Improved integer linear programming formulations for the job Sequencing and tool Switching Problem

In this article we investigate the job Sequencing and tool Switching Problem (SSP), a NP-hard combinatorial optimization problem arising from computer and manufacturing systems. Starting from the results described in Tang and Denardo (1987), Crama et al. (1994) and Laporte et al. (2004), we develop new integer linear programming formulations for the problem that are provably better than the alternative ones currently described in the literature. Computational experiments show that the lower bounds obtained by the linear relaxation of the considered formulations improve, on average, upon those currently described in the literature and suggest, at the same time, new directions for the development of future exact solution approaches.

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

[2]  Laszlo A. Belady,et al.  A Study of Replacement Algorithms for Virtual-Storage Computer , 1966, IBM Syst. J..

[3]  Gerd Finke,et al.  k-server problems with bulk requests: an application to tool switching in manufacturing , 2000, Ann. Oper. Res..

[4]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

[5]  Gerd Finke,et al.  Scheduling with resource management in manufacturing systems , 1994 .

[6]  Frits C. R. Spieksma,et al.  The tool switching problem revisited , 2007, Eur. J. Oper. Res..

[7]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[9]  M. Selim Akturk,et al.  Tool magazine arrangement and operations sequencing on CNC machines , 1996, Comput. Oper. Res..

[10]  Lyle A. McGeoch,et al.  A strongly competitive randomized paging algorithm , 1991, Algorithmica.

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

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

[13]  J. Bard.  A Heuristic for Minimizing the Number of Tool Switches on a Flexible Machine , 1988 .

[14]  Nagraj Balakrishnan,et al.  Opportunistic retooling of a flexible machine subject to failure , 2001 .

[15]  N. Biggs.  THE TRAVELING SALESMAN PROBLEM A Guided Tour of Combinatorial Optimization , 1986 .

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

[17]  G. Laporte,et al.  Heuristics for minimizing tool switches when scheduling part types on a flexible machine , 1998 .

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

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

[20]  Manbir S. Sodhi,et al.  Multiperiod tool and production assignment in flexible manufacturing systems , 1994 .