Abstract
This paper considers a real-world automobile second-tier supplier that manufactures decorative surface finishings of injected parts provided by several suppliers, and which devises its master production schedule by a manual spreadsheet-based procedure. The imprecise production time in this manufacturer’s production process is incorporated into a deterministic mathematical programming model to address this problem by two robust optimization approaches. The proposed model and the corresponding robust solution methodology improve production plans by optimizing the production, inventory and backlogging costs, and demonstrate the their feasibility for a realistic master production schedule problem that outperforms the heuristic decision-making procedure currently being applied in the firm under study.
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References
Alem DJ, Morabito R (2012) Production planning in furniture settings via robust optimization. Comput Oper Res 39:139–150. https://doi.org/10.1016/j.cor.2011.02.022
Aloulou MA, Dolgui A, Kovalyov MY (2014) A bibliography of non-deterministic lot-sizing models. Int J Prod Res 52:2293–2310. https://doi.org/10.1080/00207543.2013.855336
As’ad R, Demirli K, Goyal SK (2015) Coping with uncertainties in production planning through fuzzy mathematical programming: application to steel rolling industry. Int J Oper Res 22:1–30. https://doi.org/10.1504/IJOR.2015.065937
Atamturk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper Res 55:662–673. https://doi.org/10.1287/opre.1070.0428
Aytac B, Wu SD (2013) Characterization of demand for short life-cycle technology products. Ann Oper Res 203:255–277. https://doi.org/10.1007/s10479-010-0771-5
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805. https://doi.org/10.1287/moor.23.4.769
Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424. https://doi.org/10.1007/PL00011380
Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53. https://doi.org/10.1287/opre.1030.0065
Caulkins JJ, Morrison E, Weidemann T (2007) Spreadsheet errors and decision making: evidence from field interviews. J Organ End User Comput 19:1–23
Childerhouse P, Towill DR (2002) Analysis of the factors affecting real-world value stream performance. Int J Prod Res 40:3499–3518. https://doi.org/10.1080/00207540210152885
Chu SCK (1995) A mathematical programming approach towards optimized master production scheduling. Int J Prod Econ 38:269–279. https://doi.org/10.1016/0925-5273(95)00015-G
Conlon JR (1976) Is your master production schedule feasible? Prod Invent Manag 17:56–63
De La Vega J, Munari P, Morabito R (2017) Robust optimization for the vehicle routing problem with multiple deliverymen. Cent Eur J Oper Res. https://doi.org/10.1007/s10100-017-0511-x
Díaz-Madroñero M, Mula J, Jiménez M (2014a) Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions. Int J Prod Res 52:6971–6988. https://doi.org/10.1080/00207543.2014.920115
Díaz-Madroñero M, Mula J, Peidro D (2014b) A review of discrete-time optimization models for tactical production planning. Int J Prod Res 52:5171–5205. https://doi.org/10.1080/00207543.2014.899721
Díaz-Madroñero M, Peidro D, Mula J (2014c) A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain. Appl Math Model 38:5705–5725. https://doi.org/10.1016/j.apm.2014.04.053
Dolgui A, Ben Ammar O, Hnaien F et al (2013) Supply planning and inventory control under lead time uncertainty: a review. Stud Inform Control 22:255–268
Dzuranin AC, Slater RD (2014) Business risks all identified? If you’re using a spreadsheet, think again. J Corp Account Finance 25:25–30. https://doi.org/10.1002/jcaf.21936
Englberger J, Herrmann F, Manitz M (2016) Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment. Int J Prod Res 54:6192–6215. https://doi.org/10.1080/00207543.2016.1162917
Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: an overview. Eur J Oper Res 235:471–483
Gharakhani M, Taghipour T, Farahani KJ (2010) A robust multi-objective production planning. Int J Ind Eng Comput 1:73–78. https://doi.org/10.5267/j.ijiec.2010.01.007
González JJ, Reeves GR (1983) Master production scheduling: a multiple-objective linear programming approach. Int J Prod Res 21:553–562. https://doi.org/10.1080/00207548308942390
Gorissen BL, Yanıkoğlu İ, den Hertog D (2015) A practical guide to robust optimization. Omega 53:124–137. https://doi.org/10.1016/j.omega.2014.12.006
Grubbstrom RW, Tang O (2000) An overview of input-output analysis applied to production-inventory systems. Econ Syst Res 12:3–25. https://doi.org/10.1080/095353100111254
Grubbström RW, Bogataj M, Bogataj L (2010) Optimal lotsizing within MRP theory. Annu Rev Control 34:89–100. https://doi.org/10.1016/J.ARCONTROL.2010.02.004
Haojie Y, Lixin M, Canrong Z (2017) Capacitated lot-sizing problem with one-way substitution: a robust optimization approach. In: In 2017 3rd international conference on information management (ICIM). Institute of Electrical and Electronics Engineers Inc., pp 159–163
Kara G, Özmen A, Weber G-W (2017) Stability advances in robust portfolio optimization under parallelepiped uncertainty. Cent Eur J Oper Res. https://doi.org/10.1007/s10100-017-0508-5
Kawas B, Laumanns M, Pratsini E (2013) A robust optimization approach to enhancing reliability in production planning under non-compliance risks. OR Spectr 35:835–865. https://doi.org/10.1007/s00291-013-0339-2
Kimms A (1998) Stability measures for rolling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing. Omega 26:355–366. https://doi.org/10.1016/S0305-0483(97)00056-X
Ko M, Tiwari A, Mehnen J (2010) A review of soft computing applications in supply chain management. Appl Soft Comput 10:661–674. https://doi.org/10.1016/j.asoc.2009.09.004
Körpeolu E, Yaman H, Selim Aktürk M (2011) A multi-stage stochastic programming approach in master production scheduling. Eur J Oper Res 213:166–179. https://doi.org/10.1016/j.ejor.2011.02.032
Kovačić D, Bogataj M (2013) Reverse logistics facility location using cyclical model of extended MRP theory. Cent Eur J Oper Res 21:41–57. https://doi.org/10.1007/s10100-012-0251-x
Kuchta D (2011) A concept of a robust solution of a multicriterial linear programming problem. Cent Eur J Oper Res 19:605–613. https://doi.org/10.1007/s10100-010-0150-y
Lage Junior M, Godinho Filho M (2017) Master disassembly scheduling in a remanufacturing system with stochastic routings. Cent Eur J Oper Res 25:123–138. https://doi.org/10.1007/s10100-015-0428-1
Lee SM, Moore LJ (1974) Practical approach to production scheduling. Prod Invent Manag J 15:79–92
Lehtimaki AK (1987) Approach for solving decision planning of master scheduling by utilizing theory of fuzzy sets. Int J Prod Res 25:1781–1793
Li Z, Li Z (2015) Optimal robust optimization approximation for chance constrained optimization problem. Comput Chem Eng 74:89–99. https://doi.org/10.1016/j.compchemeng.2015.01.003
Li Z, Ding R, Floudas CA (2011) A Comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization. Ind Eng Chem Res 50:10567–10603. https://doi.org/10.1021/ie200150p
Li Z, Tang Q, Floudas CA (2012) A comparative theoretical and computational study on robust counterpart optimization: II. Probabilistic guarantees on constraint satisfaction. Ind Eng Chem Res 51:6769–6788. https://doi.org/10.1021/ie201651s
Mula J, Poler R, Garcia-Sabater J, Lario F (2006a) Models for production planning under uncertainty: a review. Int J Prod Econ 103:271–285. https://doi.org/10.1016/j.ijpe.2005.09.001
Mula J, Poler R, Garcia JP (2006b) MRP with flexible constraints: a fuzzy mathematical programming approach. Fuzzy Sets Syst 157:74–97. https://doi.org/10.1016/j.fss.2005.05.045
