Assembly line balancing under uncertainty: Robust optimization models and exact solution method

This research deals with line balancing under uncertainty and presents two robust optimization models. Interval uncertainty for operation times was assumed. The methods proposed generate line designs that are protected against this type of disruptions. A decomposition based algorithm was developed and combined with enhancement strategies to solve optimally large scale instances. The efficiency of this algorithm was tested and the experimental results were presented. The theoretical contribution of this paper lies in the novel models proposed and the decomposition based exact algorithm developed. Moreover, it is of practical interest since the production rate of the assembly lines designed with our algorithm will be more reliable as uncertainty is incorporated. Furthermore, this is a pioneering work on robust assembly line balancing and should serve as the basis for a decision support system on this subject.

[1]  S. S. Erenguc,et al.  Solving time/cost trade‐off problems with discounted cash flows using generalized benders decomposition , 1993 .

[2]  Ram Rachamadugu,et al.  Designing paced assembly lines with fixed number of stations , 1997 .

[3]  Nils Boysen,et al.  A classification of assembly line balancing problems , 2007, Eur. J. Oper. Res..

[4]  Bilal Toklu,et al.  Balancing of mixed-model two-sided assembly lines , 2009, Comput. Ind. Eng..

[5]  Alexandre Dolgui,et al.  Scenario based robust line balancing: Computational complexity , 2012, Discret. Appl. Math..

[6]  Ana S. Simaria,et al.  A genetic algorithm based approach to the mixed-model assembly line balancing problem of type II , 2004, Comput. Ind. Eng..

[7]  Jeonghan Ko,et al.  Robust manufacturing line design with controlled moderate robustness in bottleneck buffer time to manage stochastic inter-task times , 2013 .

[8]  Hadi Gökçen,et al.  A goal programming approach to simple U-line balancing problem , 2006, Eur. J. Oper. Res..

[9]  Alexandre Dolgui,et al.  Stability measure for a generalized assembly line balancing problem , 2013, Discret. Appl. Math..

[10]  Armin Scholl,et al.  State-of-the-art exact and heuristic solution procedures for simple assembly line balancing , 2006, Eur. J. Oper. Res..

[11]  John Miltenburg,et al.  The stochastic U‐line balancing problem , 2003 .

[12]  Mohamed Haouari,et al.  Discrete time/cost trade-off problem: A decomposition-based solution algorithm for the budget version , 2010, Comput. Oper. Res..

[13]  Alysson M. Costa.  A survey on benders decomposition applied to fixed-charge network design problems , 2005, Comput. Oper. Res..

[14]  Armin Scholl,et al.  Balancing and Sequencing of Assembly Lines , 1995 .

[15]  Alexandre Dolgui,et al.  Robust balancing of straight assembly lines with interval task times , 2013, J. Oper. Res. Soc..

[16]  Armin Scholl,et al.  Maximizing the production rate in simple assembly line balancing -- A branch and bound procedure , 1996 .

[17]  Alexandre Dolgui,et al.  A taxonomy of line balancing problems and their solutionapproaches , 2013 .

[18]  I. Sabuncuoglu,et al.  Stochastic assembly line balancing using beam search , 2005 .

[19]  Melvyn Sim,et al.  Robust discrete optimization and network flows , 2003, Math. Program..

[20]  Nils Boysen,et al.  Assembly line balancing: Which model to use when? , 2006 .

[21]  Brahim Rekiek,et al.  State of art of optimization methods for assembly line design , 2002, Annu. Rev. Control..

[22]  Fulya Altiparmak,et al.  Multi-objective optimization of a stochastic assembly line balancing: A hybrid simulated annealing algorithm , 2011, Comput. Ind. Eng..

[23]  Alexandre Dolgui,et al.  Enhanced mixed integer programming model for a transfer line design problem , 2012, Comput. Ind. Eng..

[24]  Alexandre Dolgui,et al.  Stability analysis of an optimal balance for an assembly line with fixed cycle time , 2006, Eur. J. Oper. Res..

[25]  Wen-Chyuan Chiang,et al.  The stochastic U-line balancing problem: A heuristic procedure , 2006, Eur. J. Oper. Res..

[26]  Roberto Montemanni,et al.  A branch and bound algorithm for the robust spanning tree problem with interval data , 2002, Eur. J. Oper. Res..

[27]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[28]  Turan Paksoy,et al.  Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing , 2009, Eur. J. Oper. Res..

[29]  A. Sprecher.  A competitive branch-and-bound algorithm for the simple assembly line balancing problem , 1999 .

[30]  Mitsuo Gen,et al.  Fuzzy assembly line balancing using genetic algorithms , 1996 .

[31]  Erdal Erel,et al.  Robust optimization models for the discrete time/cost trade-off problem , 2011 .

[32]  Nai-Chieh Wei,et al.  A solution procedure for type E simple assembly line balancing problem , 2011, Comput. Ind. Eng..

[33]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[34]  S.M.J. Mirzapour Al-e-hashem,et al.  Mixed model assembly line balancing problem under uncertainty , 2009, 2009 International Conference on Computers & Industrial Engineering.

[35]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..