Integrated vendor–buyer strategies for imperfect production systems with maintenance and warranty policy
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 435-450.

Collaboration has evolved as a key component of many modern supply chains, supporting the competitive advantages of companies in a range of operations from manufacturing to sales. With this viewpoint, the present paper develops an integrated inventory model in which manufacturing is carried out at the vendor’s end so as to fulfill demand at the buyer’s doorway. As the production process is presumed to be imperfect it shifts from an “in-control” state to “out-of-control” state at any random time and yields non-conforming items. The vendor uses regular preventive maintenance actions for the efficient operation of the production system and offers free minimal repair warranty on the products sold to the buyer. Along with preventive maintenance actions the vendor also uses the rework process and restoration process as effective steps towards minimizing the imperfections of the production system. The proposed model solves the non-linear cost minimization problem through a generalized reduced gradient method by using Lingo 15.0. The aim is to jointly optimize the order size, backorder size and the number of shipments in order to minimize the integrated cost of the vendor and the buyer. Numerical analysis and sensitivity analysis is performed on key parameters that render some important supervisory insights.

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DOI : 10.1051/ro/2019029
Classification : 90B05
Mots-clés : Inventory, imperfect production systems, preventive maintenance, warranty, shortages
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     title = {Integrated vendor{\textendash}buyer strategies for imperfect production systems with maintenance and warranty policy},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Khanna, Aditi; Gautam, Prerna; Sarkar, Biswajit; Jaggi, Chandra K. Integrated vendor–buyer strategies for imperfect production systems with maintenance and warranty policy. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 435-450. doi : 10.1051/ro/2019029. http://archive.numdam.org/articles/10.1051/ro/2019029/

[1] E.L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction. Oper. Res. 34 (1986) 137–144. | DOI | Zbl

[2] M.J. Rosenblatt and H.L. Lee, Economic production cycles with imperfect production processes. IIE Trans. 18 (1986) 48–55. | DOI

[3] C.H. Kim and Y. Hong, An optimal production run length in deteriorating production processes. Int. J. Prod. Econ. 58 (1999) 183–189. | DOI

[4] M. Ben-Daya and M. Hariga, Economic lot scheduling problem with imperfect production processes. J. Oper. Res. Soc. 51 (2000) 875–881. | DOI | Zbl

[5] M.K. Salameh and M.Y. Jaber, Economic production quantity model for items with imperfect quality. Int. J. Prod. Econ. 64 (2000) 59–64. | DOI

[6] C.K. Huang, An integrated vendor–buyer cooperative inventory model for items with imperfect quality. Prod. Plan. Control 13 (2002) 355–361. | DOI

[7] K.J. Chung and K.L. Hou, An optimal production run time with imperfect production processes and allowable shortages. Comput. Oper. Res. 30 (2003) 483–490. | DOI | Zbl

[8] R.H. Yeh, W.T. Ho and S.T. Tseng, Optimal production run length for products sold with warranty. Eur. J. Oper. Res. 120 (2000) 575–582. | DOI | Zbl

[9] M. Ben-Daya and A. Rahim, Optimal lot-sizing, quality improvement and inspection errors for multistage production systems. Int. J. Prod. Res. 41 (2003) 65–79. | DOI | Zbl

[10] C.K. Huang, An optimal policy for a single-vendor single-buyer integrated production–inventory problem with process unreliability consideration. Int. J. Prod. Econ. 91 (2004) 91–98. | DOI

[11] D. Ha and S.L. Kim, Implementation of JIT purchasing: an integrated approach. Prod. Plan. Control 8 (1997) 152–157. | DOI

[12] C.C. Hsieh and Z.Z. Lee, Joint determination of production run length and number of standbys in a deteriorating production process. Eur. J. Oper. Res. 162 (2005) 359–371. | DOI | MR | Zbl

[13] C.K. Chen and C.C. Lo, Optimal production run length for products sold with warranty in an imperfect production system with allowable shortages. Math. Comput. Model. 44 (2006) 319–331. | DOI | MR | Zbl

[14] S.S. Sana, S.K. Goyal and K. Chaudhuri, On a volume flexible inventory model for items with an imperfect production system. Int. J. Oper. Res. 2 (2006) 64–80. | DOI | Zbl

