An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment
RAIRO. Operations Research, Tome 55 (2021), pp. S2727-S2746

Brand substitution is common observed phenomenon in daily life. It is the decision makers’ economic understanding and potential scheme for business-industries. Also, it provides the flexibility in management and increases the ability to control the production. This works proposes an integrated supplier–retailer inventory model for substitutable products. Two suppliers work not works with two different brand products with their corresponding demand are involved and one retailer sells each of the products. To nullify the complexities of the joint optimization problem, we first develop a deterministic model for three cases: no substitution, partial substitution and full substitution, then we go for its fuzzification. Keeping the financial constraint of each producer, we have studied over the elasticity of the cost parameters by means of triangular dense fuzzy lock set approach with its locking and unlocking property for final decision making. Finally, sensitivity analysis and graphical illustrations are made to justify the model.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ro/2020102
Classification : 90B06
Keywords: Product substitution, multiple supplier, single retailer, defective items, triangular dense fuzzy lock set, supply chain, optimization
@article{RO_2021__55_S1_S2727_0,
     author = {Karmakar, Snigdha and De, Sujit Kumar and Datta, Tapan Kumar and Goswami, Adrijit},
     title = {An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment},
     journal = {RAIRO. Operations Research},
     pages = {S2727--S2746},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     doi = {10.1051/ro/2020102},
     mrnumber = {4223089},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2020102/}
}
TY  - JOUR
AU  - Karmakar, Snigdha
AU  - De, Sujit Kumar
AU  - Datta, Tapan Kumar
AU  - Goswami, Adrijit
TI  - An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment
JO  - RAIRO. Operations Research
PY  - 2021
SP  - S2727
EP  - S2746
VL  - 55
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2020102/
DO  - 10.1051/ro/2020102
LA  - en
ID  - RO_2021__55_S1_S2727_0
ER  - 
%0 Journal Article
%A Karmakar, Snigdha
%A De, Sujit Kumar
%A Datta, Tapan Kumar
%A Goswami, Adrijit
%T An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment
%J RAIRO. Operations Research
%D 2021
%P S2727-S2746
%V 55
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ro/2020102/
%R 10.1051/ro/2020102
%G en
%F RO_2021__55_S1_S2727_0
Karmakar, Snigdha; De, Sujit Kumar; Datta, Tapan Kumar; Goswami, Adrijit. An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment. RAIRO. Operations Research, Tome 55 (2021), pp. S2727-S2746. doi: 10.1051/ro/2020102

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

[2] L. Benkherouf, K. Skouri and I. Konstantaras, Inventory decisions for a finite horizon problem with product substitution options and time varying demand. Appl. Math. Model. 51 (2017) 669–685. | MR | DOI

[3] J. Cai, P. R. Tadikamalla, J. Shang and G. Huang, Optimal inventory decisions under vendor managed inventory: substitution effects and replenishment tactics. Appl. Math. Model. 43 (2017) 611–629. | MR | DOI

[4] X. Chen, Y. Feng, M. F. Keblis and J. Xu, Optimal inventory policy for two substitutable products with customer service objectives. Eur. J. Oper. Res. 246 (2015) 76–85. | MR | DOI

[5] S. K. De, Triangular dense fuzzy lock sets. Soft Comput. 22 (2017) 7243–7254.

[6] S. K. De, On degree of fuzziness and fuzzy decision making. Cybern. Syst. 51 (2020) 600–614. | DOI

[7] S. K. De and I. Beg, Triangular dense fuzzy sets and new defuzzification methods. J. Intel. Fuzzy Syst. 31 (2016) 469–477. | DOI

[8] S. K. De and G. C. Mahata, Decision of a fuzzy inventory with fuzzy backorder model under cloudy fuzzy demand rate. Int. J. Appl. Comput. Math. 3 (2017) 2593–2609. | MR | DOI

[9] S. K. De and G. C. Mahata, An EPQ model for three-layer supply chain with partial backordering and disruption: triangular dense fuzzy lock set approach. Sādhanā 44 (2019) 177. | MR | DOI

[10] S. K. De and M. Pal, An intelligent decision for a bi-objective inventory problem. Int. J. Syst. Sci.: Oper. Logistics 3 (2016) 49–62.

[11] S. K. De and S. S. Sana, Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index. Econ. Model. 31 (2013) 351–358. | DOI

[12] S. K. De and S. S. Sana, Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment. Pac. Sci. Rev. A: Nat. Sci. Eng. 17 (2015) 61–68.

