Abstract
This work considers the three main optimization variants of the Simple Assembly Line Balancing problem (SALBP): SALBP-1, SALBP-2 and SALBP-E. These problems have origin in typical industrial production processes, where, to obtain a final product, partially ordered operations must be processed in workstations connected by a transportation equipment. Each version determines a different objective to be optimized: SALBP-1 focuses on minimizing the number of workstations while maintaining a certain production rate, SALBP-2 tries to maximize the production rate with a bounded number of workstations, and SALBP-E attempts to maximize the line efficiency. These problems are NP-hard and have been largely studied in the literature, however, the results on their approximability are scarce. This work approaches SALBP-1, SALBP-2 and SALBP-E, proving an equivalence on approximating in polynomial time SALBP-2 and a generalization of SALBP-E, and proposing very efficient polynomial time 2-approximation algorithms for each one of these three versions of SALBP.
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Notes
In the Multiprocessor Scheduling problem, minimizing the completion time may be similar to minimizing the cycle time in SALBP-2, however, the precedence constraints of these problems enforce different conditions, implying that the problems are actually different. In SALBP-2 the precedence constraints prohibit to assign some operations to previous workstations, while in the Multiprocessor Scheduling problem, the precedence constraints obligate tasks to wait for the completion of the others, but the tasks can be scheduled at any processor.
References
Alon N, Azar Y, Woeginger GJ, Yadid T (1998) Approximation schemes for scheduling on parallel machines. J Sched 1(1):55–66. https://doi.org/10.1002/(SICI)1099-1425(199806)1:1<55::AID-JOS2>3.0.CO;2-J
Baybars I (1986) A survey of exact algorithms for the simple assembly line balancing problem. Manag Sci 32(8):900–932. https://doi.org/10.1287/mnsc.32.8.909
Becker C, Scholl A (2006) A survey on problems and methods in generalized assembly line balancing. Eur J Oper Res 168(3):694–715. https://doi.org/10.1016/j.ejor.2004.07.023
Bowman EH (1960) Assembly-line balancing by linear programming. Oper Res 8(3):385–389. https://doi.org/10.1287/opre.8.3.385
Chen JC, Chen YY, Chen TL, Kuo YH (2019) Applying two-phase adaptive genetic algorithm to solve multi-model assembly line balancing problems in tft-lcd module process. J Manuf Syst 52:86–99. https://doi.org/10.1016/j.jmsy.2019.05.009
Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. The MIT Press, Cambridge
Dinh MH, Nguyen VD, Truong VL, Do PT, Phan TT, Nguyen DN (2019) Simulated annealing for the assembly line balancing problem in the garment industry. In: Proceedings of the tenth international symposium on information and communication technology, SoICT 2019. Association for Computing Machinery, New York, pp 36–42. https://doi.org/10.1145/3368926.3369698
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman & Co., New York
Graham RL (1966) Bounds for certain multiprocessing anomalies. Bell Syst Tech J 45(9):1563–1581. https://doi.org/10.1002/j.1538-7305.1966.tb01709.x
Gutjahr AL, Nemhauser GL (1964) An algorithm for the line balancing problem. Manag Sci 11(2):308–315. https://doi.org/10.1287/mnsc.11.2.308
Hazır O, Dolgui A (2015) A decomposition based solution algorithm for U-type assembly line balancing with interval data. Comput Oper Res 59:126–131. https://doi.org/10.1016/j.cor.2015.01.010
Hochbaum DS, Shmoys DB (1987) Using dual approximation algorithms for scheduling problems theoretical and practical results. J ACM 34(1):144–162. https://doi.org/10.1145/7531.7535
Johnson DS, Niemi KA (1983) On knapsacks, partitions, and a new dynamic programming technique for trees. Math Oper Res 8(1):1–14. https://doi.org/10.1287/moor.8.1.1
Kolliopoulos SG, Steiner G (2007) Partially ordered knapsack and applications to scheduling. Discret Appl Math 155(8):889–897. https://doi.org/10.1016/j.dam.2006.08.006
Korte B, Vygen J (2006) Combinatorial optimization: theory and algorithms, chap. Bin-Packing, pp 426–441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29297-7_18
Lai TC, Sotskov YN, Dolgui A (2019) The stability radius of an optimal line balance with maximum efficiency for a simple assembly line. Eur J Oper Res 274(2):466–481. https://doi.org/10.1016/j.ejor.2018.10.013
Li Z, Çil ZA, Mete S, Kucukkoc I (2020) A fast branch, bound and remember algorithm for disassembly line balancing problem. Int J Prod Res 58(11):3220–3234. https://doi.org/10.1080/00207543.2019.1630774
Liu SB, Ng KM, Ong HL (2008) Branch-and-bound algorithms for simple assembly line balancing problem. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-006-0821-y
Lopes TC, Pastre GV, Michels AS, Magatão L (2020) Flexible multi-manned assembly line balancing problem: model, heuristic procedure, and lower bounds for line length minimization. Omega 95:102063. https://doi.org/10.1016/j.omega.2019.04.006
Miranda EA, Pereira J (2019) On the complexity of assembly line balancing problems. Comput Oper Res 108:182–186. https://doi.org/10.1016/j.cor.2019.04.005
Pereira J, Ritt M, Vásquez ÓC (2018) A memetic algorithm for the cost-oriented robotic assembly line balancing problem. Comput Oper Res 99:249–261. https://doi.org/10.1016/j.cor.2018.07.001
Queyranne M (1985) Bounds for assembly line balancing heuristics. Oper Res 33(6):1353–1359. https://doi.org/10.1287/opre.33.6.1353
Queyranne M, Schulz AS (2006) Approximation bounds for a general class of precedence constrained parallel machine scheduling problems. SIAM J Comput 35(5):1241–1253. https://doi.org/10.1137/S0097539799358094
Salehi M, Maleki HR, Niroomand S (2020) Solving a new cost-oriented assembly line balancing problem by classical and hybrid meta-heuristic algorithms. Neural Comput Appl 32(12):8217–8243. https://doi.org/10.1007/s00521-019-04293-8
Scholl A, Klein R (1997) Salome: a bidirectional branch-and-bound procedure for assembly line balancing. INFORMS J Comput 9(4):319–334. https://doi.org/10.1287/ijoc.9.4.319
Schreiber EL, Korf RE, Moffitt MD (2018) Optimal multi-way number partitioning. J ACM. https://doi.org/10.1145/3184400
Wang S, Cui W (2020) Approximation algorithms for the min-max regret identical parallel machine scheduling problem with outsourcing and uncertain processing time. Int J Prod Res. https://doi.org/10.1080/00207543.2020.1766721
Wee T, Magazine M (1982) Assembly line balancing as generalized bin packing. Oper Res Lett 1(2):56–58. https://doi.org/10.1016/0167-6377(82)90046-3
Woeginger GJ (1997) A polynomial-time approximation scheme for maximizing the minimum machine completion time. Oper Res Lett 20(4):149–154. https://doi.org/10.1016/S0167-6377(96)00055-7
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Ravelo, S.V. Approximation algorithms for simple assembly line balancing problems. J Comb Optim 43, 432–443 (2022). https://doi.org/10.1007/s10878-021-00778-2
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DOI: https://doi.org/10.1007/s10878-021-00778-2