Publications
Google Scholar Profile
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Journal Papers
J. Zou, S. Ahmed and X. Sun. ‘‘Multistage stochastic unit commitment using Stochastic Dual Dynamic Integer Programming,’’ accepted IEEE Transactions on Power Systems, 2018.(preprint)
B. Fanzeres, S. Ahmed and A. Street. ‘‘Robust Strategic Bidding in AuctionBased Markets,’’ European Journal of Operational Research, vol.272, pp.11581172, 2018.
S. Ahmed and W. Xie. ‘‘Relaxations and Approximations of Chance Constraints under Finite Distributions,’’ Mathematical Programming, vol. 170, pp.4365, 2018.
W. Xie and S. Ahmed. ‘‘Distributionally Robust Simple Integer Recourse,’’ Computational Management Science, vol.15, pp.351367, 2018.(preprint)
B. Basciftci, S. Ahmed, N. Gebraeel, M. Yildirim. ‘‘Integrated generator maintenance and operations scheduling under uncertain failure times,’’ accepted IEEE Transactions on Power Systems, 2018.(preprint)
J. Zou, S. Ahmed, X. Sun. ‘‘Stochastic Dual Dynamic integer Programming,’’ accepted Mathematical Programming, 2018.(preprint)
M.N. Hjelmeland, J. Zou, A. Helseth, S. Ahmed. ‘‘Nonconvex mediumterm hydropower scheduling by Stochastic Dual Dynamic integer Programming,’’ IEEE Transactions on Sustainable Energy, vol.10, pp.481490, 2019.
A. Torrico, S. Ahmed and A. Toriello. ‘‘A polyhedral approach to online bipartite matching,’’ Mathematical Programming, vol.172, pp.443465, 2018.(preprint)
W. Xie and S. Ahmed. ‘‘On deterministic reformulations of distributionally robust joint chance constrained optimization problems,’’ SIAM Journal on Optimization, vol.28, pp.11511182, 2018.(preprint)
W. Xie and S. Ahmed. ‘‘On quantile cuts and their closure for chance constrained optimization problems,’’ Mathematical Programming, vol.172, pp.621646, 2018.(preprint)
L. Munguia, S. Ahmed, D. Bader, G.L. Nemhauser and Y. Shao. ‘‘Alternating Criteria Search: A parallel large neighborhood search algorithm for mixed integer programs,’’ Computational Optimization and Applications, vol.69, pp.124, 2018.(preprint)
W. Xie and S. Ahmed. ‘‘Distributionally robust chance constrained optimal power flow with renewables: A conic reformulation,’’ IEEE Transactions on Power Systems, vol.33, pp.18601867, 2018.(preprint)
Y. Deng, S. Ahmed, and S. Shen. ‘‘Parallel scenario decomposition of risk averse 01 stochastic programs,’’ INFORMS Journal on Computing, vol.30, pp.90105, 2018.(preprint)
M. Siebert, K. Bartlett, H. Kim, S. Ahmed, J. Lee, D. Nazzal, G. Nemhauser, J. Sokol. ‘‘Lot Targeting and Lot Dispatching Decision Policies for Semiconductor Manufacturing: Optimization under Uncertainty with Simulation Validation,’’ International Journal of Production Research, vol.56, pp.629641, 2018.
J. Zou, S. Ahmed, X. Sun. ‘‘Partially adaptive stochastic optimization for electric power generation expansion planning,’’ INFORMS Journal on Computing, vol.30, pp.388401, 2018.(preprint)
J. Yu and S. Ahmed. ‘‘Polyhedral results for a class of cardinality constrained submodular minimization problems,’’ Discrete Optimization, vol.24, pp.87102, 2017. (preprint)
M. Costley, M.J. Feizollahi, S. Ahmed and S. Grijalva. ‘‘A rollinghorizon unit commitment framework with flexible periodicity,’’ International Journal of Electrical Power and Energy Systems, vol.190, pp.280291, 2017.
C. Andrade, S. Ahmed, G. Nemhauser and Y. Shao. ‘‘A hybrid primal heuristic for finding feasible solutions to mixed integer programs,’’ European Journal of Operations Research, vol. 263, pp.6371, 2017.
