Suvrajeet Sen - Academia.edu (original) (raw)

Papers by Suvrajeet Sen

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mi... more This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification schemes which use multi-term disjunctive cuts to obtain approximations of the second stage mixed-integer programs. We prove that the proposed methods are finitely convergent. One of the main advantages of our decomposition scheme is that we use a Benders-based branch-and-cut approach in which linear programming approximations are strengthened sequentially. Moreover as in many decomposition schemes, these subproblems can be solved in parallel. We also illustrate these algorithms using several variants of an SMIP example from the literature, as well as a new set of test problems, which we refer ...

This paper considers the two stage stochastic integer programming problems with an emphasis on pr... more This paper considers the two stage stochastic integer programming problems with an emphasis on problems in which integer variables appear in the second stage Drawing heavily on the theory of disjunctive programming we characterize convexi cations of the second stage problem and develop a decomposition based algorithm for the solution of such problems In particular we verify that problems with xed recourse are characterized by scenario dependent second stage convexi cations that have a great deal in common We refer to this characterization as the C Common Cut Coe cients Theorem Based on the C Theorem we develop an algorithmic methodology that we refer to as Disjunctive Decomposition D We show that when the second stage consists of MILP problems we can obtain accurate second stage objective function estimates after nitely many steps We also set the stage for comparisons between problems in which the rst stage includes only variables and those that allow both continuous and integer var...

Applications of Stochastic Programming, 2005

There are numerous applications in which revenues are generated by the use of resources that are ... more There are numerous applications in which revenues are generated by the use of resources that are distributed over a network. In some cases, these networks are spatial, while in others they are temporal. Nodes in a spatial network, such as those in air transportation and telecommunications industries, correspond to locations on the network, and arcs correspond to the ability to transport goods or provide services between nodes. On the other hand, temporal networks are formed by discretizing time and are commonly used for yield management models for automobile rental companies, hotels, etc. In these models, nodes are often associated with points in time, and arcs correspond to bookings over time. In either case, it is important to recognize that demand is often served by using resources associated with multiple arcs of the network. Airline customers may use multiple flights to complete their itineraries, calls may be routed across multiple links in a telecommunication network, and rental car and hotel customers may retain facilities for multiple days. Furthermore, these networks typically serve multiple classes of customers, some of whom pay higher rates than others. For example, if a television network has a “breaking’’ story for which video conferencing is necessary immediately, they may be willing to pay at a higher rate than a university that has paid in advance to transmit lectures over the same network. Similarly, customers in the airline industry are categorized by fare classes, as are hotel and car rental customers. In any of these applications, the revenue generated by the network depends, in large measure, on the admission control policy used for network management. Intuitively, good control policies will result in a system that serves as many high-paying customers as possible, while maintaining a high level of resource utilization. This paper introduces models that may be used to facilitate the efficient management

Nonconvex Optimization and Its Applications, 1996

The Stochastic Decomposition algorithms presented in previous chapters are designed to take compu... more The Stochastic Decomposition algorithms presented in previous chapters are designed to take computational advantage of the special structure of a two stage stochastic linear program with recourse. This structure resides in the large “core” of subproblem data that is common to all realizations of the random variable \(\tilde \omega \). To see this, recall that a two stage SLP may be stated as follows.

Nonconvex Optimization and Its Applications, 1996

The principles developed in Chapter 3 lay the foundation for Stochastic Decomposition (SD) algori... more The principles developed in Chapter 3 lay the foundation for Stochastic Decomposition (SD) algorithms. We note that although the objective function approximations developed by an SD algorithm are considerably less accurate than the sample mean function, the SD approximations are sufficiently accurate to ensure asymptotic optimality for a subsequence of iterates. Moreover, the manner in which the objective function approximation is updated as additional observations of \( \bar{\omega } \) are obtained streamlines the computational requirements of the method. Example 3.2, which is depicted in Figure 3.4, illustrates the impact of the procedure for updating the cutting planes. Specifically, while this mechanism ensures that the objective function approximation is asymptotically accurate near the iterates, it also ensures that any given cutting plane will eventually become redundant.

