Joint replenishment strategy for deteriorating multi-item through multi-echelon supply chain model with imperfect production under imprecise and inflationary environment
RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 3071-3096

As the industry environment becomes more competitive, the supply chain management for multi items has become an essential part of the industries. In this paper, a multi-echelon inventory model for deteriorating multi items with imperfect production has been developed under the environment of fuzzy and inflation. A single producer, multi-supplier, and multi-retailer are considered from the integrated point of view. Here, the producer only produces the retailer’s need to have a tremendous advantage and minimum loss. It is observed that the inflation rate is almost uncertain for deteriorating goods in every supply chain. In this paper, the inflation rate is taken as a triangular fuzzy number, and the centroid method is used to defuzzify the profit function. The shortage is not allowed in any part, an imperfect production process is considered, but it is not reworkable in this supply chain. Different inflation rates are considered for additional items because inflation has strained the most vulnerable consumers (the daily wage earners), who mainly demand goods in short and small quantities. This entire model is developed based on the retailer’s demand and due to which, the profit potential is maximized. The central premise of this study is to get maximum benefit by creating a production model for deterioration items. Finally, a numerical example and sensitivity analysis illustrate the present study. It is observed that if the number of shipments taken from the supplier increases during the production period, the total profit increases in crisp and fuzzy. If a positive change occurs in the number of shipments received through the producer to the retailer, then the fuzzy model has positive, but a slight negative change occurs in the crisp model. This paper shows the effect of a joint replenishment policy for multi-item compared with the independent approaches.

DOI : 10.1051/ro/2022071
Classification : 90B05
Keywords: Multi-echelon supply chain, multi items, inflation, triangular fuzzy number, imperfect production
@article{RO_2022__56_4_3071_0,
     author = {Singh Padiyar, Surendra Vikram and Vandana and Bhagat, Naveen and Singh, Shiv Raj and Sarkar, Biswajit},
     title = {Joint replenishment strategy for deteriorating multi-item through multi-echelon supply chain model with imperfect production under imprecise and inflationary environment},
     journal = {RAIRO. Operations Research},
     pages = {3071--3096},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {4},
     doi = {10.1051/ro/2022071},
     mrnumber = {4474352},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2022071/}
}
TY  - JOUR
AU  - Singh Padiyar, Surendra Vikram
AU  - Vandana
AU  - Bhagat, Naveen
AU  - Singh, Shiv Raj
AU  - Sarkar, Biswajit
TI  - Joint replenishment strategy for deteriorating multi-item through multi-echelon supply chain model with imperfect production under imprecise and inflationary environment
JO  - RAIRO. Operations Research
PY  - 2022
SP  - 3071
EP  - 3096
VL  - 56
IS  - 4
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2022071/
DO  - 10.1051/ro/2022071
LA  - en
ID  - RO_2022__56_4_3071_0
ER  - 
%0 Journal Article
%A Singh Padiyar, Surendra Vikram
%A Vandana
%A Bhagat, Naveen
%A Singh, Shiv Raj
%A Sarkar, Biswajit
%T Joint replenishment strategy for deteriorating multi-item through multi-echelon supply chain model with imperfect production under imprecise and inflationary environment
%J RAIRO. Operations Research
%D 2022
%P 3071-3096
%V 56
%N 4
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ro/2022071/
%R 10.1051/ro/2022071
%G en
%F RO_2022__56_4_3071_0
Singh Padiyar, Surendra Vikram; Vandana; Bhagat, Naveen; Singh, Shiv Raj; Sarkar, Biswajit. Joint replenishment strategy for deteriorating multi-item through multi-echelon supply chain model with imperfect production under imprecise and inflationary environment. RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 3071-3096. doi: 10.1051/ro/2022071

[1] R. Ali, S. Rani and A. Agarwal, Inventory model for deteriorating items in green supply chain with credit period dependent demand. Int. J. Appl. Eng. Res. 15 (2020) 157–172.

