Using Column Generation to Solve a Coal Blending Problem

In this paper, we formulate and solve a real life coal blending problem using a Column Generation Approach. The objective of the model is to prescribe optimal mixes of coal to produce coke. The problem is formulated as a mixed integer program. It involves various types of constraints arising from technical considerations of the blending process. The model also incorporates nonlinear constraints. It results in a large-scale problem that cannot be solved by classical operations research methods. Defining three heuristic methods based on column generation techniques, this paper proposes reasonable solutions for the industry.

[1]  J. Dávila,et al.  Efficiency in overlapping generations economies with longevity choices and fair annuities , 2015 .

[2]  D. Peeters,et al.  Is cities delineation a pre requisite for urban modelling? The example of land price determinants in Brussels , 2015 .

[3]  Erik Schokkaert,et al.  Inequality, income and well-being , 2014 .

[4]  J. Gabszewicz,et al.  Social awareness and price competition , 2015 .

[5]  Francis J. Vasko,et al.  Coal blending models for optimum cokemaking and blast furnace operation , 2005, J. Oper. Res. Soc..

[6]  P. D. Jong,et al.  The Financial Impact of ISO 14001 Certification: Top-Line, Bottom-Line, or Both? , 2014 .

[7]  Per J. Agrell,et al.  Brand Equity, Efficiency and Valuation of Professional Sports Franchises: The Case of Major League Baseball , 2015 .

[8]  F. Mayneris,et al.  High-End Variety Exporters Defying Gravity: Micro Facts and Aggregate Implications , 2015 .

[9]  Mathieu Van Vyve,et al.  Securely Solving Classical Network Flow Problems , 2014, ICISC.

[10]  Anthony Papavasiliou,et al.  Congestion management through topological corrections: A case study of Central Western Europe , 2015 .

[11]  H. Paul Williams,et al.  Model solving in mathematical programming , 1993 .

[12]  Laurence A. Wolsey,et al.  Sufficiency of cut-generating functions , 2015, Math. Program..

[13]  Ruhul A. Sarker,et al.  A simple SLP algorithm for solving a class of nonlinear programs , 1997 .

[14]  Marco Di Summa,et al.  A branch-price-and-cut algorithm for the minimum evolution problem , 2015, Eur. J. Oper. Res..

[15]  A. Peichl,et al.  Comparing inequality aversion across countries when labor supply responses differ , 2014, SSRN Electronic Journal.

[16]  M. Lübbecke.  Column Generation , 2010 .

[17]  Laurence A. Wolsey,et al.  An exact algorithm for IP column generation , 1994, Oper. Res. Lett..

[18]  François Vanderbeck,et al.  On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm , 2000, Oper. Res..

[19]  P. Dooren,et al.  Binary factorizations of the matrix of all ones , 2015 .

[20]  Per J. Agrell,et al.  The efficiency of the regulation for horizontal mergers among electricity distribution operators in Norway , 2015, 2015 12th International Conference on the European Energy Market (EEM).

[21]  Véronique Gille.  Distribution of human capital and income: An empirical study on Indian States , 2015 .

[22]  Pierre Pestieau,et al.  Le modèle social européen: performance et équité. Introduction , 2014 .

[23]  A. Paulraj,et al.  Supply chain collaboration and sustainability: a profile deviation analysis , 2014 .

[24]  David A. Kendrick,et al.  GAMS : a user's guide, Release 2.25 , 1992 .

[25]  Dominique Peeters,et al.  Greener and larger neighbourhoods make cities more sustainable! A 2D urban economics perspective , 2015, Comput. Environ. Urban Syst..

[26]  Martine Labbé,et al.  Improved integer linear programming formulations for the job Sequencing and tool Switching Problem , 2015, Eur. J. Oper. Res..

[28]  Daniel De Wolf,et al.  Using column generation to solve an industrial mixing problem , 2003 .

[29]  Anthony Papavasiliou,et al.  Applying High Performance Computing to Transmission-Constrained Stochastic Unit Commitment for Renewable Energy Integration , 2015, IEEE Transactions on Power Systems.

[30]  Anthony Papavasiliou,et al.  Wind farm portfolio optimization under network capacity constraints , 2015, Eur. J. Oper. Res..

[31]  T. Stengos,et al.  Grades, Aspirations and Post-Secondary Education Outcomes , 2012, SSRN Electronic Journal.

[32]  Claude d'Aspremont,et al.  Investissement stratégique et fluctuations endogènes , 2015 .

[33]  Richard C. Larson,et al.  Model Building in Mathematical Programming , 1979 .

[34]  M. Queyranne,et al.  Combinatorial approach to inference in partially identified incomplete structural models , 2015 .

[35]  Yurii Nesterov,et al.  Primal-Dual Methods for Solving Infinite-Dimensional Games , 2015, J. Optim. Theory Appl..

[36]  Yurii Nesterov,et al.  Universal gradient methods for convex optimization problems , 2015, Math. Program..

[37]  Harvey J. Greenberg,et al.  Analyzing the Pooling Problem , 1995, INFORMS J. Comput..

[38]  Yurii Nesterov,et al.  Primal-Dual Subgradient Method for Huge-Scale Linear Conic Problems , 2014, SIAM J. Optim..

[39]  D. Peeters,et al.  On the Morphology of a Growing City: A Heuristic Experiment Merging Static Economics with Dynamic Geography , 2015, PloS one.

[40]  Mohsen Rostamy-Malkhalifeh,et al.  Extended symmetric and asymmetric weight assignment methods in data envelopment analysis , 2015, Comput. Ind. Eng..

[41]  F. Mayneris,et al.  Chinese Firms'Entry to Export Markets: The Role of Foreign Export Spillovers , 2013 .