linear Program (CDLP), which has an exponential number of columns. Column generation has been proposed but finding an entering column is NP-hard when segment consideration sets overlap. In this paper we propose a new approach called segment-based deterministic concave Program (SDCP) based on segments and their consideration sets. SDCP is a relaxation of CDLP and hence forms a looser upper bound on the Dynamic Program, but coincides with CDLP for the case of nonoverlapping segments. If the number of elements in a consideration set for a segment is not very large, SDCP can be applied to any discrete-choice model of consumer behavior. We tighten the SDCP bound by (i) simulations, called the ra...
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A new compact linear Programming formulation for choice network revenue management
2012Co-Authors: Sumit Kunnumkal, Kalyan T TalluriAbstract:The choice network revenue management model incorporates customer purchase behavior as a function of the offered products, and is the appropriate model for airline and hotel network revenue management, Dynamic sales of bundles, and Dynamic assortment optimization. The optimization problem is a stochastic Dynamic Program and is intractable. A certainty equivalence relaxation of the Dynamic Program, called the choice deterministic linear Program (CDLP) is usually used to generate Dynamic controls. Recently, a compact linear Programming formulation of this linear Program was given for the multi-segment multinomial-logit (MNL) model of customer choice with non-overlapping consideration sets. Our objective is to obtain a tighter bound than this formulation while retaining the appealing properties of a compact linear Programming representation. To this end, it is natural to consider the affine relaxation of the Dynamic Program. We first show that the affine relaxation is NP-complete even for a single-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a new compact linear Program that approximates the Dynamic Programming value function better than CDLP, provably between the CDLP value and the affine relaxation, and often coming close to the latter in our numerical experiments. When the segment consideration sets overlap, we show that some strong equalities called product cuts developed for the CDLP remain valid for our new formulation. Finally we perform extensive numerical comparisons on the various bounds to evaluate their performance.
Akhilesh Tyagi - One of the best experts on this subject based on the ideXlab platform.
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DRMTICS - Software tamper resistance through Dynamic Program monitoring
Digital Rights Management. Technologies Issues Challenges and Systems, 2006Co-Authors: Brian Blietz, Akhilesh TyagiAbstract:This paper describes a two instruction-stream (two-process) model for tamper resistance. One process (Monitor process, M-Process) is designed explicitly to monitor the control flow of the main Program process (P-Process). The compilation phase compiles the software into two co-processes: P-process and M-process. The monitor process contains the control flow consistency conditions for the P-process. The P-process sends information on its instantiated control flow at a compiler specified fixed period to the M-process. If there is a violation of the control flow conditions captured within the M-process, the M-process takes an anti-tamper action such as termination of the P-process. By its very design, the monitor process is expected to be compact. Hence, we can afford to protect the M-process with a more expensive technique, a variant of Aucsmith's scheme. This scheme has been implemented with the Gnu C compiler gcc. There are several other monitoring, obfuscation, and Dynamic decryption techniques that are embedded in this system. We quantify the performance overhead of the scheme for a variety of Programs. The performance of such an anti-tamper schema can be significantly improved by leveraging a decoupled processor architecture to support the decoupled M- and P- processes. We describe one instance of such a two-stream decoupled architecture that can make the scheme more robust and efficient.
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Software tamper resistance through Dynamic Program monitoring
Lecture Notes in Computer Science, 2006Co-Authors: Brian Blietz, Akhilesh TyagiAbstract:This paper describes a two instruction-stream (two-process) model for tamper resistance. One process (Monitor process, M-Process) is designed explicitly to monitor the control flow of the main Program process (P-Process). The compilation phase compiles the software into two co-processes: P-process and M-process. The monitor process contains the control flow consistency conditions for the P-process. The P-process sends information on its instantiated control flow at a compiler specified fixed period to the M-process. If there is a violation of the control flow conditions captured within the M-process, the M-process takes an anti-tamper action such as termination of the P-process. By its very design, the monitor process is expected to be compact. Hence, we can afford to protect the M-process with a more expensive technique, a variant of Aucsmith's scheme. This scheme has been implemented with the Gnu C compiler gcc. There are several other monitoring, obfuscation, and Dynamic decryption techniques that are embedded in this system. We quantify the performance overhead of the scheme for a variety of Programs. The performance of such an anti-tamper schema can be significantly improved by leveraging a decoupled processor architecture to support the decoupled M- and P- processes. We describe one instance of such a two-stream decoupled architecture that can make the scheme more robust and efficient.