[2] T. H. Chou, Integrated two-stage inventory model for deteriorating items. Master’s Thesis, Chung Yuan Christian University Taiwan, ROC (2000).

[3] A. J. Clark and H. Scarf, Optimal policies for multi echelon inventory problem. Manage. Sci. 6 (1960) 475–490. | DOI

[4] Z. Dai, F. Aqlan and K. Gao, Optimizing multi echelon inventory with three types of demand in supply chain. Transp. Res. Part E Logistic Transp. Rev. 107 (2017) 141–177. | DOI

[5] S. K. De and I. Beg, Triangular dense fuzzy sets and new defuzzification method. J. Intell. Fuzzy Syst. 31 (2016) 469–477. | Zbl

[6] S. K. De and G. C. Mathata, A cloudy fuzzy economic quantity model for imperfect quality items with allowable proportionate discounts. J. Ind. Eng. Int. 15 (2019) 571–583. | DOI

[7] I. Moon, W. Y. Yun and B. Sarkar, Effects of variable setup cost, reliability, and production costs under controlled carbon emissions in a reliable production system. Euro. J. Indust. Eng. (2022). | DOI

[8] A. Sarkar, R. Guchhait and B. Sarkar, Application of the artificial neural network with multithreading within an inventory model under uncertainty and inflation. Int. J. Fuzzy Syst. (2022). | DOI

[9] A. Diabat, A. A. Taleizadeh and M. Lashgari, A lot sizing model with partial downstream delayed payment, partial upstream advance payment, and partial backordering for deteriorating items. J. Manuf. Syst. 45 (2017) 322–342. | DOI

[10] Y. He, S. Y. Wang and K. K. Lai, An optimal production inventory model for deteriorating items with multiple market demand. Eur. J. Oper. Res. 203 (2010) 593–600. | Zbl | DOI

[11] C. K. Jaggi, S. Pareek, N. Sharma, Nidhi, Fuzzy inventory model for deteriorating items with time varying demand and shortage. Am. J. Oper. Res. 2 (2012) 81–92.

[12] W. A. Jauhari, N. A. F. P. Adam, C. N. Rosyidi, I. N. Pujawan and N. H. Shah, A closed loop supply chain model with rework, Waste disposal, and carbon emission. Oper. Res. Perspect. 7 (2020) 100155. | MR

[13] S. Karmakar, S. K. De and A. Goswami, A study of an EOQ model under fuzzy demand rate. Int. Conf. Math. Comput. 834 (2018) 149–163. | MR | Zbl | DOI

[14] M. Lashgari, A. A. Taleizadeh and S. S. Sana, An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. J. Ind. Manage. Optim. 12 (2016) 1091–1119. | MR | Zbl | DOI

[15] M. Lashgari, A. A. Taleizadeh and S. J. Sadjadi, Ordering policies for non-instantaneous deteriorating items under hybrid partial prepayment, partial trade credit and partial backordering. J. Oper. Res. Soc. 69 (2018) 1167–1196. | DOI

[16] C. J. Lu, T. S. Lee, M. Gu and C. T. Yang, A multi-stage sustainable production inventory model with carbon emission reduction and price dependent demand under stackelberg game. Appl. Sci. 10 (2020) 4878. | DOI

[17] R. Maihami, K. Govindan and M. Fattahi, The inventory and pricing decisions in a three-echelon supply chain of deteriorating items under probabilistic environment. Transp. Res. Part E: Logistic Transp. Rev. 131 (2019) 118–138. | DOI

[18] B. Sarkar and S. Bhuniya, A sustainable flexible manufacturing-remanufacturing model with improved service and green investment under variable demand. Exp. Syst. App. 202 (2022) 117154. | DOI

[19] B. Mohammadi, A. A. Taleizadeh, R. Noorossana and H. Samimi, Optimizing integrated manufacturing and products inspection policy for deteriorating manufacturing system with imperfect. J. Manuf. Syst. 37 (2015) 299–315. | DOI

[20] A. H. Nobil, A. Kazemi and A. A. Taleizadeh, Single-machine lot scheduling problem for deteriorating items with negative exponential deterioration rate. RAIRO: Oper. Res. 53 (2019) 1297–1307. | MR | Numdam | DOI

[21] S. V. S. Padiyar, S. R. Singh and N. Punetha, Inventory system with price dependent consumption for deteriorating items with shortages under fuzzy environment. Int. J. Sustainable Agr. Manage. Inf. 7 (2021) 218–231.

