A branch-and-bound approach to schedule a no-wait flow shop to minimize the CVaR of the residual work content

Abstract The aerospace industry ranks among the largest manufacturing industries in the world facing a significant growing phase as well as an increased competition. This paper addresses the scheduling of a set of jobs in a paced assembly line in presence of uncertainty affecting the availability of production resources, stemming from the assembly process in the aircraft manufacturing industry. The production problem is modeled as a no-wait paced permutation flow shop and solved providing a robust scheduling solution minimizing the conditional value-at-risk (CVaR) of the residual work content, i.e., the amount of workload that cannot be completed during the cycle time in the stations, due to a lack of available resources. A branch-and-bound approach is developed and applied to randomly generated instances as well as to an industrial problem related to the production of aircrafts.

[1]  Hamed Samarghandi,et al.  On the exact solution of the no-wait flow shop problem with due date constraints , 2017, Comput. Oper. Res..

[2]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[3]  Ali Allahverdi,et al.  New heuristics for no-wait flowshops to minimize makespan , 2003, Comput. Oper. Res..

[4]  Jatinder N. D. Gupta,et al.  A Hungarian penalty-based construction algorithm to minimize makespan and total flow time in no-wait flow shops , 2016, Comput. Ind. Eng..

[5]  Ali Allahverdi,et al.  A survey of scheduling problems with no-wait in process , 2016, Eur. J. Oper. Res..

[6]  József Váncza,et al.  A branch-and-bound approach for the single machine maximum lateness stochastic scheduling problem to minimize the value-at-risk , 2018, Flexible Services and Manufacturing Journal.

[7]  Yeong-Dae Kim.  Minimizing total tardiness in permutation flowshops , 1995 .

[8]  Tullio Tolio,et al.  A two-stage stochastic programming project scheduling approach to production planning , 2012 .

[9]  Tullio Tolio,et al.  Robust production control against propagation of disruptions , 2011 .

[10]  Erik Demeulemeester,et al.  Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities , 2008, J. Sched..

[11]  Hanif D. Sherali,et al.  Minimizing conditional-value-at-risk for stochastic scheduling problems , 2014, J. Sched..

[12]  Catherine Roucairol,et al.  Bob++: Framework for Solving Optimization Problems with Branch-and-Bound methods , 2006, 2006 15th IEEE International Conference on High Performance Distributed Computing.

[13]  J. Framiñan,et al.  An efficient heuristic for total flowtime minimisation in no-wait flowshops , 2010 .

[14]  Ömer Kirca,et al.  A branch and bound algorithm to minimize the total tardiness for m , 2006, Eur. J. Oper. Res..

[15]  Inyong Ham,et al.  A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem , 1983 .

[16]  Stanislav Uryasev,et al.  Conditional Value-at-Risk for General Loss Distributions , 2002 .

[17]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[18]  Christian Artigues,et al.  Robust optimization for resource-constrained project scheduling with uncertain activity durations , 2011, Flexible Services and Manufacturing Journal.

[19]  George L. Vairaktarakis,et al.  Flow Shop Scheduling , 2013 .

[20]  Chelliah Sriskandarajah,et al.  A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process , 1996, Oper. Res..

[21]  Tullio Tolio,et al.  A risk management-based evaluation of inventory allocations for make-to-order production , 2013 .

[22]  George L. Vairaktarakis,et al.  Workforce planning in synchronous production systems , 2002, Eur. J. Oper. Res..