J. Yu and S. Ahmed. ‘‘Maximizing a class of submodular utility functions with constraints,’’ Mathematical Programming, vol.162, pp.145164, 2017 .(preprint)
S. Ahmed, J. Luedtke, Y. Song, W. Xie. ‘‘Nonanticipative duality, relaxations and formulations for chanceconstrained stochastic programs,’’ Mathematical Programming, vol.162, pp.5181,2017. (preprint)
J. Feizollahi, S. Ahmed, A. Sun. ‘‘Exact augmented Lagrangian duality for mixed integer linear programming,’’ Mathematical Programming, vol.161, pp.365387, 2017. (preprint)
A. Gupte, S. Ahmed, M.S. Cheon, S.S. Dey. ‘‘Relaxations and discretizations for the pooling problem,’’ Journal of Global Optimization, vol.67, pp.631669, 2017. (preprint)
L.M. Munguia, S. Ahmed, D.A. Bader, G.L. Nemhauser, V. Goel, Y. Shao. ‘‘A parallel local search framework for the fixedcharge multicommodity network flow problem,’’ Computers and Operations Research, vol.77, pp.4457, 2017. (preprint)
S. Ahmed, Q. He, S. Li, and G.L. Nemhauser. ‘‘On the computational complexity of minimumconcavecostflow in a twodimensional grid,’’ SIAM Journal on Optimization, vol.26, pp.20592079, 2016. (preprint)
G. Angulo, S. Ahmed, S.S. Dey. ‘‘Improving the integer Lshaped method,’’ INFORMS Journal on Computing, vol.28, pp.483399, 2016. (preprint)
J. Yu and S. Ahmed. ‘‘Maximizing expected utility over a knapsack constraint,’’ Operations Research Letters, vol.44, pp.180185, 2016. (preprint)
S. Bruno, S. Ahmed, A. Shapiro, A. Street. ‘‘Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty,’’ European Journal of Operational Research, vol.250, pp.979989, 2016.
F. Qiu, S. Ahmed, S.S. Dey. ‘‘Strengthened bounds for the probability of koutofn events,’’ Discrete Applied Mathematics, vol.198, pp.232240, 2016. (preprint)
M.J. Feizollahi, M. Costley, S. Ahmed, S. Grijalva.‘‘Large scale decentralized unit commitment,’’ International Journal of Electrical Power and Energy Systems, vol.73, pp.97106, 2015. (preprint)
G. Angulo, S. Ahmed, S.S. Dey, V. Kaibel. ‘‘Forbidden vertices,’’ Mathematics of Operations Research, vol.40, pp.350360, 2015. (preprint)
Q. He, S. Ahmed and G.L. Nemhauser. ‘‘Minimum concave cost flow over a grid network,’’ Mathematical Programming, vol.150, pp.7998, 2015. (preprint)
F. Qiu, S. Ahmed, S.S. Dey, L. Wolsey. ‘‘Covering linear programming with violations,’’ INFORMS Journal on Computing, vol. 26, pp. 531546, 2014. (preprint)
B. Na, S. Ahmed, G.L. Nemhauser, J. Sokol. ‘‘A cutting and scheduling problem in float glass manufacturing,’’ Journal of Scheduling, vol.17, pp. 95107, 2014. (preprint)
G. Angulo, S. Ahmed, S.S. Dey. ‘‘Semicontinuous network flow problems,’’ Mathematical Programming, vol.145, pp.565599, 2014. (preprint)
R. Carvajal, S. Ahmed, G.L. Nemhauser, K. Furman, V. Goel, Y. Shao. ‘‘Using diversification, communication and parallelism to solve mixedinteger linear programs,’’ Operations Research Letters, vol.42, pp. 186189, 2014. (preprint)
K. Bartlett, J. Lee, S. Ahmed, G.L. Nemhauser, J. Sokol, B. Na. ‘‘Congestionaware dynamic routing in automated material handling systems’’, Computers and Industrial Engineering, vol. 70, pp. 176182, 2014.
M.J. Feizollahi, S. Ahmed, M. Modarres. ‘‘The robust redundancy allocation problem in seriesparallel systems with budgeted uncertainty,’’ IEEE Transactions on Reliability, vol.63, pp.239250, 2014.
