Additive manufacturing (AM) is a candidate to be one of the future general-purpose technologies. AM is called with 3D printing, Rapid Prototyping, Direct Digital Manufacturing, layered manufacturing, and/or additive manufacturing. Today, AM is a tool for producing customized small products with small lot sizes. Tomorrow, it will be possible for AM to enter every home and to be used for general purposes. The literature about AM has focused mainly on the technology to decrease the cost of AM, to increase the speed of AM machines, and to increase the common availability of those machines. There are so few papers investigating AM machines in view of scheduling problems. This paper considers a single AM machine that produces multiple parts in batches and then these parts are assembled to produce desired goods. Most AM machines have limitations because of the area of the machine tray and the height of the machine. Therefore, products are separated into small parts considering the area and height of the machine. Then, these separated small parts are assembled to produce the desired goods. In view of scheduling problems, the proposed problem includes single machine batch scheduling and assembly operations. In this paper, we propose a mixed-integer programming (MIP) model and a fast heuristic method with a simple local search mechanism for the problem. We investigate two cases for the same problem. In the first, we consider only the one-dimensional assignment of parts to baches and we just design our solution approaches to assign parts to the batch, if the total area of parts is less than or equal to the machine tray's area. In the second, we modify our solution approaches to consider parts' lengths and widths while assigning parts to batches in a 2D assignment. In the end, we compare the proposed heuristic with the proposed MIP by using some test problems within time limits for all cases. Experimental results show that the proposed heuristic provides promising results.
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Achillas C, Aidonis D, Iakovou E et al (2015) A methodological framework for the inclusion of modern additive manufacturing into the production portfolio of a focused factory. J Manuf Syst 37:328–339. https://doi.org/10.1016/j.jmsy.2014.07.014
Chergui A, Hadj-Hamou K, Vignat F (2018) Production scheduling and nesting in additive manufacturing. Comput Ind Eng 126:292–301. https://doi.org/10.1016/j.cie.2018.09.048
Dvorak F, Micali M, Mathieu M (2018) Planning and scheduling in additive manufacturing. Intel Artif 21:40–52. https://doi.org/10.4114/intartif.vol21iss62pp40-52
Fera M, Fruggiero F, Lambiase A et al (2018) A modified genetic algorithm for time and cost optimization of an additive manufacturing single-machine scheduling. Int J Ind Eng Comput 9:423–438. https://doi.org/10.5267/j.ijiec.2018.1.001
Kovalyov MY, Potts CN, Strusevich VA (2004) Batching decisions for assembly production systems. Eur J Oper Res 157:620–642. https://doi.org/10.1016/S0377-2217(03)00250-9
Kucukkoc I (2019) MILP models to minimise makespan in additive manufacturing machine scheduling problems. Comput Oper Res 105:58–67. https://doi.org/10.1016/j.cor.2019.01.006
Kucukkoc I, Li Q, He N, Zhang DZ (2018) Scheduling of multiple additive manufacturing and 3D printing machines to minimise maximum lateness. Twent Int Work Semin Prod Econ 1:237–247
Li Q, Kucukkoc I, Zhang DZ (2015) No title. Prod Plan Addit Manuf 3D Print (Dataset), ORE-Repository
Li Q, Kucukkoc I, Zhang DZ (2017) Production planning in additive manufacturing and 3D printing. Comput Oper Res 83:157–172. https://doi.org/10.1016/j.cor.2017.01.013
Li Q, Kucukkoc I, He N et al (2018) Order acceptance and scheduling in metal additive manufacturing: an optimal foraging approach. Twent Int Work Semin Prod Econ 1:1–11
Li Q, Zhang D, Wang S, Kucukkoc I (2019) A dynamic order acceptance and scheduling approach for additive manufacturing on-demand production. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-019-03796-x
Li X, Zhang K (2018) Single batch processing machine scheduling with two-dimensional bin packing constraints. Int J Prod Econ 196:113–121. https://doi.org/10.1016/j.ijpe.2017.11.015
Liao C-J, Lee C-H, Lee H-C (2015) An efficient heuristic for a two-stage assembly scheduling problem with batch setup times to minimize makespan. Comput Ind Eng 88:317–325. https://doi.org/10.1016/j.cie.2015.07.018
Lin BMT, Cheng TCE (2002) Fabrication and assembly scheduling in a two-machine flowshop. IIE Trans 34:1015–1020. https://doi.org/10.1023/A:1016190815843
Lin BMT, Cheng TCE, Chou ASC (2006) Scheduling in an assembly-type production chain with batch transfer. Omega 35:143–151. https://doi.org/10.1016/j.omega.2005.04.004
Loukil T, Teghem J, Fortemps P (2007) A multi-objective production scheduling case study solved by simulated annealing. Eur J Oper Res 179:709–722. https://doi.org/10.1016/j.ejor.2005.03.073
Luzon Y, Khmelnitsky E (2019) Job sizing and sequencing in additive manufacturing to control process deterioration. IISE Trans 51:181–191. https://doi.org/10.1080/24725854.2018.1460518
Martello S, Toth P (1990) Lower bounds and reduction procedures for the bin packing problem. Discret Appl Math 28:59–70. https://doi.org/10.1016/0166-218X(90)90094-S
Oh Y, Zhou C, Behdad S (2018) Production planning for mass customization in additive manufacturing: Build orientation determination, 2D packing and scheduling. In: Proceedings of the ASME design engineering technical conference
Ransikarbum K, Ha S, Ma J, Kim N (2017) Multi-objective optimization analysis for part-to-Printer assignment in a network of 3D fused deposition modeling. J Manuf Syst 43:35–46. https://doi.org/10.1016/j.jmsy.2017.02.012
Rudolph J-P, Emmelmann C (2017) A cloud-based platform for automated order processing in additive manufacturing. In: Procedia CIRP, pp 412–417
Tajbakhsh Z, Fattahi P, Behnamian J (2014) Multi-objective assembly permutation flow shop scheduling problem: a mathematical model and a meta-heuristic algorithm. J Oper Res Soc 65:1580–1592. https://doi.org/10.1057/jors.2013.105
Zhang J, Yao X, Li Y (2019) Improved evolutionary algorithm for parallel batch processing machine scheduling in additive manufacturing. Int J Prod Res. https://doi.org/10.1080/00207543.2019.1617447
Zhou L, Zhang L, Laili Y et al (2018) Multi-task scheduling of distributed 3D printing services in cloud manufacturing. Int J Adv Manuf Technol 96:3003–3017. https://doi.org/10.1007/s00170-017-1543-z
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Arık , O.A. Additive manufacturing scheduling problem considering assembly operations of parts. Oper Res Int J (2021). https://doi.org/10.1007/s12351-021-00649-y
- Additive manufacturing
- 3D printing
Mathematics Subject Classification