Fuzzy supply chain coordination mechanism with imperfect quality items
Abstract
We study the supply chain (SC) returning strategy and quantity discount coordination under the condition of product quality defects. We assume that the demand is a triangular fuzzy number (TFN), considering the SC coordination problem consisting of a manufacturer and a retailer. The decentralized SC coordination model and the integrated SC coordination model under a fuzzy environment are established respectively. The fuzzy set theory is used to study the manufacturer’s quantity discount and the retailer’s coordination of return policy. The signed distance is used as the ranking method to find the optimal order quantity in SC, and the optimization theory is used to maximize the participants’ profits. We first demonstrate that the retailer’s profit will be reduced in a typical integrated channel, and then we propose a quantitative discount return policy to coordinate the profits of the manufacturer and the retailer. Finally, the coordination steps are designed, and the manufacturer’s return policy is given. Meanwhile, some illustrative cases are provided to illustrate the feasibility of the proposed model.
Keyword : supply chain, uncertain demand, imperfect quality, return policy, quantity discounts, coordination mechanism, signed distance, fuzzy set theory
How to Cite
Liu, S., Gao, J., & Xu, Z. (2019). Fuzzy supply chain coordination mechanism with imperfect quality items. Technological and Economic Development of Economy, 25(2), 239-257. https://doi.org/10.3846/tede.2019.6620
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Cachon, G. P. (2003). Supply chain coordination with contracts. In S. Graves, & T. de Kok (Eds.), Handbooks in operations research and management science: Supply chain management (Chapter 11). North Holland, Amsterdam. https://doi.org/10.1016/S0927-0507(03)11006-7
Cachon, G. P., & Lariviere, M. A. (2000). Supply chain coordination with revenue sharing contracts: Strengths and limitation (Working Paper). The Wharton School of Business, University of Pennsylvania, Philadelphia.
Chang, H. C. (2004). An application of fuzzy sets theory to the EOQ model with imperfect quality items. Computer & Operations Research, 31(12), 2079-2092. https://doi.org/10.1016/S0305-0548(03)00166-7
Chen, L. H., & Kang, F. S. (2010). Coordination between vendor and buyer considering trade credit and items of imperfect quality. International Journal Production Economics, 123(1), 52-61. https://doi.org/10.1016/j.ijpe.2009.06.043
Chen, S. H., Wang, C. C., & Chang, S. M. (2007). Fuzzy economic production quantity model for items with imperfect quality. International Journal of Innovative computing, Information and Control, 3(1), 85-95.
Chen, S. P., & Ho, Y. H. (2011). Analysis of the newsboy problem with fuzzy demands and incremental discounts. International Journal Production Economics, 129(1), 169-177. https://doi.org/10.1016/j.ijpe.2010.09.014
Chung, K. J., Her, C. C., & Lin, S. D. (2009). A two-warehouse inventory model with imperfect quality production processes. Computer & Industrial Engineering, 56(1), 193-197. https://doi.org/10.1016/j.cie.2008.05.005
Das, P., De, S. K., & Sana, S. S. (2015). An EOQ model for time dependent backlogging over idle time: A step order fuzzy approach. International Journal of Applied and Computational Mathematics, 1(2), 171-185. https://doi.org/10.1007/s40819-014-0001-y
De, S. K., & Sana, S. S. (2015). An alternative fuzzy EOQ model with backlogging for selling price and promotional effort sensitive demand. International Journal of Applied and Computational Mathematics, 1(1), 69-86.