[13] S. K. De and S. S. Sana, Two-layer supply chain model for cauchy-type stochastic demand under fuzzy environment. Int. J. Intel. Comput. Cybern. 11 (2018) 285–308. | DOI

[14] Z. Drezner, H. Gurnani and B. A. Pasternack, An EOQ model with substitutions between products. J. Oper. Res. Soc. 46 (1995) 887–891. | Zbl | DOI

[15] S. Ghosh, S. Khanra and K. Chaudhuri, Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale. Appl. Math. Comput. 217 (2011) 6047–6053. | MR | Zbl

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

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

[18] S. K. Goyal, C. K. Huang and K. C. Chen, A simple integrated production policy of an imperfect item for vendor and buyer. Prod. Planning Control 14 (2003) 596–602. | DOI

[19] H. Gurnani and Z. Drezner, Deterministic hierarchical substitution inventory models. J. Oper. Res. Soc. 51 (2000) 129–133. | Zbl | DOI

[20] J. T. Hsu and L. F. Hsu, An integrated vendor–buyer cooperative inventory model for items with imperfect quality and shortage backordering. Adv. Decis. Sci. 2012 (2012) 679083. | MR | Zbl

[21] G. Jamali, S. S. Sana and R. Moghdani, Hybrid improved cuckoo search algorithm and genetic algorithm for solving markov-modulated demand. RAIRO:OR 52 (2018) 473–497. | MR | Numdam | DOI

[22] S. Karmakar, S. K. De and A. Goswami, A pollution sensitive dense fuzzy economic production quantity model with cycle time dependent production rate. J. Cleaner Prod. 154 (2017) 139–150. | DOI

[23] R. S. Kumar, S. De and A. Goswami, Fuzzy EOQ models with ramp type demand rate, partial backlogging and time dependent deterioration rate. Int. J. Math. Oper. Res. 4 (2012) 473–502. | MR | DOI

[24] S. Maity, S. K. De and S. P. Mondal, A study of a backorder EOQ model for cloud-type intuitionistic dense fuzzy demand rate. Int. J. Fuzzy Syst. 22 (2020) 201–211. | DOI

[25] R. Mcgillivray and E. Silver, Some concepts for inventory control under substitutable demand. INFOR: Info. Syst. Oper. Res. 16 (1978) 47–63. | MR | Zbl

[26] V. K. Mishra, Optimal ordering quantities for substitutable deteriorating items under joint replenishment with cost of substitution. J. Ind. Eng. Int. 13 (2017) 381–391. | DOI

[27] R. Moghdani, S. S. Sana and H. Shahbandarzadeh, Multi-item fuzzy economic production quantity model with multiple deliveries. Soft Comput. 24 (2020) 10363–10387. | DOI

[28] A. Mukhopadhyay and A. Goswami, An inventory model with shortages for imperfect items using substitution of two products. Int. J. Oper. Res. 30 (2017) 193–219. | MR | DOI

[29] B. Pal, S. S. Sana and K. Chaudhuri, A three layer multi-item production–inventory model for multiple suppliers and retailers. Econ. Model. 29 (2012) 2704–2710. | DOI

[30] M. Parlar and S. Goyal, Optimal ordering decisions for two substitutable products with stochastic demands. Opsearch 21 (1984) 1–15. | Zbl

[31] B. A. Pasternack and Z. Drezner, Optimal inventory policies for substitutable commodities with stochastic demand. Nav. Res. Logistics (NRL) 38 (1991) 221–240. | MR | Zbl | DOI

[32] 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

[33] S. S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain. Decis. Supp. Syst. 50 (2011) 539–547. | DOI

[34] S. S. Sana, Optimal contract strategies for two stage supply chain. Econ. Model. 30 (2013) 253–260. | DOI

[35] S. S. Sana, J. A. Chedid and K. S. Navarro, A three layer supply chain model with multiple suppliers, manufacturers and retailers for multiple items. Appl. Math. Comput. 229 (2014) 139–150. | MR

[36] B. Sarkar, Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Math. Prob. Eng. 2016 (2016) 6318737. | MR | DOI

[37] B. Sarkar and I. Moon, An EPQ model with inflation in an imperfect production system. Appl. Math. Comput. 217 (2011) 6159–6167. | MR | Zbl

[38] S. Sinha, N. M. Modak and S. S. Sana, An entropic order quantity inventory model for quality assessment considering price sensitive demand. Opsearch 57 (2020) 88–103. | MR | DOI

[39] H. N. Soni and K. A. Patel, Optimal strategy for an integrated inventory system involving variable production and defective items under retailer partial trade credit policy. Decis. Supp. Syst. 54 (2012) 235–247. | DOI

[40] M. A. Takami, R. Sheikh and S. S. Sana, A hesitant fuzzy set theory based approach for project portfolio selection with interactions under uncertainty. J. Inf. Sci. Eng. 34 (2018) 65–79.

[41] C. S. Tang and R. Yin, Joint ordering and pricing strategies for managing substitutable products. Prod. Oper. Manage. 16 (2007) 138–153. | DOI

[42] S. Transchel, Inventory management under price-based and stockout-based substitution. Eur. J. Oper. Res. 262 (2017) 996–1008. | MR | DOI

[43] R. Uthayakumar and M. Palanivel, An inventory model for defective items with trade credit and inflation. Prod. Manuf. Res. 2 (2014) 355–379.

[44] H. M. Wee, J. Yu and M. C. Chen, Optimal inventory model for items with imperfect quality and shortage backordering. Omega 35 (2007) 7–11. | DOI

[45] L. Zadeh, Fuzzy sets. Inf. Control 8 (1965) 338–353. | MR | Zbl | DOI

Cité par Sources :