Nonconvex Optimization and Its Applications, 1996

Over the past several decades, linear programming (LP) has established itself as one of the most ... more Over the past several decades, linear programming (LP) has established itself as one of the most fundamental tools for planning. Its applications have become routine in several disciplines including those within engineering, business, economics, environmental studies and many others. One may attribute this wide spread acceptance to: (a) an understanding of the power and scope of LP among practitioners, (b) good algorithms, and (c) widely available and reliable software. Furthermore, research on specialized problems (e.g. assignment, transportation, networks etc.) has made LP methodology indispensible to numerous industries including transportation, energy, manufacturing and telecommunications, to name a few. Notwithstanding its success, we note that traditional LP models are deterministic models. That is, all objective function and constraint coefficients are assumed to be known with precision. The assumption that all model parameters are known with certainty serves to limit the usefulness of the approach when planning under uncertainty.

System Modelling and Optimization, 2000

In this paper, we study primal and dual formulations of multistage stochastic programs (SP). Usin... more In this paper, we study primal and dual formulations of multistage stochastic programs (SP). Using a dual formulation, we discuss a decomposition/cutting plane algorithm that can be used to solve such problems. The algorithm, which is based on a scenario decomposition derived from the dual statement of the problem, is best viewed as a conceptual algorithm. Nevertheless, it lends itself to the use of sampled data, and enhancements necessary to produce a computationally viable method are discussed. 1.

Encyclopedia of Operations Research and Management Science, 2013

Encyclopedia of Optimization

A hydraulic quick disconnect coupling wherein the female half is free of external moving parts an... more A hydraulic quick disconnect coupling wherein the female half is free of external moving parts and a spring loaded internal fitting is employed to maintain the halves in either coupled or uncoupled condition.

IEEE Global Telecommunications Conference, 1989, and Exhibition. 'Communications Technology for the 1990s and Beyond

Geographically diverse routing is an important aspect for the design of robust facilities network... more Geographically diverse routing is an important aspect for the design of robust facilities networks. In the present work, the authors discuss an algorithm that extends the routing module in UFO (Unified Facilities Optimizer) to allow diverse routing in layers corresponding to optical fiber transmission. The algorithm considers the primary and protection routing problems simultaneously, thus ensuring that a diverse route can be found, if one exists. The current implementation of the UFO simply determines a primary route for each point-to-point pair. With the extensions given, the UFO will provide a more robust design that is less vulnerable to catastrophic accidents

International Series in Operations Research & Management Science, 2010

... Res. 85, 173–192 (1999) Sen, S., Doverspike, RD, Cosares, S.: Network planning with random de... more ... Res. 85, 173–192 (1999) Sen, S., Doverspike, RD, Cosares, S.: Network planning with random demand. Telecommun. ... Ann. Stat. 9(6), 1187–1195 (1981) Van Slyke, RM, Wets, RJ-B: L-shaped linear programs with applications to optimal control and stochastic programming. ...

IEEE Transactions on Power Systems, 2016

We present a stochastic programming framework for a multiple timescale economic dispatch problem ... more We present a stochastic programming framework for a multiple timescale economic dispatch problem to address integration of renewable energy resources into power systems. This framework allows certain slow-response energy resources to be controlled at an hourly timescale, while fast-response resources, including renewable resources, and related network decisions can be controlled at a sub-hourly timescale. To this end, we study two models motivated by actual scheduling practices of system operators. Using an external simulator as driver for sub-hourly wind generation, we optimize these economic dispatch models using stochastic decomposition, a sample-based approach for stochastic programming. Computational experiments, conducted on the IEEE-RTS96 system and the Illinois system, reveal that optimization with sub-hourly dispatch not only results in lower expected operational costs, but also predicts these costs with far greater accuracy than with models allowing only hourly dispatch. Our results also demonstrate that when compared with standard approaches using the extensive formulation of stochastic programming, the sequential sampling approach of stochastic decomposition provides better predictions with much less computational time.