Dolan, R. J. (1987). Quamtity discounts: Managerial issues and research opportunities. Marketing Science, 6(1), 1-27. https://doi.org/10.1287/mksc.6.1.1
Dubois, D., & Prade, H. (1987). The mean value of a fuzzy number. Fuzzy Sets and Systems, 24(3), 279-300. https://doi.org/10.1016/0165-0114(87)90028-5
Emmons, H., & Gibert, S. M. (1998). Note. The role of returns policies in pricing and inventory decisions for catalogue goods. Management Science, 44(2), 276-283. https://doi.org/10.1287/mnsc.44.2.276
Hsu, J. T., & Hsu, L. F. (2013). An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns. International Journal of Production Economics, 143(1), 162-170. https://doi.org/10.1016/j.ijpe.2012.12.025
Hsu, J., & Hsu, L. (2014). A supplement to an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales return. International Journal of Industrial Engineering Computations, 5(2), 199-210. https://doi.org/10.5267/j.ijiec.2014.2.001
Hu, J. S., Zheng, H., Guo, C. Y., & Ji, Y. P. (2010). Optimal production run length with imperfect production processes and backorder in fuzzy random environment. Computer & Industrial Engineering, 59(1), 9-15. https://doi.org/10.1016/j.cie.2010.01.012
Jaber, M. Y., Goyal, S. K., & Imran, M. (2008). Economic production quantity model for items with imperfect quality subject to learning effects. International Journal Production Economics, 115(1), 143-150. https://doi.org/10.1016/j.ijpe.2008.05.007
Kao, C., & Hsu, W. K. (2002). A single period inventory model with fuzzy demand. Computers and Mathematics with Applications, 43(6-7), 841-848. https://doi.org/10.1016/S0898-1221(01)00325-X
Kazemi, N., Olugu, E. U., Abdul-Rashid, S. H., & Ghazilla, R. A. B. R. (2015a). Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters. Journal of Intelligent & Fuzzy Systems, 28(5), 2377-2389. https://doi.org/10.3233/IFS-141519
Kazemi, N., Shekarian, E., Cárdenas-Barrón, L. E., & Olugu, E. U. (2015b). Incorporating human learning into a fuzzy EOQ inventory model with backorders. Computers & Industrial Engineering, 87, 540-542. https://doi.org/10.1016/j.cie.2015.05.014
Khan, M., Jaber, M. Y., & Bonney, M. (2011). An economic order quantity for items with imperfect quality and inspection errors. International Journal Production Economics, 133(1), 113-118. https://doi.org/10.1016/j.ijpe.2010.01.023
Khan, M., Jaber, M. Y., & Wahab, M. I. M. (2010). Economic order quantity model for items with imperfect quality with learning in inspection. International Journal Production Economics, 124(1), 87-96. https://doi.org/10.1016/j.ijpe.2009.10.011
Kumar, R. S., Tiwari, M. K., & Goswami, A. (2016). Two-echelon fuzzy stochastic supply chain for the manufacturer-buyer integrated production-inventory system. Journal of Intelligent Manufacturing, 27(4), 875-888. https://doi.org/10.1007/s10845-014-0921-8
Kurdhi, N. A., Lestari, S. M. P., & Susanti, Y. (2015). A fuzzy collaborative supply chain inventory model with controllable setup cost and service level constraint for imperfect items. International Journal of Applied Management Science, 7(2), 93-122. https://doi.org/10.1504/IJAMS.2015.069265
Lin, T. Y. (2010). An economic order quantity with imperfect quality and quantity discounts. Applied Mathematical Modelling, 34(10), 3158-3165. https://doi.org/10.1016/j.apm.2010.02.004
Lin, T. Y., & Yeh, D. H. (2010). Optimal coordination policy for supply chain system under imperfect quality consideration. Journal of Marine Science and Technology, 18(3), 449-457.
Maddah, B., & Jaber, M. Y. (2008). Economic order quantity for items with imperfect quality: Revisited. International Journal Production Economics, 112(2), 808-815. https://doi.org/10.1016/j.ijpe.2007.07.003
Mahata, G. C., & Goswami, A. (2013). Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables. Computers & Industrial Engineering, 64(1), 190-199. https://doi.org/10.1016/j.cie.2012.09.003
Manna, A. K., Dey, J. K., & Mondal, S. K. (2014). Three-layer supply chain in an imperfect production inventory model with two storage facilities under fuzzy rough environment. Journal of Uncertainty Analysis and Applications, 2(1), 17. https://doi.org/10.1186/s40467-014-0017-1
Pal, S., Mahapatra, G. S., & Samanta, G. P. (2016). A three-layer supply chain EPQ model for price and stock-dependent stochastic demand with imperfect item under rework. Journal of Uncertainty Analysis and Applications, 4(1), 10. https://doi.org/10.1186/s40467-016-0050-3
Rad, M. A., Khoshalhan, F., & Glock, C. H. (2014). Optimizing inventory and sales decisions in a two-stage supply chain with imperfect production and backorders. Computers & Industrial Engineering, 74, 219-227. https://doi.org/10.1016/j.cie.2014.05.004
Roy, A., & Samanta, G. P. (2009). Fuzzy continuous review inventory model without backorder for deteriorating items. Electronic Journal of Applied Statistical Analysis, 2(1), 58-66.