Mula J, Poler R, Garcia-Sabater JP (2008) Capacity and material requirement planning modelling by comparing deterministic and fuzzy models. Int J Prod Res 46:5589–5606. https://doi.org/10.1080/00207540701413912
Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281. https://doi.org/10.1287/opre.43.2.264
Nannapaneni S, Mahadevan S (2014) Uncertainty quantification in performance evaluation of manufacturing processes. In: 2014 IEEE international conference on Big Data (Big Data). IEEE, pp 996–1005
Ng TS, Fowler J (2007) Semiconductor production planning using robust optimization. In: 2007 IEEE international conference on industrial engineering and engineering management. IEEE, pp 1073–1077
Peidro D, Mula J, Poler RR, Lario F-C (2009) Quantitative models for supply chain planning under uncertainty: a review. Int J Adv Manuf Technol 43:400–420. https://doi.org/10.1007/s00170-008-1715-y
Pochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer, Berlin
Powell SG, Baker KR, Lawson B (2008) A critical review of the literature on spreadsheet errors. Decis Support Syst 46:128–138. https://doi.org/10.1016/j.dss.2008.06.001
Rahmani D, Ramezanian R, Fattahi P, Heydari M (2013) A robust optimization model for multi-product two-stage capacitated production planning under uncertainty. Appl Math Model 37:8957–8971. https://doi.org/10.1016/j.apm.2013.04.016
Sahinidis NV (2004) Optimization under uncertainty: state-of-the-art and opportunities. Comput Chem Eng 28:971–983. https://doi.org/10.1016/j.compchemeng.2003.09.017
Sakhaii M, Tavakkoli-Moghaddam R, Bagheri M, Vatani B (2015) A robust optimization approach for an integrated dynamic cellular manufacturing system and production planning with unreliable machines. Appl Math Model 40:169–191. https://doi.org/10.1016/j.apm.2015.05.005
Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157. https://doi.org/10.1287/opre.21.5.1154
Supriyanto I, Noche B (2011) Fuzzy multi-objective linear programming and simulation approach to the development of valid and realistic master production schedule. Logist J. https://doi.org/10.2195/lj_proc_supriyanto_de_201108_01
Tavakkoli-Moghaddam R, Sakhaii M, Vatani B et al (2014) A robust model for a dynamic cellular manufacturing system with production planning. Int J Eng 27:587–598. https://doi.org/10.5829/idosi.ije.2014.27.04a.09
Vargas V, Metters R (2011) A master production scheduling procedure for stochastic demand and rolling planning horizons. Int J Prod Econ 132:296–302. https://doi.org/10.1016/j.ijpe.2011.04.025
Wang J, Shu Y-F (2005) Fuzzy decision modeling for supply chain management. Fuzzy Sets Syst 150:107–127
Weng ZK, Parlar M (2005) Managing build-to-order short life-cycle products: benefits of pre-season price incentives with standardization. J Oper Manag 23:482–495. https://doi.org/10.1016/j.jom.2004.10.008
Werner R (2008) Cascading: an adjusted exchange method for robust conic programming. Cent Eur J Oper Res 16:179–189. https://doi.org/10.1007/s10100-007-0047-6
Yu C-S, Li H-L (2000) A robust optimization model for stochastic logistic problems. Int J Prod Econ 64:385–397. https://doi.org/10.1016/S0925-5273(99)00074-2
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Funding was provided by Horizon 2020 Framework Programme (Grant Agreement No. 636909) in the frame of the “Cloud Collaborative Manufacturing Networks” (C2NET) project.
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Martín, A.G., Díaz-Madroñero, M. & Mula, J. Master production schedule using robust optimization approaches in an automobile second-tier supplier. Cent Eur J Oper Res 28, 143–166 (2020). https://doi.org/10.1007/s10100-019-00607-2
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DOI: https://doi.org/10.1007/s10100-019-00607-2