A polynomially solvable case of the pooling problem

Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview of known complexity results and remaining open problems to further characterize the border between (strongly) NP-hard and polynomially solvable cases of the pooling problem.

[1]  N. Sahinidis,et al.  Convexification and Global Optimization in Continuous And , 2002 .

[2]  R. Buck.  Partition of Space , 1943 .

[3]  Leon S. Lasdon,et al.  The Evolution of Texaco's Blending Systems: From OMEGA to StarBlend , 1995 .

[4]  Natashia Boland,et al.  New multi-commodity flow formulations for the pooling problem , 2016, J. Glob. Optim..

[5]  Viswanathan Visweswaran,et al.  MINLP: Applications in Blending and Pooling Problems , 2009, Encyclopedia of Optimization.

[6]  Leon S. Lasdon,et al.  OMEGA: An Improved Gasoline Blending System for Texaco , 1989 .

[7]  Mohammed Alfaki,et al.  Strong formulations for the pooling problem , 2013, J. Glob. Optim..

[8]  Aharon Ben-Tal,et al.  Global minimization by reducing the duality gap , 1994, Math. Program..

[9]  Santanu S. Dey,et al.  Analysis of MILP Techniques for the Pooling Problem , 2015, Oper. Res..

[10]  Eligius M. T. Hendrix,et al.  Pooling Problems with Polynomial-Time Algorithms , 2016, J. Optim. Theory Appl..

[11]  Pierre Hansen,et al.  Pooling Problem: Alternate Formulations and Solution Methods , 2000, Manag. Sci..

[12]  Mohammed Alfaki,et al.  A multi-commodity flow formulation for the generalized pooling problem , 2013, J. Glob. Optim..

[13]  Inmaculada García,et al.  Proceedings of the XII Global Optimization Workshop, Mathematical and Applied Global Optimization, MAGO 2014 , 2014 .

[14]  Myun-Seok Cheon,et al.  Relaxations and discretizations for the pooling problem , 2016, Journal of Global Optimization.

[15]  Nikolaos V. Sahinidis,et al.  Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming , 2002 .

[16]  N. Boland,et al.  Discrete flow pooling problems in coal supply chains , 2015 .

[17]  C. A. Haverly.  Studies of the behavior of recursion for the pooling problem , 1978, SMAP.

[18]  Dag Haugland,et al.  The computational complexity of the pooling problem , 2016, J. Glob. Optim..

[19]  M. Savelsbergh,et al.  A special case of the generalized pooling problem arising in the mining industry * , 2014 .

[20]  RigbyBilly,et al.  The Evolution of Texaco's Blending Systems , 1995 .