Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict tactical solutions to a given operational problem. In this context, the tactical solution is less detailed than the operational one but it has to be computed in very short time and under imperfect information. The problem is of importance in various applications where tactical and operational planning problems are interrelated and information about the operational problem is revealed over time. This is for instance the case in certain capacity planning and demand management systems. We formulate the problem as a two-stage optimal prediction stochastic program whose solution we predict with a supervised machine learning algorithm. The training data set consists of a large number of deterministic (second stage) problems generated by controlled probabilistic sampling. The labels are computed based on solutions to the deterministic problems (solved independently and offline) employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application in load planning for rail transportation show that deep learning algorithms produce highly accurate predictions in very short computing time (milliseconds or less). The prediction accuracy is comparable to solutions computed by sample average approximation of the stochastic program.

[1]  Peter Kall,et al.  Stochastic Programming , 1995 .

[2]  André I. Khuri,et al.  Response surface methodology , 2010 .

[3]  Averill Law,et al.  Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management) , 2006 .

[4]  Michael C. Fu,et al.  Handbook of Simulation Optimization , 2014 .

[5]  Tatsiana Levina,et al.  Network Cargo Capacity Management , 2011, Oper. Res..

[6]  Stein W. Wallace,et al.  Decision Making Under Uncertainty: Is Sensitivity Analysis of Any Use? , 2000, Oper. Res..

[7]  Kate A. Smith,et al.  Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research , 1999 .

[8]  Gilbert Laporte,et al.  Stochastic Vehicle Routing Problems , 2009, Encyclopedia of Optimization.

[9]  Zelda B. Zabinsky Stochastic Adaptive Search Methods: Theory and Implementation , 2015 .

[10]  Yoshua Bengio,et al.  Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon , 2018, Eur. J. Oper. Res..

[11]  M. Fu,et al.  An Overview of Stochastic Approximation , 2015 .

[12]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[13]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[14]  Alexander Shapiro,et al.  Lectures on Stochastic Programming - Modeling and Theory, Second Edition , 2014, MOS-SIAM Series on Optimization.

[15]  Katya Scheinberg,et al.  Optimization Methods for Supervised Machine Learning: From Linear Models to Deep Learning , 2017, ArXiv.

[16]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[17]  Teodor Gabriel Crainic,et al.  The load planning problem for double-stack intermodal trains , 2017, Eur. J. Oper. Res..

[18]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[19]  Matteo Fischetti,et al.  On handling indicator constraints in mixed integer programming , 2016, Comput. Optim. Appl..

[20]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[21]  Christiane Barz,et al.  Air Cargo Network Revenue Management , 2016, Transp. Sci..

[22]  A. Shapiro Monte Carlo Sampling Methods , 2003 .

[23]  Yoshua Bengio,et al.  Random Search for Hyper-Parameter Optimization , 2012, J. Mach. Learn. Res..

[24]  Dimitris Bertsimas,et al.  Classification and Regression via Integer Optimization , 2007, Oper. Res..

[25]  Andrea Lodi,et al.  On learning and branching: a survey , 2017 .

[26]  Michel Gendreau,et al.  Stochastic Vehicle Routing Problems , 2014, Vehicle Routing.

[27]  Jiaqiao Hu,et al.  Model-Based Stochastic Search Methods , 2015 .

[28]  Navdeep Jaitly,et al.  Pointer Networks , 2015, NIPS.

[29]  Babak Abbasi,et al.  Predicting solutions of large-scale optimization problems via machine learning: A case study in blood supply chain management , 2020, Comput. Oper. Res..

[30]  Sigrún Andradóttir,et al.  A Review of Random Search Methods , 2015 .

[31]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[32]  Tito Homem-de-Mello,et al.  Monte Carlo sampling-based methods for stochastic optimization , 2014 .

[33]  Iain Dunning,et al.  Learning Fast Optimizers for Contextual Stochastic Integer Programs , 2018, UAI.

[34]  Sriram Sankaranarayanan,et al.  A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs , 2019, CPAIOR.

[35]  R. Pasupathy,et al.  A Guide to Sample Average Approximation , 2015 .

[36]  Marco Fraccaro,et al.  Using OR + AI to Predict the Optimal Production of Offshore Wind Parks: A Preliminary Study , 2017 .

[37]  Oktay Günlük,et al.  Optimal Generalized Decision Trees via Integer Programming , 2016, ArXiv.