S. Ahmed. ‘‘Convex relaxations of chance constrained optimization problems,’’ Optimization Letters, vol.8, pp.112, 2014. (preprint)
S. Ahmed. ‘‘A scenario decomposition algorithm for 01 stochastic programs,’’ Operations Research Letters, vol. 41, pp. 565569, 2013. (preprint) (Errata)
B. Na, S. Ahmed, G.L. Nemhauser, J. Sokol. ‘‘Optimization of automated float glass lines,’’ International Journal of Production Economics (Special issue on Cutting and Packing), vol.145, pp. 561572, 2013. (preprint)
A. Gupte, S. Ahmed, M.S. Cheon, and S.S. Dey. ‘‘Solving mixed integer bilinear problems using MIP formulations,’’ SIAM Journal on Optimization, vol.23, pp.721744, 2013. (preprint)
S. Ahmed and D.J. Papageorgiou. ‘‘Probabilistic set covering with correlations,’’ Operations Research, vol.61, pp.438452, 2013. (preprint)
N. Kong, A.J. Schaefer, and S. Ahmed. ‘‘Totally unimodular stochastic programs,’’ Mathematical Programming, vol.138, pp.113, 2013.
J.P. Vielma, S. Ahmed, and G.L. Nemhauser. ‘‘Mixed integer linear programming formulations for probabilistic constraints,’’ Operations Research Letters, vol.40, pp.153158, 2012. (preprint)
Q. He, S. Ahmed, and G.L. Nemhauser. ‘‘Sell or hold: A simple twostage stochastic combinatorial optimization problem,’’ Operations Research Letters, vol.40, pp.6973, 2012. (preprint)
Q. He, S. Ahmed, and G.L. Nemhauser. ‘‘A probabilistic comparison of split and type 1 triangle cuts for two row mixedinteger programs,’’ SIAM Journal on Optimization, vol.21, pp.617632, 2011. (preprint)
S. Ahmed and A. Atamturk. ‘‘Maximizing a class of submodular utility functions,’’ Mathematical Programming, vol.128, pp.149169, 2011 (preprint)
S. Shen, J.C. Smith, and S. Ahmed. ‘‘Expectation and chanceconstrained models and algorithms for insuring critical paths,’’ Management Science, vol.56, pp.17941814, 2010.(eprint)
J.P. Vielma, S. Ahmed, and G.L. Nemhauser. ‘‘A note on: 'A superior representation method for piecewise linear functions’ by Li, Lu, Huang and Hu,’’ INFORMS Journal on Computing, vol.22, pp.493497, 2010. (preprint)
S. Ahmed, O. Gozbasi, M. Savelsbergh, I. Crocker, T. Fox, and E. Schreibmann. ‘‘An automated IntensityModulated Radiation Therapy planning system,’’ INFORMS Journal on Computing, vol.22, pp.568583, 2010. (preprint)
J.P. Vielma, S. Ahmed and G.L. Nemhauser. ‘‘Mixedinteger models for nonseparable piecewise linear optimization: Unifying framework and extensions,’’ Operations Research, vol.58, pp.303315, 2010. (preprint)
K. Huang and S. Ahmed. ‘‘A stochastic programming approach for planning horizons of infinite horizon capacity planning problems,’’ European Journal of Operational Research, vol.200, pp.7484, 2010.
J. Luedtke, S. Ahmed and G.L. Nemhauser. ‘‘An integer programming approach for linear programs with probabilistic constraints,’’ Mathematical Programming, vol.122, pp.247, 2010 (preprint)
Z.C. Taskin, J.C. Smith, S. Ahmed, and A.J, Schaefer. ‘‘Cutting plane algorithms for solving a robust edgepartition problem,’’ Discrete Optimization, vol.6, pp.420435, 2009.
F. KilincKarzan, A. Toriello, S. Ahmed, G.L. Nemhauser, and M. Savelsbergh. ‘‘Approximating the stability region for binary mixedinteger programs,’’ Operations Research Letters, vol.37, pp.250254, 2009 (preprint)
P. Schutz, A. Tomasgard and S. Ahmed. ‘‘Supply chain design under uncertainty using sample average approximation and dual decomposition,’’ European Journal of Operational Research, vol.199, pp.409419, 2009.