Brian Blietz - One of the best experts on this subject based on the ideXlab platform.
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DRMTICS - Software tamper resistance through Dynamic Program monitoring
Digital Rights Management. Technologies Issues Challenges and Systems, 2006Co-Authors: Brian Blietz, Akhilesh TyagiAbstract:This paper describes a two instruction-stream (two-process) model for tamper resistance. One process (Monitor process, M-Process) is designed explicitly to monitor the control flow of the main Program process (P-Process). The compilation phase compiles the software into two co-processes: P-process and M-process. The monitor process contains the control flow consistency conditions for the P-process. The P-process sends information on its instantiated control flow at a compiler specified fixed period to the M-process. If there is a violation of the control flow conditions captured within the M-process, the M-process takes an anti-tamper action such as termination of the P-process. By its very design, the monitor process is expected to be compact. Hence, we can afford to protect the M-process with a more expensive technique, a variant of Aucsmith's scheme. This scheme has been implemented with the Gnu C compiler gcc. There are several other monitoring, obfuscation, and Dynamic decryption techniques that are embedded in this system. We quantify the performance overhead of the scheme for a variety of Programs. The performance of such an anti-tamper schema can be significantly improved by leveraging a decoupled processor architecture to support the decoupled M- and P- processes. We describe one instance of such a two-stream decoupled architecture that can make the scheme more robust and efficient.
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Software tamper resistance through Dynamic Program monitoring
Lecture Notes in Computer Science, 2006Co-Authors: Brian Blietz, Akhilesh TyagiAbstract:This paper describes a two instruction-stream (two-process) model for tamper resistance. One process (Monitor process, M-Process) is designed explicitly to monitor the control flow of the main Program process (P-Process). The compilation phase compiles the software into two co-processes: P-process and M-process. The monitor process contains the control flow consistency conditions for the P-process. The P-process sends information on its instantiated control flow at a compiler specified fixed period to the M-process. If there is a violation of the control flow conditions captured within the M-process, the M-process takes an anti-tamper action such as termination of the P-process. By its very design, the monitor process is expected to be compact. Hence, we can afford to protect the M-process with a more expensive technique, a variant of Aucsmith's scheme. This scheme has been implemented with the Gnu C compiler gcc. There are several other monitoring, obfuscation, and Dynamic decryption techniques that are embedded in this system. We quantify the performance overhead of the scheme for a variety of Programs. The performance of such an anti-tamper schema can be significantly improved by leveraging a decoupled processor architecture to support the decoupled M- and P- processes. We describe one instance of such a two-stream decoupled architecture that can make the scheme more robust and efficient.
Paul Denholm - One of the best experts on this subject based on the ideXlab platform.
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a Dynamic Programming approach to estimate the capacity value of energy storage
IEEE Transactions on Power Systems, 2014Co-Authors: Ramteen Sioshansi, Seyed Hossein Madaeni, Paul DenholmAbstract:We present a method to estimate the capacity value of storage. Our method uses a Dynamic Program to model the effect of power system outages on the operation and state of charge of storage in subsequent periods. We combine the optimized dispatch from the Dynamic Program with estimated system loss of load probabilities to compute a probability distribution for the state of charge of storage in each period. This probability distribution can be used as a forced outage rate for storage in standard reliability-based capacity value estimation methods. Our proposed method has the advantage over existing approximations that it explicitly captures the effect of system shortage events on the state of charge of storage in subsequent periods. We also use a numerical case study, based on five utility systems in the U.S., to demonstrate our technique and compare it to existing approximation methods.
