# New formulations for the setup assembly line balancing and scheduling problem

- 362 Downloads
- 1 Citations

## Abstract

We present three new formulations for the setup assembly line balancing and scheduling problem (SUALBSP). Unlike the simple assembly line balancing problem, sequence-dependent setup times are considered between the tasks in the SUALBSP. These setup times may significantly influence the station times. Thus, there is a need for scheduling the list of tasks within each station so as to optimize the overall performance of the assembly line. In this study, we first scrutinize the previous formulation of the problem, which is a *station-based* model. Then, three new formulations are developed by the use of new sets of decision variables. In one of these formulations, the *schedule-based* formulation, SUALBSP is completely formulated as a scheduling problem. That is, no decision variable in the model directly denotes a station. All the proposed formulations will be improved by the use of several enhancement techniques such as preprocessing and valid inequalities. These improved formulations can be applied to establishing lower bounds on the problem. To assess the performance of new formulations, results of an extensive computational study on the benchmark data sets are also reported.

## Keywords

Setup assembly line balancing and scheduling problem Mathematical formulation## References

- Andrés C, Miralles C, Pastor R (2008) Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. Eur J Oper Res 187(3):1212–1223CrossRefGoogle Scholar
- Battaïa O, Dolgui A (2013) A taxonomy of line balancing problems and their solutionapproaches. Int J Prod Econ 142(2):259–277 (anticipation of risks impacts and industrial performance evaluation in distributed organizations life cycles)Google Scholar
- Baybars İ (1986) A survey of exact algorithms for the simple assembly line balancing problem. Manag Sci 32(8):909–932CrossRefGoogle Scholar
- Becker C, Scholl A (2009) Balancing assembly lines with variable parallel workplaces: problem definition and effective solution procedure. Eur J Oper Res 199(2):359–374CrossRefGoogle Scholar
- Bowman EH (1960) Assembly-line balancing by linear programming. Oper Res 8(3):385–389CrossRefGoogle Scholar
- Dolgui A, Kovalev S, Kovalyov MY, Nossack J, Pesch E (2014) Minimizing setup costs in a transfer line design problem with sequential operation processing. Int J Prod Econ 151:186–194CrossRefGoogle Scholar
- Erel E, Sarin SC (1998) A survey of the assembly line balancing procedures. Prod Plan Control 9(5):414–434CrossRefGoogle Scholar
- Esmaeilbeigi R, Charkhgard P, Charkhgard H (2015a) Order acceptance and scheduling problems in two-machine flow shops: new mixed integer programming formulations. Eur J Oper Res 000:1–13. doi: 10.1016/j.ejor.2015.11.036
- Esmaeilbeigi R, Naderi B, Charkhgard P (2015b) The type e simple assembly line balancing problem: a mixed integer linear programming formulation. Comput Oper Res 64:168–177CrossRefGoogle Scholar
- Kucukkoc I, Zhang DZ (2015) Balancing of parallel u-shaped assembly lines. Comput Oper Res 64:233–244CrossRefGoogle Scholar
- Martino L, Pastor R (2010) Heuristic procedures for solving the general assembly line balancing problem with setups. Int J Prod Res 48(6):1787–1804CrossRefGoogle Scholar
- Pape T (2015) Heuristics and lower bounds for the simple assembly line balancing problem type 1: overview, computational tests and improvements. Eur J Oper Res 240(1):32–42CrossRefGoogle Scholar
- Pastor R, Ferrer L (2009) An improved mathematical program to solve the simple assembly line balancing problem. Int J Prod Res 47(11):2943–2959CrossRefGoogle Scholar
- Patterson JH, Albracht JJ (1975) Technical noteassembly-line balancing: Zero-one programming with fibonacci search. Oper Res 23(1):166–172CrossRefGoogle Scholar
- Scholl A, Boysen N, Fliedner M (2008) The sequence-dependent assembly line balancing problem. OR Spectr 30(3):579–609CrossRefGoogle Scholar
- Scholl A, Boysen N, Fliedner M (2013) The assembly line balancing and scheduling problem with sequence-dependent setup times: problem extension, model formulation and efficient heuristics. OR Spectr 35(1):291–320CrossRefGoogle Scholar
- Scholl A, Fliedner M, Boysen N (2010) Absalom: Balancing assembly lines with assignment restrictions. Eur J Oper Res 200(3):688–701CrossRefGoogle Scholar
- Sewell EC, Jacobson SH (2012) A branch, bound, and remember algorithm for the simple assembly line balancing problem. INFORMS J Comput 24(3):433–442CrossRefGoogle Scholar
- White WW (1961) Letter to the editorcomments on a paper by bowman. Oper Res 9(2):274–276CrossRefGoogle Scholar
- Yolmeh A, Kianfar F (2012) An efficient hybrid genetic algorithm to solve assembly line balancing problem with sequence-dependent setup times. Comput Ind Eng 62(4):936–945CrossRefGoogle Scholar