B. Pagnoncelli, S. Ahmed, and A. Shapiro. ‘‘The sample average approximation method for chance constrained programming: theory and applications,’’ Journal of Optimization theory and Applications, vol.142, pp.399416, 2009 (preprint)
K. Huang and S. Ahmed. ‘‘The value of multistage stochastic programming in capacity planning under uncertainty,’’ Operations Research, vol.57, pp.893904, 2009 (preprint)
Y. Guan, S. Ahmed and G.L. Nemhauser. ‘‘Cutting planes for multistage stochastic integer programs,’’ Operations Research, vol.57, pp.287298, 2009 (preprint)
S. Ahmed, D. Filipovic, and G. Svindland. ‘‘A note on natural risk statistics,’’ Operations Research Letters, vol.36, pp.662664, 2008 (preprint)
J. Luedtke and S. Ahmed. ‘‘A sample approximation approach for optimization with probabilistic constraints,’’ SIAM Journal on Optimization, vol.19, pp.674699, 2008 (preprint)
W. Wang and S. Ahmed. ‘‘Sample average approximation of expected value constrained stochastic programs,’’ Operations Research Letters, vol.36, pp.515519, 2008 (preprint)
J.P. Vielma, S. Ahmed and G.L. Nemhauser. ‘‘A lifted linear programming branchandbound algorithm for mixed integer conic quadratic programs,’’ INFORMS Journal on Computing, vol.20, pp.438450, 2008 (preprint)
K. Huang and S. Ahmed. ‘‘On a multistage stochastic programming model for inventory planning,’’ Information Systems and Operational Research, vol. 46, pp. 155163, 2008.
S. Ahmed and N. V. Sahinidis. ‘‘Selection, acquisition, and allocation of manufacturing technology in a multiproduct environment,’’ European Journal of Operational Research, vol. 189, pp. 807821, 2008.
S. Ahmed, U. Cakmak and A. Shapiro. ‘‘Coherent risk measures in inventory problems,’’ European Journal of Operational Research, vol.182, pp.226238, 2007 (preprint)
Y. Guan, S. Ahmed and G. L. Nemhauser. ‘‘Sequential pairing of mixed integer inequalities,’’ Discrete Optimization, vol.4, pp.2139, 2007 (preprint)
S. Ahmed. ‘‘Convexity and decomposition of meanrisk stochastic programs ,’’ Mathematical Programming, vol.106, pp.433446, 2006 (preprint)
Y. Guan, S. Ahmed, A. J. Miller, and G. L. Nemhauser. ‘‘On formulations of the stochastic uncapacitated lotsizing problem,’’ Operations Research Letters, vol.34, pp.241250, 2006.
M.S. Cheon, S. Ahmed and F. AlKhayyal. ‘‘A branchreducecut algorithm for the global optimization of probabilistically constrained linear programs,’’ Mathematical Programming, vol.108, pp.617634, 2006 (preprint)
Y. Guan, S. Ahmed, G.L. Nemhauser and A.J. Miller. ‘‘A branchandcut algorithm for the stochastic uncapacitated lotsizing problem,’’ Mathematical Programming, vol.105, pp.5584, 2006 (preprint)
S. Ahmed and Y. Guan. ‘‘The Inverse Optimal Value Problem,’’ Mathematical Programming, vol.102, pp.91110, 2005 (preprint)
T. Santoso, S. Ahmed, M. Goetschalckx, and A. Shapiro. ‘‘A stochastic programming approach for supply chain network design under uncertainty,’’ European Journal of Operational Research, vol.167, pp.96115, 2005 (preprint)
A. Shapiro and S. Ahmed. ‘‘On a class of minimax stochastic programs,’’ SIAM Journal on Optimization, vol.14, pp.12371249, 2004 (preprint)
S. Ahmed, M. Tawarmalani, and N. V. Sahinidis. ‘‘A finite branch and bound algorithm for twostage stochastic integer programs,’’ Mathematical Programming, vol.100, pp.355377, 2004 (preprint)
S. Takriti and S. Ahmed. ‘‘On Robust Optimization of TwoStage Systems,’’ Mathematical Programming, vol.99, pp.109126, 2004 (preprint)
G. Parija, S. Ahmed, and A. J. King. ‘‘On bridging the gap between stochastic integer programming and mixedinteger solver technologies,’’ INFORMS Journal on Computing, vol.16, 2004 (preprint)
S. Ahmed and R. Garcia. ‘‘Dynamic capacity acquisition and assignment under uncertainty,’’ Annals of Operations Research, vol.124, pp. 267283, 2003 (preprint)
B. Verweij, S. Ahmed, A. J. Kleywegt, G. Nemhauser, and A. Shapiro. ‘‘The sample average approximation method applied to stochastic routing problems: A computational study,’’ Computational and Applied Optimization, vol.24, pp.289333, 2003 (preprint)
S. Ahmed and N. V. Sahinidis. ‘‘An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion,’’ Operations Research, vol.51, pp.461471, 2003 (preprint)
S. Ahmed, A. J. King, and G. Parija. ‘‘A MultiStage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty,’’ Journal of Global Optimization, vol. 26, pp.324, 2003 (preprint)
M. Tawarmalani, S. Ahmed, and N. V. Sahinidis. ‘‘Product disaggregation and relaxations of mixedinteger rational programs,’’ Optimization and Engineering, vol.3, pp. 281303, 2002.