The IMA Volumes in Mathematics and its Applications, 2002

Many economic equilibrium models have a structure that consists of econometrically estimated dema... more Many economic equilibrium models have a structure that consists of econometrically estimated demand models and supply models that contain explicit representations of the supply technologies, known as process models. Econometric models measure the consequences of peoples’ decisions and are typically used to estimate demand because it is impossible to represent each individual decision and its consequences. Process modeling is an outgrowth of input-output analysis and linear programming and began with Markowitz [1955]. Here the technologies and possible decisions are modeled explicitly in an optimization model. The solution to the model consists of the decisions of optimizing firms and their consequences. Each modeling approach has had a long history and combining the two types of models into one economic equilibrium model is quite common. Examples are the energy-market models, PIES (Hogan [1975]), IFFS (Murphy, Conti, Sanders and Shaw [1988]), and NEMS (Energy Information Administration [1998]). For a summary of all three, see Murphy and Shaw [1995].

homepages.cwi.nl

... 81-86. Sen, SRD Doverspike and S. Cosares 1994]. \Network Planning with Random Demand," ... more ... 81-86. Sen, SRD Doverspike and S. Cosares 1994]. \Network Planning with Random Demand," Telecommunication Systems, 3, pp. ... A Simulation-based approach to stochastic programming with recourse," Mathematical Programming, 81, pp. 301-325. Van Slyke, R. and R. JB. ...

Operations Research Letters, 2012

The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obt... more The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obtain the solution of general mixed-integer linear programs (MILP) with bounded integer variables. In this paper, we present our computational experience with variants of the CPT algorithm. Because the CPT algorithm is based on discovering multi-term disjunctions, this paper is the first to present computational results with multi-term disjunctions. We implement two variants for cut generation using alternative normalization schemes. Our results demonstrate that even a preliminary implementation of the CPT algorithm (with either normalization) is able to close a significant portion of the integrality gap without resorting to branch-and-cut. As a by-product of our experiments, we also conclude that one of the cut generation schemes (namely minimizing the 1 norm of cut coefficients) appears to have an edge over the other.

Operations Research, 2007

All too often, the hard work that members of the scholarly community do to support our profession... more All too often, the hard work that members of the scholarly community do to support our profession goes unrecognized. For the eighth year, the Editorial Board of Operations Research has decided to reward outstanding service to the journal’s scholarly mission. Associate editors and referees who did an exceptionally professional job by submitting timely, unbiased, and thoughtful reviews were considered for the award. This award is just a small token of the appreciation for exceptional work performed on behalf of Operations Research and our profession. We thank these individuals for their effort to make Operations Research the premier journal of the field.

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mi... more This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification schemes which use multi-term disjunctive cuts to obtain approximations of the second stage mixed-integer programs. We prove that the proposed methods are finitely convergent. One of the main advantages of our decomposition scheme is that we use a Benders-based branch-and-cut approach in which linear programming approximations are strengthened sequentially. Moreover as in many decomposition schemes, these subproblems can be solved in parallel. We also illustrate these algorithms using several variants of an SMIP example from the literature, as well as a new set of test problems, which we refer ...

This paper considers the two stage stochastic integer programming problems with an emphasis on pr... more This paper considers the two stage stochastic integer programming problems with an emphasis on problems in which integer variables appear in the second stage Drawing heavily on the theory of disjunctive programming we characterize convexi cations of the second stage problem and develop a decomposition based algorithm for the solution of such problems In particular we verify that problems with xed recourse are characterized by scenario dependent second stage convexi cations that have a great deal in common We refer to this characterization as the C Common Cut Coe cients Theorem Based on the C Theorem we develop an algorithmic methodology that we refer to as Disjunctive Decomposition D We show that when the second stage consists of MILP problems we can obtain accurate second stage objective function estimates after nitely many steps We also set the stage for comparisons between problems in which the rst stage includes only variables and those that allow both continuous and integer var...

Applications of Stochastic Programming, 2005

There are numerous applications in which revenues are generated by the use of resources that are ... more There are numerous applications in which revenues are generated by the use of resources that are distributed over a network. In some cases, these networks are spatial, while in others they are temporal. Nodes in a spatial network, such as those in air transportation and telecommunications industries, correspond to locations on the network, and arcs correspond to the ability to transport goods or provide services between nodes. On the other hand, temporal networks are formed by discretizing time and are commonly used for yield management models for automobile rental companies, hotels, etc. In these models, nodes are often associated with points in time, and arcs correspond to bookings over time. In either case, it is important to recognize that demand is often served by using resources associated with multiple arcs of the network. Airline customers may use multiple flights to complete their itineraries, calls may be routed across multiple links in a telecommunication network, and rental car and hotel customers may retain facilities for multiple days. Furthermore, these networks typically serve multiple classes of customers, some of whom pay higher rates than others. For example, if a television network has a “breaking’’ story for which video conferencing is necessary immediately, they may be willing to pay at a higher rate than a university that has paid in advance to transmit lectures over the same network. Similarly, customers in the airline industry are categorized by fare classes, as are hotel and car rental customers. In any of these applications, the revenue generated by the network depends, in large measure, on the admission control policy used for network management. Intuitively, good control policies will result in a system that serves as many high-paying customers as possible, while maintaining a high level of resource utilization. This paper introduces models that may be used to facilitate the efficient management