Roy, A., Maity, K., kar, S., & Maiti, M. (2009). A production-inventory model with remanufacturing for defective and usable items in fuzzy-environment. Computer & Industrial Engineering, 56(1), 87-96. https://doi.org/10.1016/j.cie.2008.04.004
Salameh, M. K., & Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal Production Economics, 64(1-3) 59-64. https://doi.org/10.1016/S0925-5273(99)00044-4
Sana, S. S. (2011). A production-inventory model of imperfect quality products in a three-layer supply chain. Decision Support Systems, 50(2), 539-547. https://doi.org/10.1016/j.dss.2010.11.012
Taleizadeh, A. A., Noori-daryan, M., & Tavakkoli-Moghaddam, R. (2015). Pricing and ordering decisions in a supply chain with imperfect quality items and inspection under buyback of defective items. International Journal of Production Research, 53(15), 4553-4582. https://doi.org/10.1080/00207543.2014.997399
Wang, W. T., Wee, H. M., Cheng, Y. L., Wen, C. L., & Cárdenas-Barrón, L. E. (2015). EOQ model for imperfect quality items with partial backorders and screening constraint. European Journal of Industrial Engineering, 9(6), 744-773. https://doi.org/10.1504/EJIE.2015.074384
Yao, J. S., & Wu, K. (2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems, 116(2), 275-288. https://doi.org/10.1016/S0165-0114(98)00122-5
Yu, Y., & Jin, T. D. (2011). The return policy model with fuzzy demands and asymmetric information. Applied Soft Computing, 11(2), 1669-1678. https://doi.org/10.1016/j.asoc.2010.05.004
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zheng, H., Liu, J. C., & Wang, W. (2010). Supply chain coordination for fuzzy newsboy problem with imperfect quality. International Journal of Information and Management Science, 21(2), 157-175.
Zimmermann, H. J. (2011). Fuzzy set theory and its applications (4th ed.). Boston: Kluwer Nijhoff.
Bhaya, S., Pal, M., & Nayak, P. K. (2014). Intuitionistic fuzzy optimization technique in EOQ model with two types of imperfect quality items. Advanced Modeling and Optimization, 16(1), 33-50.
Cachon, G. P. (2003). Supply chain coordination with contracts. In S. Graves, & T. de Kok (Eds.), Handbooks in operations research and management science: Supply chain management (Chapter 11). North Holland, Amsterdam. https://doi.org/10.1016/S0927-0507(03)11006-7
Cachon, G. P., & Lariviere, M. A. (2000). Supply chain coordination with revenue sharing contracts: Strengths and limitation (Working Paper). The Wharton School of Business, University of Pennsylvania, Philadelphia.
Chang, H. C. (2004). An application of fuzzy sets theory to the EOQ model with imperfect quality items. Computer & Operations Research, 31(12), 2079-2092. https://doi.org/10.1016/S0305-0548(03)00166-7
Chen, L. H., & Kang, F. S. (2010). Coordination between vendor and buyer considering trade credit and items of imperfect quality. International Journal Production Economics, 123(1), 52-61. https://doi.org/10.1016/j.ijpe.2009.06.043
Chen, S. H., Wang, C. C., & Chang, S. M. (2007). Fuzzy economic production quantity model for items with imperfect quality. International Journal of Innovative computing, Information and Control, 3(1), 85-95.
