# The blocking job shop with rail-bound transportation

## Abstract

The blocking job shop with rail-bound transportation (BJS-RT) considered here is a version of the job shop scheduling problem characterized by the absence of buffers and the use of a rail-bound transportation system. The jobs are processed on machines and are transported from one machine to the next by mobile devices (called robots) that move on a single rail. The robots cannot pass each other, must maintain a minimum distance from each other, but can also “move out of the way”. The objective of the BJS-RT is to determine for each machining operation its starting time and for each transport operation its assigned robot and starting time, as well as the trajectory of each robot, in order to minimize the makespan. Building on previous work of the authors on the flexible blocking job shop and an analysis of the feasible trajectory problem, a formulation of the BJS-RT in a disjunctive graph is derived. Based on the framework of job insertion in this graph, a local search heuristic generating consistently feasible neighbor solutions is proposed. Computational results are presented, supporting the value of the approach.

## Keywords

Job shop scheduling Blocking Rail-bound transportation Robots Disjunctive graph Job insertion Tabu search## Notes

### Acknowledgments

We thank an anonymous referee for her or his lucid and constructive remarks which led to several improvements in the exposition of the paper.

## References

- Aron I, Genç-Kaya L, Harjunkoski I, Hoda S, Hooker J (2010) Factory crane scheduling by dynamic programming. In: Wood RK, Dell RF (eds) Operations research, computing and homeland defense (ICS 2011 Proceedings), INFORMS, pp 93–107Google Scholar
- Bilge U, Ulusoy G (1995) A time window approach to simultaneous scheduling of machines and material handling system in an FMS. Oper Res 43(6):1058–1070CrossRefzbMATHGoogle Scholar
- Brizuela CA, Zhao Y, Sannomiya N (2001) No-wait and blocking job-shops:challenging problems for GA’s. In: IEEE international conference on systems, man, and cybernetics, pp 2349–2354Google Scholar
- Brucker P, Knust S (2011) Complex scheduling, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
- Brucker P, Strotmann C (2002) Local search procedures for job-shop problems with identical transport robots. In: Eight international workshop on project management and scheduling, Valencia, SpainGoogle Scholar
- Brucker P, Thiele O (1996) A branch & bound method for the general-shop problem with sequence dependent setup-times. Oper Res Spectr 18(3):145–161MathSciNetCrossRefzbMATHGoogle Scholar
- Brucker P, Heitmann S, Hurink J, Nieberg T (2006) Job-shop scheduling with limited capacity buffers. Oper Res Spectr 28(2):151–176MathSciNetCrossRefzbMATHGoogle Scholar
- Brucker P, Burke EK, Groenemeyer S (2012) A branch and bound algorithm for the cyclic job-shop problem with transportation. Comput Oper Res 39(12):3200–3214MathSciNetCrossRefzbMATHGoogle Scholar
- Bürgy R, Gröflin H (2013) Optimal job insertion in the no-wait job shop. J Comb Optim 26(2):345–371MathSciNetCrossRefzbMATHGoogle Scholar
- Cook WJ, Cunningham WH, Pulleyblank WR, Schrijver A (1997) Combinatorial optimization. Wiley, New YorkCrossRefzbMATHGoogle Scholar
- Deroussi L, Gourgand M, Tchernev N (2008) A simple metaheuristic approach to the simultaneous scheduling of machines and automated guided vehicles. Int J Prod Res 46(8):2143–2164CrossRefzbMATHGoogle Scholar
- Gröflin H, Klinkert A (2007) Feasible insertions in job shop scheduling, short cycles and stable sets. Eur J Oper Res 177(2):763–785CrossRefzbMATHGoogle Scholar
- Gröflin H, Klinkert A (2009) A new neighborhood and tabu search for the blocking job shop. Discret Appl Math 157(17):3643–3655CrossRefzbMATHMathSciNetGoogle Scholar
- Gröflin H, Pham DN, Bürgy R (2011) The flexible blocking job shop with transfer and set-up times. J Comb Optim 22(2):121–144MathSciNetCrossRefzbMATHGoogle Scholar
- Hurink J, Knust S (2005) Tabu search algorithms for job-shop problems with a single transport robot. Eur J Oper Res 162(1):99–111CrossRefzbMATHGoogle Scholar
- Khayat GE, Langevin A, Riopel D (2006) Integrated production and material handling scheduling using mathematical programming and constraint programming. Eur J Oper Res 175(3):1818–1832CrossRefzbMATHGoogle Scholar
- Locomme P, Larabi M, Tchernev N (2010) Job-shop based framework for simultaneous scheduling of machines and automated guided vehicles. Int J Prod Econ 143:24CrossRefGoogle Scholar
- Lawrence S (1984) Supplement to resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques. Carnegie Mellon University, GSIA, PittsburghGoogle Scholar
- Leung JMY, Zhang G (2003) Optimal cyclic scheduling for printed circuit board production lines with multiple hoists and general processing sequence. IEEE Trans Robot Autom 19(3):480–484CrossRefGoogle Scholar
- Leung JMY, Zhang G, Yang X, Mak R, Lam K (2004) Optimal cyclic multi-hoist scheduling: a mixed integer programming approach. Oper Res 52(6):965–976MathSciNetCrossRefzbMATHGoogle Scholar
- Li W, Wu Y, Petering M, Goh M, de Souza R (2009) Discrete time model and algorithms for container yard crane scheduling. Eur J Oper Res 198(1):165–172CrossRefzbMATHGoogle Scholar
- Manier MA, Bloch C (2003) A classification for hoist scheduling problems. Int J Flex Manuf Syst 15(1):37–55CrossRefGoogle Scholar
- Manier MA, Varnier C, Baptiste P (2000) Constraint-based model for the cyclic multi-hoists scheduling problem. Prod Plan Control 11(3):244–257CrossRefGoogle Scholar
- Mascis A, Pacciarelli D (2002) Job-shop scheduling with blocking and no-wait constraints. Eur J Oper Res 143(3):498–517MathSciNetCrossRefzbMATHGoogle Scholar
- Ng W (2005) Crane scheduling in container yards with inter-crane interference. Eur J Oper Res 164(1):64–78CrossRefzbMATHMathSciNetGoogle Scholar
- Nowicki E, Smutnicki C (1996) A fast taboo search algorithm for the job shop problem. Manag Sci 42(6):797–813CrossRefzbMATHGoogle Scholar
- Orlin J (1993) A faster strongly polynomial minimum cost flow algorithm. Oper Res 41(2):338–350MathSciNetCrossRefzbMATHGoogle Scholar
- Vygen J (2002) On dual minimum cost flow algorithms. Math Methods Oper Res 56(1):101–126MathSciNetCrossRefzbMATHGoogle Scholar