A comparison of piecewise linear programming formulations for stochastic disassembly line balancing

Recently, several mathematical programming formulations and solution approaches have been developed for the stochastic disassembly line balancing problem (DLBP). This paper aims at finding optimal solutions for the stochastic DLBP. Two second-order cone programming (SOCP1 and SOCP2) models and five piecewise linear mixed integer programming (PwLP) models are presented. The PwLP formulations involve two specially ordered sets of type 2 (S1 and S2) models and three convex combination (CC1, CC2 and CC3) models. In each modelling category, the latter models strengthen the initial S1 and CC1 models. Our computational analysis of a total 240 instances of ten problems demonstrates that all the seven models can be used to solve practical-sized DLBP problems to optimality using GUROBI. The SOCP2 model and the strengthened S2 and CC2 models lead to lower computation times, compared to SOCP1, S1, CC1 and CC3, respectively. Using the strengthened S2 and CC2 formulations, the CPU times of the CC3 model available in the literature can be reduced by 50 and 40%, respectively. Besides analysing the optimal solutions and the differences of the computation times, we present insights gained from our results.

[1]  Fred N. Silverman,et al.  A Cost-Based Methodology for Stochastic Line Balancing with Intermittent Line Stoppages , 1986 .

[2]  J.-M. Henrioud,et al.  APPLYING EQUAL PILES APPROACH TO DISASSEMBLY LINE BALANCING PROBLEM , 2005 .

[3]  Manfred Padberg,et al.  Location, Scheduling, Design and Integer Programming , 2011, J. Oper. Res. Soc..

[4]  Yixiong Feng,et al.  A new multi-objective ant colony algorithm for solving the disassembly line balancing problem , 2010 .

[5]  Alexandre Dolgui,et al.  Disassembly Line Balancing and Sequencing under Uncertainty , 2014 .

[6]  Alexandre Dolgui,et al.  A decomposition method for stochastic partial disassembly line balancing with profit maximization , 2013, 2013 IEEE International Conference on Automation Science and Engineering (CASE).

[7]  Ugur Özcan,et al.  Balancing stochastic two-sided assembly lines: A chance-constrained, piecewise-linear, mixed integer program and a simulated annealing algorithm , 2010, Eur. J. Oper. Res..

[8]  Surendra M. Gupta,et al.  Combinatorial optimization analysis of the unary NP-complete disassembly line balancing problem , 2007 .

[9]  Ihsan Sabuncuoglu,et al.  Two exact formulations for disassembly line balancing problems with task precedence diagram construction using an AND/OR graph , 2009 .

[10]  Alexandre Dolgui,et al.  A Stochastic Formulation of the Disassembly Line Balancing Problem , 2012, APMS.

[11]  Rajeev Jain,et al.  A Fuzzy AHP and PROMETHEE method-based heuristic for disassembly line balancing problems , 2014 .

[12]  Surendra M. Gupta,et al.  A hybrid genetic algorithm for sequence-dependent disassembly line balancing problem , 2016, Ann. Oper. Res..

[13]  Alexandre Dolgui,et al.  An exact solution approach for disassembly line balancing problem under uncertainty of the task processing times , 2015 .

[14]  Jon Lee,et al.  Polyhedral methods for piecewise-linear functions I: the lambda method , 2001, Discret. Appl. Math..

[15]  Surendra M. Gupta,et al.  Disassembly to order system under uncertainty , 2006 .

[16]  Alexandre Dolgui,et al.  Disassembly Line Balancing Problem with Fixed Number of Workstations under Uncertainty , 2014 .

[17]  Manoj Kumar Tiwari,et al.  A collaborative ant colony algorithm to stochastic mixed-model U-shaped disassembly line balancing and sequencing problem , 2008 .

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

[19]  F. Tevhide Altekin,et al.  A Piecewise Linear Model for Stochastic Disassembly Line Balancing , 2016 .

[20]  F. Tevhide Altekin,et al.  Remedial actions for disassembly lines with stochastic task times , 2016, Comput. Ind. Eng..

[21]  Alexandre Dolgui,et al.  Chance Constrained Programming Model for Stochastic Profit-Oriented Disassembly Line Balancing in the Presence of Hazardous Parts , 2013, APMS.

[22]  C. M. Shetty,et al.  Assembly Line Balancing by Zero-One Integer Programming , 1971 .

[23]  Alysson M. Costa,et al.  A comparison of formulations for the simple assembly line balancing problem , 2011, ArXiv.

[24]  C. L. Moodie,et al.  A HEURISTIC METHOD OF ASSEMBLY LINE BALANCING FOR ASSUMPTIONS OF CONSTANTOR VARIABLE WORK ELEMENT TIMES , 1964 .

[25]  Alexandre Dolgui,et al.  Lagrangian Relaxation for Stochastic Disassembly Line Balancing Problem , 2014 .

[26]  P. Sivasankaran,et al.  Literature review of assembly line balancing problems , 2014 .