M. Tawarmalani, S. Ahmed, and N. V. Sahinidis. ‘‘Global optimization of 01 hyperbolic programs,’’ Journal of Global Optimization, vol. 24, pp. 385417, 2002.
S. Ahmed and N. V. Sahinidis. ‘‘Analytical investigations of the process planning problem,’’ Computers & Chemical Engineering, vol. 23, pp. 16051621, 2000.
S. Ahmed, N. V. Sahinidis, and E. N. Pistikopoulos. ‘‘An improved decomposition algorithm for process planning under uncertainty,’’ Computers & Chemical Engineering, vol. 23, pp. 15891604, 2000.
S. Ahmed and N. V. Sahinidis. ‘‘Robust process planning under uncertainty,’’ Industrial & Engineering Chemistry Research, vol. 37, pp. 18831892, 1998.
Book/Book Chapters
T. Terlaky, M. Anjos, and S. Ahmed (eds.), ‘‘Advances and trends in optimization with engineering applications,’’ MOSSIAM Series on Optimization, 2017.
S. Ahmed. ‘‘Two stage stochastic integer programming,’’ in the Encylopedia of Optimization (T. Choran (Ed.)), Wiley, 2010. (preprint)
S. Ahmed and A. Shapiro. ‘‘Solving chanceconstrained stochastic programs via sampling and integer programming,’’ in Tutorials in Operations Research, Z.L. Chen and S. Raghavan (eds.), INFORMS, 2008. (preprint)
M. Goetschalckx, S. Ahmed, A. Shapiro, and T. Santoso. ‘‘Strategic design of robust global supply chains under uncertainty,” in Progress in Material Handling Research: 2004, R. Meller et al. (eds.), The Material Handling Institute, NC, pp. 103117, 2004.
S. Ahmed and N. V. Sahinidis. ‘‘Techniques in long range planning of chemical manufacturing systems,’’ in ComputerAided Design, Engineering, and Manufacturing: Systems Techniques and Applications, Volume V: The Design of Manufacturing Systems, C. T. Leondes (ed.), CRC Press LLC, Boca Raton, FL, pp.125, 2001.
S. Ahmed and N. V. Sahinidis. ‘‘Chemical process planning,’’ in The Encyclopedia of Optimization, C. A. Floudas and P. M. Pardalos (eds.), Kluwer Academic Publishers, Vol.1, pp.246252, 2001.
Conference Proceedings
E.B. Khalil, B. Dilkina, G. Nemhauser, S. Ahmed, Y. Shao. ‘‘Learning to Run Heuristics in Tree Search,’’
In 26th International Joint Conference on Artificial Intelligence (IJCAI), 2017.
K. Ryan, D. Rajan, S. Ahmed. ‘‘Scenario Decomposition for 01 Stochastic Programs: Improvements and Asynchronous Implementation,’’ IEEE Workshop on Parallel Computing and Combinatorial Optimization, 2016.
W. Xie and S. Ahmed. ‘‘On the quantile cut closure of chanceconstrained problems,’’ 18th International Integer Programming and Combinatorial Optimization (IPCO) Conference, 2016.
A. Torrico, S. Ahmed and A. Toriello. ‘‘A Polyhedral Approach to Online Bipartite Matching,’’ 18th International Integer Programming and Combinatorial Optimization (IPCO) Conference, 2016.
J. Luedtke, S. Ahmed and G.L. Nemhauser. ‘‘An integer programming approach for linear programs with probabilistic constraints,’’ in Proceedings of the 12th International Integer Programming and Combinatorial Optimization (IPCO) Conference, Lecture Notes in Computer Science, pp. 310423, 2007.