[15] S.S. Sana, S.K. Goyal and K. Chaudhuri, An imperfect production process in a volume flexible inventory model. Int. J. Prod. Econ. 105 (2007) 548–559. | DOI

[16] D. Ojha, B.R. Sarker and P. Biswas, An optimal batch size for an imperfect production system with quality assurance and rework. Int. J. Prod. Res. 45 (2007) 3191–3214. | DOI | Zbl

[17] U. Buscher, S. Rudert and C. Schwarz, A note on: an optimal batch size for an imperfect production system with quality assurance and rework. Int. J. Prod. Res. 47 (2009) 7063–7067. | DOI | Zbl

[18] S.S. Sana, A production–inventory model in an imperfect production process. Eur. J. Oper. Res. 200 (2010) 451–464. | DOI | MR | Zbl

[19] P.A. Hayek and M.K. Salameh, Production lot sizing with the reworking of imperfect quality items produced. Prod. Plan. Control 12 (2001) 584–590. | DOI

[20] Y.P. Chiu, Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging. Eng. Optim. 35 (2003) 427–437. | DOI

[21] S.W. Chiu, D.C. Gong and H.M. Wee, Effects of random defective rate and imperfect rework process on economic production quantity model. Jpn J. Ind. Appl. Math. 21 (2004) 375. | DOI | MR | Zbl

[22] Y.S.P. Chiu, S.W. Chiu and H.C. Chao, Numerical method for determination of reworking or scraping the defective items in a finite production rate model. Int. J. Numer. Methods Biomed. Eng. 22 (2006) 377–386. | Zbl

[23] S.S. Sana, An economic production lot size model in an imperfect production system. Eur. J. Oper. Res. 201 (2010) 158–170. | DOI | Zbl

[24] B. Sarkar, S.S. Sana and K. Chaudhuri, Optimal reliability, production lot size and safety stock in an imperfect production system. Int. J. Math. Oper. Res. 2 (2010) 467–490. | DOI | MR | Zbl

[25] B. Sarkar, S.S. Sana and K. Chaudhuri, An economic production quantity model with stochastic demand in an imperfect production system. Int. J. Serv. Oper. Manage. 9 (2011) 259–283.

[26] O. Dey and B.C. Giri, Optimal vendor investment for reducing defect rate in a vendor–buyer integrated system with imperfect production process. Int. J. Prod. Econ. 155 (2014) 222–228. | DOI

[27] R.R. Inman, S. Bhaskaran and D.E. Blumenfeld, In-plant material buffer sizes for pull system and level-material-shipping environments in the automotive industry. Int. J. Prod. Res. 35 (1997) 1213–1228. | DOI | Zbl

[28] V.S. Kouikoglou and Y.A. Phillis, A continuous-flow model for production networks with finite buffers, unreliable machines, and multiple products. Int. J. Prod. Res. 35 (1997) 381–397. | DOI | Zbl

[29] Y. Dallery, An improved decomposition method for the analysis of production lines with unreliable machines and finite buffers. Int. J. Prod. Res. 37 (1999) 1093–1117. | DOI | Zbl

[30] E. Enginarlar, J. Li, S.M. Meerkov and R.Q. Zhang, Buffer capacity for accommodating machine downtime in serial production lines. Int. J. Prod. Res. 40 (2002) 601–624. | DOI | Zbl

[31] J. Miltenburg, The effect of breakdowns on U-shaped production lines. Int. J. Prod. Res. 38 (2000) 353–364. | DOI | Zbl

[32] M.K. Salameh and R.E. Ghattas, Optimal just-in-time buffer inventory for regular preventive maintenance. Int. J. Prod. Econ. 74 (2001) 157–161. | DOI

[33] R.I. Zequeira, B. Prida and J.E. Valdés, Optimal buffer inventory and preventive maintenance for an imperfect production process. Int. J. Prod. Res. 42 (2004) 959–974. | DOI

[34] T. Chakraborty and B.C. Giri, Lot sizing in a deteriorating production system under inspections, imperfect maintenance and reworks. Oper. Res. 14 (2014) 29–50.