[27]  Sencer Yeralan,et al.  A disassembly line balancing problem with fixed number of workstations , 2016, Eur. J. Oper. Res..

[28]  Manfred W. Padberg,et al.  Approximating Separable Nonlinear Functions Via Mixed Zero-One Programs , 1998, Oper. Res. Lett..

[29]  Surendra M. Gupta,et al.  Artificial bee colony algorithm for solving sequence-dependent disassembly line balancing problem , 2013, Expert Syst. Appl..

[30]  Askiner Gungor,et al.  A solution approach to the disassembly line balancing problem in the presence of task failures , 2001 .

[31]  William W. White,et al.  Letter to the Editor---Comments on a Paper by Bowman , 1961 .

[32]  Eren Özceylan,et al.  A solution approach based on beam search algorithm for disassembly line balancing problem , 2016 .

[33]  Surendra M. Gupta,et al.  Ant colony optimization for sequence‐dependent disassembly line balancing problem , 2013 .

[34]  Turan Paksoy,et al.  Mixed model disassembly line balancing problem with fuzzy goals , 2013 .

[35]  James R. Luedtke,et al.  Locally ideal formulations for piecewise linear functions with indicator variables , 2013, Oper. Res. Lett..

[36]  Rajeev Jain,et al.  A Heuristic for U-Shaped Disassembly Line Balancing Problems , 2013 .

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

[38]  Levent Kandiller,et al.  Profit-oriented disassembly-line balancing , 2008 .

[39]  Rafael Pastor,et al.  An improved mathematical program to solve the simple assembly line balancing problem , 2009 .

[40]  Armin Scholl,et al.  A survey on problems and methods in generalized assembly line balancing , 2006, Eur. J. Oper. Res..

[41]  Alexandre Dolgui,et al.  A bibliographic review of production line design and balancing under uncertainty , 2015 .

[42]  Wen-Chyuan Chiang,et al.  Balancing stochastic two-sided assembly lines , 2016 .

[43]  Juan Pablo Vielma,et al.  Mixed Integer Linear Programming Formulation Techniques , 2015, SIAM Rev..

[44]  Hadi Gökçen,et al.  A chance-constrained approach to stochastic line balancing problem , 2007, Eur. J. Oper. Res..

[45]  Alexandre Dolgui,et al.  Dealing with uncertainty in disassembly line design , 2014 .

[46]  Ayyuce Aydemir-Karadag,et al.  Multi-objective optimization of stochastic disassembly line balancing with station paralleling , 2013, Comput. Ind. Eng..

[47]  Alexandre Dolgui,et al.  A sample average approximation method for disassembly line balancing problem under uncertainty , 2014, Comput. Oper. Res..

[48]  James H. Patterson,et al.  Technical Note - Assembly-Line Balancing: Zero-One Programming with Fibonacci Search , 1975, Oper. Res..

[49]  J Figueira,et al.  Stochastic Programming , 1998, J. Oper. Res. Soc..

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

[51]  Surendra M. Gupta,et al.  Ant colony optimization for disassembly sequencing with multiple objectives , 2006 .

[52]  Surendra M. Gupta,et al.  A particle swarm optimization algorithm with neighborhood-based mutation for sequence-dependent disassembly line balancing problem , 2013, The International Journal of Advanced Manufacturing Technology.

[53]  Alfred J.D. Lambert,et al.  Linear programming in disassembly/clustering sequence generation , 1999 .

[54]  Jörgen Winkel,et al.  Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hfm.20078 A Case Study of Serial-Flow Car Disassembly: Ergonomics, Productivity and Potential System Performance , 2022 .

[55]  E. H. Bowman.  Assembly-Line Balancing by Linear Programming , 1960 .

[56]  Wen-Chyuan Chiang,et al.  An optimal piecewise-linear program for the U-line balancing problem with stochastic task times , 2006, Eur. J. Oper. Res..

[57]  Surendra M. Gupta,et al.  A balancing method and genetic algorithm for disassembly line balancing , 2007, Eur. J. Oper. Res..

[58]  Surendra M. Gupta,et al.  Disassembly line in product recovery , 2002 .

[59]  Hon-Shiang Lau,et al.  A Total Operating Cost Model for Paced Lines with Stochastic Task Times , 1976 .

[60]  George L. Nemhauser,et al.  Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions , 2010, Oper. Res..

[61]  Surendra M. Gupta,et al.  A tabu search algorithm for balancing a sequence-dependent disassembly line , 2014 .

[62]  Subhash C. Sarin,et al.  A survey of the assembly line balancing procedures , 1998 .

[63]  Hon-Shiang Lau,et al.  An Exploratory Study on Stopping a Paced Line When Incompletions Occur , 1987 .

[64]  George L. Nemhauser,et al.  Models for representing piecewise linear cost functions , 2004, Oper. Res. Lett..

[65]  Alexandre Dolgui,et al.  Second order conic approximation for disassembly line design with joint probabilistic constraints , 2015, Eur. J. Oper. Res..