Chen, S. P., & Ho, Y. H. (2011). Analysis of the newsboy problem with fuzzy demands and incremental discounts. International Journal Production Economics, 129(1), 169-177. https://doi.org/10.1016/j.ijpe.2010.09.014
Chung, K. J., Her, C. C., & Lin, S. D. (2009). A two-warehouse inventory model with imperfect quality production processes. Computer & Industrial Engineering, 56(1), 193-197. https://doi.org/10.1016/j.cie.2008.05.005
Das, P., De, S. K., & Sana, S. S. (2015). An EOQ model for time dependent backlogging over idle time: A step order fuzzy approach. International Journal of Applied and Computational Mathematics, 1(2), 171-185. https://doi.org/10.1007/s40819-014-0001-y
De, S. K., & Sana, S. S. (2015). An alternative fuzzy EOQ model with backlogging for selling price and promotional effort sensitive demand. International Journal of Applied and Computational Mathematics, 1(1), 69-86.
Dolan, R. J. (1987). Quamtity discounts: Managerial issues and research opportunities. Marketing Science, 6(1), 1-27. https://doi.org/10.1287/mksc.6.1.1
Dubois, D., & Prade, H. (1987). The mean value of a fuzzy number. Fuzzy Sets and Systems, 24(3), 279-300. https://doi.org/10.1016/0165-0114(87)90028-5
Emmons, H., & Gibert, S. M. (1998). Note. The role of returns policies in pricing and inventory decisions for catalogue goods. Management Science, 44(2), 276-283. https://doi.org/10.1287/mnsc.44.2.276
Hsu, J. T., & Hsu, L. F. (2013). An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns. International Journal of Production Economics, 143(1), 162-170. https://doi.org/10.1016/j.ijpe.2012.12.025
Hsu, J., & Hsu, L. (2014). A supplement to an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales return. International Journal of Industrial Engineering Computations, 5(2), 199-210. https://doi.org/10.5267/j.ijiec.2014.2.001
Hu, J. S., Zheng, H., Guo, C. Y., & Ji, Y. P. (2010). Optimal production run length with imperfect production processes and backorder in fuzzy random environment. Computer & Industrial Engineering, 59(1), 9-15. https://doi.org/10.1016/j.cie.2010.01.012
Jaber, M. Y., Goyal, S. K., & Imran, M. (2008). Economic production quantity model for items with imperfect quality subject to learning effects. International Journal Production Economics, 115(1), 143-150. https://doi.org/10.1016/j.ijpe.2008.05.007
Kao, C., & Hsu, W. K. (2002). A single period inventory model with fuzzy demand. Computers and Mathematics with Applications, 43(6-7), 841-848. https://doi.org/10.1016/S0898-1221(01)00325-X
Kazemi, N., Olugu, E. U., Abdul-Rashid, S. H., & Ghazilla, R. A. B. R. (2015a). Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters. Journal of Intelligent & Fuzzy Systems, 28(5), 2377-2389. https://doi.org/10.3233/IFS-141519
Kazemi, N., Shekarian, E., Cárdenas-Barrón, L. E., & Olugu, E. U. (2015b). Incorporating human learning into a fuzzy EOQ inventory model with backorders. Computers & Industrial Engineering, 87, 540-542. https://doi.org/10.1016/j.cie.2015.05.014
Khan, M., Jaber, M. Y., & Bonney, M. (2011). An economic order quantity for items with imperfect quality and inspection errors. International Journal Production Economics, 133(1), 113-118. https://doi.org/10.1016/j.ijpe.2010.01.023
Khan, M., Jaber, M. Y., & Wahab, M. I. M. (2010). Economic order quantity model for items with imperfect quality with learning in inspection. International Journal Production Economics, 124(1), 87-96. https://doi.org/10.1016/j.ijpe.2009.10.011
Kumar, R. S., Tiwari, M. K., & Goswami, A. (2016). Two-echelon fuzzy stochastic supply chain for the manufacturer-buyer integrated production-inventory system. Journal of Intelligent Manufacturing, 27(4), 875-888. https://doi.org/10.1007/s10845-014-0921-8
Kurdhi, N. A., Lestari, S. M. P., & Susanti, Y. (2015). A fuzzy collaborative supply chain inventory model with controllable setup cost and service level constraint for imperfect items. International Journal of Applied Management Science, 7(2), 93-122. https://doi.org/10.1504/IJAMS.2015.069265
Lin, T. Y. (2010). An economic order quantity with imperfect quality and quantity discounts. Applied Mathematical Modelling, 34(10), 3158-3165. https://doi.org/10.1016/j.apm.2010.02.004
Lin, T. Y., & Yeh, D. H. (2010). Optimal coordination policy for supply chain system under imperfect quality consideration. Journal of Marine Science and Technology, 18(3), 449-457.
