Scheduling identical parallel machines with tooling constraints

We model and solve the problem of sequencing a set of jobs with specified processing times and tool requirements on a set of identical parallel machines. Decisions concern the assignment of jobs to machines, their sequencing, and the allocation of tools on each machine. The objective function minimizes the makespan. We propose two mathematical formulations of the problem and an adaptive large neighborhood search metaheuristic in which the destroy and repair operators exploit the structures of two well-known and related combinatorial optimization problems, namely the parallel machine scheduling problem and the job sequencing and tool switching problem on a single machine. Computational experiments conducted on two data sets of 1440 instances show that our algorithm produces excellent results and outperforms existing heuristics.

[1]  G Frizelle,et al.  Minimizing the number of tool switches on a flexible machine: An empirical study , 2001 .

[2]  GILBERT LAPORTE,et al.  Exact algorithms for the job sequencing and tool switching problem , 2002 .

[3]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[4]  Kathryn E. Stecke,et al.  A synthesis of decision models for tool management in automated manufacturing , 1993 .

[5]  Yves Crama,et al.  Combinatorial optimization models for production scheduling in automated manufacturing systems , 1997 .

[6]  Chung-Yee Lee,et al.  Parallel machines scheduling with nonsimultaneous machine available time , 1991, Discret. Appl. Math..

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

[8]  Gianpaolo Ghiani,et al.  Solving the Job Sequencing and Tool Switching Problem as a nonlinear least cost Hamiltonian cycle problem , 2010 .

[9]  Pablo Moscato,et al.  Comparing meta-heuristic approaches for parallel machine scheduling problems , 2002 .

[10]  Arthur Tórgo Gómez,et al.  Modelagem de sistemas de manufatura flexíveis considerando restrições temporais e a capacidade do magazine , 1998 .

[11]  Gabriela P. Henning,et al.  Integrated scheduling of resource-constrained flexible manufacturing systems using constraint programming , 2014, Expert Syst. Appl..

[12]  Lifeng Xi,et al.  A beam-search-based algorithm for the tool switching problem on a flexible machine , 2005 .

[13]  Felix T.S. Chan,et al.  Ant colony optimization approach to a fuzzy goal programming model for a machine tool selection and operation allocation problem in an FMS , 2006 .

[14]  Ji-Bo Wang,et al.  Parallel machines scheduling with simple linear job deterioration and non-simultaneous machine available times , 2014, Comput. Ind. Eng..

[15]  Alain Hertz,et al.  An Improved Tabu Search Approach for Solving the Job Shop Scheduling Problem with Tooling Constraints , 1996, Discret. Appl. Math..

[16]  Chung-Yee Lee,et al.  A note on "parallel machine scheduling with non-simultaneous machine available time" , 2000, Discret. Appl. Math..

[17]  Mostafa Zandieh,et al.  Parallel-machine scheduling problems with sequence-dependent setup times using an ACO, SA and VNS hybrid algorithm , 2009, Expert Syst. Appl..

[18]  Tankut Atan,et al.  Auxiliary tool allocation in flexible manufacturing systems , 1996 .

[19]  Glaydston Mattos Ribeiro,et al.  An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem , 2012, Comput. Oper. Res..

[20]  R. Gary Parker.  Deterministic scheduling theory , 1995 .

[21]  R. Sridharan,et al.  Simulation modelling and analysis of part and tool flow control decisions in a flexible manufacturing system , 2009 .

[22]  Kathryn E. Stecke,et al.  A Branch and Bound Approach for Machine Load Balancing in Flexible Manufacturing Systems , 1986 .

[23]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[24]  Kathryn E. Stecke,et al.  Design, planning, scheduling, and control problems of flexible manufacturing systems , 1985 .

[25]  Chung-Yee Lee,et al.  Multiprocessor scheduling: combining LPT and MULTIFIT , 1988, Discret. Appl. Math..

[26]  David Pisinger,et al.  A general heuristic for vehicle routing problems , 2007, Comput. Oper. Res..

[27]  Horacio Hideki Yanasse,et al.  Um algoritmo enumerativo baseado em ordenamento parcial para resolução do problema de minimização de trocas de ferramentas , 2009 .

[28]  L. J. Zeballos,et al.  A constraint programming approach to tool allocation and production scheduling in flexible manufacturing systems , 2010 .

[29]  David Pisinger,et al.  An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows , 2006, Transp. Sci..

[30]  Kangbok Lee,et al.  The effect of machine availability on the worst-case performance of LPT , 2005, Discret. Appl. Math..

[31]  David Pisinger,et al.  A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times , 2012, Eur. J. Oper. Res..

[32]  Ali Allahverdi,et al.  The third comprehensive survey on scheduling problems with setup times/costs , 2015, Eur. J. Oper. Res..

[33]  Steven A. Melnyk,et al.  Tooling constraints and shop floor scheduling: A simulation study☆ , 1989 .