Nonconvex Optimization and Its Applications, 1996

The Stochastic Decomposition algorithms presented in previous chapters are designed to take compu... more The Stochastic Decomposition algorithms presented in previous chapters are designed to take computational advantage of the special structure of a two stage stochastic linear program with recourse. This structure resides in the large “core” of subproblem data that is common to all realizations of the random variable \(\tilde \omega \). To see this, recall that a two stage SLP may be stated as follows.

Nonconvex Optimization and Its Applications, 1996

The principles developed in Chapter 3 lay the foundation for Stochastic Decomposition (SD) algori... more The principles developed in Chapter 3 lay the foundation for Stochastic Decomposition (SD) algorithms. We note that although the objective function approximations developed by an SD algorithm are considerably less accurate than the sample mean function, the SD approximations are sufficiently accurate to ensure asymptotic optimality for a subsequence of iterates. Moreover, the manner in which the objective function approximation is updated as additional observations of \( \bar{\omega } \) are obtained streamlines the computational requirements of the method. Example 3.2, which is depicted in Figure 3.4, illustrates the impact of the procedure for updating the cutting planes. Specifically, while this mechanism ensures that the objective function approximation is asymptotically accurate near the iterates, it also ensures that any given cutting plane will eventually become redundant.

Nonconvex Optimization and Its Applications, 1996

Over the past several decades, linear programming (LP) has established itself as one of the most ... more Over the past several decades, linear programming (LP) has established itself as one of the most fundamental tools for planning. Its applications have become routine in several disciplines including those within engineering, business, economics, environmental studies and many others. One may attribute this wide spread acceptance to: (a) an understanding of the power and scope of LP among practitioners, (b) good algorithms, and (c) widely available and reliable software. Furthermore, research on specialized problems (e.g. assignment, transportation, networks etc.) has made LP methodology indispensible to numerous industries including transportation, energy, manufacturing and telecommunications, to name a few. Notwithstanding its success, we note that traditional LP models are deterministic models. That is, all objective function and constraint coefficients are assumed to be known with precision. The assumption that all model parameters are known with certainty serves to limit the usefulness of the approach when planning under uncertainty.

System Modelling and Optimization, 2000

In this paper, we study primal and dual formulations of multistage stochastic programs (SP). Usin... more In this paper, we study primal and dual formulations of multistage stochastic programs (SP). Using a dual formulation, we discuss a decomposition/cutting plane algorithm that can be used to solve such problems. The algorithm, which is based on a scenario decomposition derived from the dual statement of the problem, is best viewed as a conceptual algorithm. Nevertheless, it lends itself to the use of sampled data, and enhancements necessary to produce a computationally viable method are discussed. 1.

Encyclopedia of Operations Research and Management Science, 2013

Encyclopedia of Optimization

A hydraulic quick disconnect coupling wherein the female half is free of external moving parts an... more A hydraulic quick disconnect coupling wherein the female half is free of external moving parts and a spring loaded internal fitting is employed to maintain the halves in either coupled or uncoupled condition.