Maddah, B., & Jaber, M. Y. (2008). Economic order quantity for items with imperfect quality: Revisited. International Journal Production Economics, 112(2), 808-815. https://doi.org/10.1016/j.ijpe.2007.07.003
Mahata, G. C., & Goswami, A. (2013). Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables. Computers & Industrial Engineering, 64(1), 190-199. https://doi.org/10.1016/j.cie.2012.09.003
Manna, A. K., Dey, J. K., & Mondal, S. K. (2014). Three-layer supply chain in an imperfect production inventory model with two storage facilities under fuzzy rough environment. Journal of Uncertainty Analysis and Applications, 2(1), 17. https://doi.org/10.1186/s40467-014-0017-1
Pal, S., Mahapatra, G. S., & Samanta, G. P. (2016). A three-layer supply chain EPQ model for price and stock-dependent stochastic demand with imperfect item under rework. Journal of Uncertainty Analysis and Applications, 4(1), 10. https://doi.org/10.1186/s40467-016-0050-3
Rad, M. A., Khoshalhan, F., & Glock, C. H. (2014). Optimizing inventory and sales decisions in a two-stage supply chain with imperfect production and backorders. Computers & Industrial Engineering, 74, 219-227. https://doi.org/10.1016/j.cie.2014.05.004
Roy, A., & Samanta, G. P. (2009). Fuzzy continuous review inventory model without backorder for deteriorating items. Electronic Journal of Applied Statistical Analysis, 2(1), 58-66.
Roy, A., Maity, K., kar, S., & Maiti, M. (2009). A production-inventory model with remanufacturing for defective and usable items in fuzzy-environment. Computer & Industrial Engineering, 56(1), 87-96. https://doi.org/10.1016/j.cie.2008.04.004
Salameh, M. K., & Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal Production Economics, 64(1-3) 59-64. https://doi.org/10.1016/S0925-5273(99)00044-4
Sana, S. S. (2011). A production-inventory model of imperfect quality products in a three-layer supply chain. Decision Support Systems, 50(2), 539-547. https://doi.org/10.1016/j.dss.2010.11.012
Taleizadeh, A. A., Noori-daryan, M., & Tavakkoli-Moghaddam, R. (2015). Pricing and ordering decisions in a supply chain with imperfect quality items and inspection under buyback of defective items. International Journal of Production Research, 53(15), 4553-4582. https://doi.org/10.1080/00207543.2014.997399
Wang, W. T., Wee, H. M., Cheng, Y. L., Wen, C. L., & Cárdenas-Barrón, L. E. (2015). EOQ model for imperfect quality items with partial backorders and screening constraint. European Journal of Industrial Engineering, 9(6), 744-773. https://doi.org/10.1504/EJIE.2015.074384
Yao, J. S., & Wu, K. (2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems, 116(2), 275-288. https://doi.org/10.1016/S0165-0114(98)00122-5
Yu, Y., & Jin, T. D. (2011). The return policy model with fuzzy demands and asymmetric information. Applied Soft Computing, 11(2), 1669-1678. https://doi.org/10.1016/j.asoc.2010.05.004
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zheng, H., Liu, J. C., & Wang, W. (2010). Supply chain coordination for fuzzy newsboy problem with imperfect quality. International Journal of Information and Management Science, 21(2), 157-175.
Zimmermann, H. J. (2011). Fuzzy set theory and its applications (4th ed.). Boston: Kluwer Nijhoff.