[34]  Kanchan Das,et al.  Optimization of operation and changeover time for production planning and scheduling in a flexible manufacturing system , 2009, Comput. Ind. Eng..

[35]  S. S. Panwalkar,et al.  A Survey of Scheduling Rules , 1977, Oper. Res..

[36]  Christos Koulamas.  Total tool requirements in multi-level machining systems , 1991 .

[37]  John J. Bernardo,et al.  Tool planning models for flexible manufacturing systems , 1997 .

[38]  K. S. Al-Sultan,et al.  A tabu search based algorithm for minimizing the number of tool switches on a flexible machine , 2003 .

[39]  Edward G. Coffman,et al.  An Application of Bin-Packing to Multiprocessor Scheduling , 1978, SIAM J. Comput..

[40]  Robert H. Storer,et al.  Due date and cost-based FMS loading, scheduling and tool management , 2007 .

[41]  Robert U. Ayres.  Future Trends in Factory Automation , 1987 .

[42]  Frits C. R. Spieksma,et al.  Minimizing the number of tool switches on a flexible machine , 1994 .

[43]  Kari Salonen,et al.  A note on the tool switching problem of a flexible machine , 2006, Comput. Ind. Eng..

[44]  Alessandro Agnetis,et al.  Joint job/tool scheduling in a flexible manufacturing cell with no on-board tool magazine , 1997 .

[45]  노환균,et al.  Due-date based loading and scheduling methods in a flexible manufacturing system with an automatic tool transporter = 공구이송이 가능한 유연제조시스템에서 납기를 고려한 부품과 공구 할당 및 일정 계획에 관한 연구 , 1996 .

[46]  Frits C. R. Spieksma,et al.  Production planning in automated manufacturing , 1994 .

[47]  Luiz Antonio Nogueira Lorena,et al.  Hybrid method with CS and BRKGA applied to the minimization of tool switches problem , 2016, Comput. Oper. Res..

[48]  Andrew W. H. Ip,et al.  A genetic algorithm approach to the multiple machine tool selection problem , 2001, J. Intell. Manuf..

[49]  Kathryn E. Stecke,et al.  Formulation and Solution of Nonlinear Integer Production Planning Problems for Flexible Manufacturing Systems , 1983 .

[50]  Ronald G. Askin,et al.  Heuristic scheduling of parallel machines with sequence-dependent set-up times , 2001 .

[51]  Gerd Finke,et al.  Modelling a tool switching problem on a single NC-machine , 1995, J. Intell. Manuf..

[52]  Carlos Cotta,et al.  Solving the tool switching problem with memetic algorithms , 2011, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[53]  Christos Koulamas,et al.  A modified LPT algorithm for the two uniform parallel machine makespan minimization problem , 2009, Eur. J. Oper. Res..

[54]  Horacio Hideki Yanasse,et al.  Uma nova heurística para o problema de minimização de trocas de ferramentas , 2012 .

[55]  John W. Fowler,et al.  A hybridized genetic algorithm to solve parallel machine scheduling problems with sequence dependent setups , 2003 .

[56]  Nebil Buyurgan,et al.  Tool allocation in flexible manufacturing systems with tool alternatives , 2004 .

[57]  Lionel Amodeo,et al.  A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times , 2006 .

[58]  Peter J. Denning,et al.  Operating Systems Theory , 1973 .

[59]  Nguyen Van Hop,et al.  The scheduling problem of PCBs for multiple non-identical parallel machines , 2004, Eur. J. Oper. Res..

[60]  Teodor Gabriel Crainic,et al.  An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics , 2012, Comput. Oper. Res..

[61]  Denis Borenstein e João Luiz Becker,et al.  Simflex: um avaliador de sistemas flexíveis de manufatura , 1994 .

[62]  Michel Gendreau,et al.  A divide and merge heuristic for the multiprocessor scheduling problem with sequence dependent setup times , 2001, Eur. J. Oper. Res..

[63]  Gilbert Laporte,et al.  An adaptive large neighborhood search heuristic for the Pollution-Routing Problem , 2012, Eur. J. Oper. Res..

[64]  Moshe M. Barash,et al.  Cutting-tool management in computer-integrated manufacturing , 1992 .

[65]  Carlos Cotta,et al.  A Memetic Algorithm for the Tool Switching Problem , 2008, Hybrid Metaheuristics.

[66]  Zhenqiang Yao,et al.  Parallel Machines Scheduling with Sequence-Dependent Setup Times Constraints , 2011 .

[67]  Christopher S. Tang,et al.  Models Arising from a Flexible Manufacturing Machine, Part I: Minimization of the Number of Tool Switches , 1988, Oper. Res..

[68]  Yahya Fathi,et al.  Heuristic procedures for the parallel machine problem with tool switches , 2002 .

[69]  Paul Shaw,et al.  A new local search algorithm providing high quality solutions to vehicle routing problems , 1997 .