Y. Guan, S. Ahmed and G. L. Nemhauser. ‘‘Sequential pairing of mixed integer inequalities,’’ in Proceedings of the 11th International Integer Programming and Combinatorial Optimization (IPCO) Conference, Lecture Notes in Computer Science, pp. 2334, 2005.
S. Ahmed. ‘‘Semiconductor tool planning via multistage stochastic programming,’’ Proceedings of the International Conference on Modeling and Analysis in Semiconductor Manufacturing, Mackulak et al. (eds.), pp. 153157, 2002.
Working Papers and Technical Reports
M. Siebert, S. Ahmed, G. Nemhauser. ‘‘A Linear Programming Based Approach to the Steiner Tree Problem with a Fixed Number of Terminals,’’ submitted 2018.
B. Basciftci, S. Ahmed, N. Gebraeel. ‘‘DataDriven Maintenance and Operations Scheduling in Power Systems under DecisionDependent Uncertainty,’’ submitted 2018.
H. Hashemi Doulabi, S. Ahmed, G. Nemhauser. StateVariable Modeling for Joint Chance Constrained Optimization Problems, submitted 2018.
H. Hashemi Doulabi, S. Ahmed, G. Nemhauser. StateVariable Modeling for a Class of TwoStage Stochastic Optimization Problems, submitted 2018.
L. Munguia, S. Ahmed, D. Bader, G. Nemhauser, Y. Shao, D.J. Papageorgiou. ‘‘Rapid prototyping of parallel primal heuristics for domain specific MIPs: Application to maritime inventory routing,’’ submitted 2018.
X. Yu, S. Ahmed, S. Shen. ‘‘On the Value of Multistage Stochastic Facility Location with (or without) Risk Aversion,’’ submitted 2018.
E. Karabulut, S. Ahmed, G. Nemhauser. ‘‘Decentralized Algorithms for Distributed Integer Programming Problems with a Coupling Cardinality Constraint,’’ submitted 2018.
A. I. Mahmutogullari, S. Ahmed, O. Cavus, M.S. Akturk. ‘‘The value of multistage stochastic programming in riskaverse unit commitment under uncertainty,’’ submitted 2018.
R. Rahmaniani, S. Ahmed, T.G. Crainic, M. Gendreau, and W. Rei. ‘‘The Benders Dual Decomposition Method,’’ submitted 2018.
W. Xie and S. Ahmed. ‘‘Bicriteria Approximation of Chance Constrained Covering Problems,’’ submitted 2018.
W. Xie, S. Ahmed and R. Jiang. ‘‘Optimized Bonferroni approximations of distributionally robust joint chance constraints,’’ submitted 2017.
Y. Deng, S. Ahmed, J. Lee and S. Shen. ‘‘Scenario grouping and decomposition algorithms for chanceconstrained programs,’’ submitted 2017.
M. Bodur, S. Ahmed, N. Boland, G. Nemhauser. ‘‘Decomposition of loosely coupled integer programs: A multiobjective perspective,’’ submitted 2016.
K. Ryan, S. Ahmed, S.S. Dey and D. Rajan. ‘‘Optimization driven scenario grouping,’’ submitted, 2016.
S. Ahmed. ‘‘Smooth minimization of twostage stochastic linear programs,’’ ISyE Technical Report 2006.
A. Parmar, S. Ahmed, J. Sokol. ‘‘An integer programming approach to the OSPF weight setting problem,’’ ISyE Technical Report 2006.
S. Ahmed. ‘‘Meanrisk objectives in stochastic programming,’’ ISyE Technical Report 2004.
S. Ahmed and A. Shapiro. ‘‘The sample average approximation method for stochastic programs with integer recourse, ISyE Technical Report, 2002.
S. Takriti and S. Ahmed. ‘‘Managing shortterm electricity contracts under uncertainty: A minimax approach, ISyE Technical Report, 2002.
S. Ahmed and M. A. Haque. ‘‘Multifacility retail locationing using pchoice models,’’ ISyE Technical Report, 2001.
A. J. King, S. Takriti, and S. Ahmed. ‘‘Issues in risk modeling for multistage systems,’’ IBM Research Report No. RC20993, 1997.