IEEE Global Telecommunications Conference, 1989, and Exhibition. 'Communications Technology for the 1990s and Beyond

Geographically diverse routing is an important aspect for the design of robust facilities network... more Geographically diverse routing is an important aspect for the design of robust facilities networks. In the present work, the authors discuss an algorithm that extends the routing module in UFO (Unified Facilities Optimizer) to allow diverse routing in layers corresponding to optical fiber transmission. The algorithm considers the primary and protection routing problems simultaneously, thus ensuring that a diverse route can be found, if one exists. The current implementation of the UFO simply determines a primary route for each point-to-point pair. With the extensions given, the UFO will provide a more robust design that is less vulnerable to catastrophic accidents

International Series in Operations Research & Management Science, 2010

... Res. 85, 173–192 (1999) Sen, S., Doverspike, RD, Cosares, S.: Network planning with random de... more ... Res. 85, 173–192 (1999) Sen, S., Doverspike, RD, Cosares, S.: Network planning with random demand. Telecommun. ... Ann. Stat. 9(6), 1187–1195 (1981) Van Slyke, RM, Wets, RJ-B: L-shaped linear programs with applications to optimal control and stochastic programming. ...

IEEE Transactions on Power Systems, 2016

We present a stochastic programming framework for a multiple timescale economic dispatch problem ... more We present a stochastic programming framework for a multiple timescale economic dispatch problem to address integration of renewable energy resources into power systems. This framework allows certain slow-response energy resources to be controlled at an hourly timescale, while fast-response resources, including renewable resources, and related network decisions can be controlled at a sub-hourly timescale. To this end, we study two models motivated by actual scheduling practices of system operators. Using an external simulator as driver for sub-hourly wind generation, we optimize these economic dispatch models using stochastic decomposition, a sample-based approach for stochastic programming. Computational experiments, conducted on the IEEE-RTS96 system and the Illinois system, reveal that optimization with sub-hourly dispatch not only results in lower expected operational costs, but also predicts these costs with far greater accuracy than with models allowing only hourly dispatch. Our results also demonstrate that when compared with standard approaches using the extensive formulation of stochastic programming, the sequential sampling approach of stochastic decomposition provides better predictions with much less computational time.

The IMA Volumes in Mathematics and its Applications, 2002

Many economic equilibrium models have a structure that consists of econometrically estimated dema... more Many economic equilibrium models have a structure that consists of econometrically estimated demand models and supply models that contain explicit representations of the supply technologies, known as process models. Econometric models measure the consequences of peoples’ decisions and are typically used to estimate demand because it is impossible to represent each individual decision and its consequences. Process modeling is an outgrowth of input-output analysis and linear programming and began with Markowitz [1955]. Here the technologies and possible decisions are modeled explicitly in an optimization model. The solution to the model consists of the decisions of optimizing firms and their consequences. Each modeling approach has had a long history and combining the two types of models into one economic equilibrium model is quite common. Examples are the energy-market models, PIES (Hogan [1975]), IFFS (Murphy, Conti, Sanders and Shaw [1988]), and NEMS (Energy Information Administration [1998]). For a summary of all three, see Murphy and Shaw [1995].

homepages.cwi.nl

... 81-86. Sen, SRD Doverspike and S. Cosares 1994]. \Network Planning with Random Demand," ... more ... 81-86. Sen, SRD Doverspike and S. Cosares 1994]. \Network Planning with Random Demand," Telecommunication Systems, 3, pp. ... A Simulation-based approach to stochastic programming with recourse," Mathematical Programming, 81, pp. 301-325. Van Slyke, R. and R. JB. ...

Operations Research Letters, 2012

The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obt... more The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obtain the solution of general mixed-integer linear programs (MILP) with bounded integer variables. In this paper, we present our computational experience with variants of the CPT algorithm. Because the CPT algorithm is based on discovering multi-term disjunctions, this paper is the first to present computational results with multi-term disjunctions. We implement two variants for cut generation using alternative normalization schemes. Our results demonstrate that even a preliminary implementation of the CPT algorithm (with either normalization) is able to close a significant portion of the integrality gap without resorting to branch-and-cut. As a by-product of our experiments, we also conclude that one of the cut generation schemes (namely minimizing the 1 norm of cut coefficients) appears to have an edge over the other.

Operations Research, 2007

All too often, the hard work that members of the scholarly community do to support our profession... more All too often, the hard work that members of the scholarly community do to support our profession goes unrecognized. For the eighth year, the Editorial Board of Operations Research has decided to reward outstanding service to the journal’s scholarly mission. Associate editors and referees who did an exceptionally professional job by submitting timely, unbiased, and thoughtful reviews were considered for the award. This award is just a small token of the appreciation for exceptional work performed on behalf of Operations Research and our profession. We thank these individuals for their effort to make Operations Research the premier journal of the field.