[35] S.S. Sana and K. Chaudhuri, An EMQ model in an imperfect production process. Int. J. Syst. Sci. 41 (2010) 635–646. | DOI | MR | Zbl

[36] S.S. Sana, Preventive maintenance and optimal buffer inventory for products sold with warranty in an imperfect production system. Int. J. Prod. Res. 50 (2012) 6763–6774. | DOI

[37] T. Nakagawa, A summary of imperfect preventive maintenance policies with minimal repair. RAIRO-Oper. Res. 14 (1980) 249–255. | DOI | Numdam | MR | Zbl

[38] C. Jiao and X. Zhu, Optimal design of sales and maintenance under the renewable warranty. RAIRO-Oper. Res. 52 (2018) 529–542. | DOI | Numdam | MR

[39] G.Q. Cheng, B.H. Zhou and L. Li, Integrated production, quality control and condition-based maintenance for imperfect production systems. Reliab. Eng. Syst. Saf. 175 (2018) 251–264. | DOI

[40] S.K. Goyal, An integrated inventory model for a single supplier-single customer problem. Int. J. Prod. Res. 15 (1977) 107–111. | DOI

[41] A. Banerjee, A joint economic lot size model for purchaser and vendor. Decis. Sci. 17 (1986) 292–311. | DOI

[42] S.K. Goyal, “A joint economic lot size model for purchaser and vendor”: a comment. Decis. Sci. 19 (1988) 236–241. | DOI

[43] S.K. Goyal and Y.P. Gupta, Integrated inventory models: the buyer–vendor coordination. Eur. J. Oper. Res. 41 (1989) 261–269. | DOI

[44] S.K. Goyal and F. Nebebe, Determination of economic production–shipment policy for a single-vendor-single-buyer system. Eur. J. Oper. Res. 121 (2000) 175–178. | DOI | Zbl

[45] S.K. Goyal, A one-vendor multi-buyer integrated inventory model: a comment’.’. Eur. J. Oper. Res. 82 (1995) 209–210. | DOI | Zbl

[46] R.M. Hill, The single-vendor single-buyer integrated production-inventory model with a generalised policy. Eur. J. Oper. Res. 97 (1997) 493–499. | DOI | Zbl

[47] K.S. Wu and L.Y. Ouyang, An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Prod. Plan. Control 14 (2003) 555–561. | DOI

[48] A. Banerjee, A joint economic-lot-size model for purchaser and vendor. Decis. Sci. 17 (1986) 292–311. | DOI

[49] A. Banerjee and S.L. Kim, An integrated JIT inventory model. Int. J. Oper. Prod. Manage. 15 (1995) 237–244. | DOI

[50] K.J. Chung, An improvement of an integrated single-vendor single-buyer inventory model with shortage. Prod. Plan. Control 19 (2008) 275–277. | DOI

[51] J.T. Hsu and L.F. Hsu, An integrated vendor–buyer cooperative inventory model in an imperfect production process with shortage backordering. Int. J. Prod. Adv. Manuf. Technol. 65 (2013) 493–505. | DOI

[52] H.M. Wee and G.A. Widyadana, Single-vendor single-buyer inventory model with discrete delivery order, random machine unavailability time and lost sales. Int. J. Prod. Econ. 143 (2013) 574–579. | DOI

[53] G. Treviño-Garza, K.K. Castillo-Villar and L.E. Cárdenas-Barrón, Joint determination of the lot size and number of shipments for a family of integrated vendor–buyer systems considering defective products. Int. J. Syst. Sci. 46 (2015) 1705–1716. | DOI | Zbl

[54] A.H. Nobil, L.E. Cárdenas-Barrón and E. Nobil, Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage. RAIRO-Oper. Res. 52 (2018) 755–778. | DOI | Numdam | MR | Zbl

[55] D.J. Mohanty, R.S. Kumar and A. Goswami, Vendor-buyer integrated production-inventory system for imperfect quality item under trade credit finance and variable setup cost. RAIRO-Oper. Res. 52 (2018) 1277–1293. | DOI | Numdam | MR | Zbl

[56] M.M. Sher, S.L. Kim, A. Banerjee and M.T. Paz, A supply chain coordination mechanism for common items subject to failure in the electronics, defense, and medical industries. Int. J. Prod. Econ. 203 (2018) 164–173. | DOI

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