[22] G. C. Panda, A. A. Khan and A. A. Shaikh, A credit policy approach in two warehouse inventory model for deteriorating items with price and stock dependent demand under partial backlogging. J. Ind. Eng. Int. 15 (2019) 147–170. | DOI

[23] N. Rajput, R. K. Pandey, A. P. Singh and A. Chauhan, An optimization of fuzzy EOQ model in healthcare industries with three different demand patterns using signed distance technique. Math. Eng. Sci. Aerosp. 10 (2019) 205–218.

[24] N. Rajput, A. Chauhan and R. K. Pandey, Fuzzy EOQ model with reliability induced demand and defuzzification by Graded Mean Integration. In: Chapter in Book: Recent Advances in Mathematics for Engineering (2020) 305–326.

[25] M. Rani and H. Kishan, A multi echelon supply chain inventory model with variable demand rate for deteriorating items. Pure Appl. Math. Sci. LXXIV (2011) 31–44.

[26] S. Saha, Fuzzy inventory model for deterioration items in a supply chain system with price dependent demand and without backorder. Am. J. Eng. Res. 6 (2017) 183–187.

[27] R. Saranya and R. Varadarajan, A fuzzy inventory model with acceptable shortage using graded integration value method. J. Phys. Conf. Ser. 1000 (2018) 012009. | DOI

[28] M. S. Habib, M. Omair, M. B. Ramzan, T. N. Chaudhary, M. Farooq and B. Sarkar, A robust possibilistic flexible programming approach toward a resilient and cost-efficient biodiesel supply chain network. J. Clean. Prod. (2022) 132752. | DOI

[29] A. S. H. Kugele, W. Ahmed and B. Sarkar, Geometric programming solution of second degree difficulty for carbon ejection controlled reliable smart production system. RAIRO: Oper. Res. 56 (2022) 1013–1029. | MR | Zbl | Numdam | DOI

[30] A. S. Mahapatra, M. S. Mahapatra, B. Sarkar and S. K. Majumder, Benefit of preservation technology with promotion and time-dependent deterioration under fuzzy learning. Exp. Syst. App. 201 (2022) 117169. | DOI

[31] B. R. Sarker, A. M. Jamal and S. Wang, Supply chain model for perishable product under inflation and perishable delay in payment. Comput. Oper. Res. 27 (2000) 59–75. | Zbl | DOI

[32] M. Sebatjane and O. Adetunji, A three echelon supply chain for economics growing quantity model with price and freshness dependent demand, pricing, ordering and shipment decisions. Oper. Res. Perspect. 7 (2020) 100153. | MR

[33] A. K. Shaikh, G. C. Panda, M. A. Khan, A. H. Mashud and A. Biswas, An inventory model for deteriorating items with preservation facility of ramp type demand and trade credit. Int. J. Oper. Res. 17 (2020) 414–551. | MR | Zbl

[34] S. Sharma, S. R. Singh and M. Kumar, A reverse logistics inventory model with multiple production and remanufacturing batches under fuzzy environment. RAIRO: Oper. Res. 55 (2021) 571–588. | MR | Zbl | Numdam | DOI

[35] D. Sharmila and R. Uthayakumar, Inventory model for deterioration items involving fuzzy with shortage and exponential demand. Int. J. Supply Oper. Manage. 2 (2015) 888–904.

[36] S. R. Singh and S. Tayal, Replenishment policy for deteriorating items with trade credit and allowable shortage under inflationary environment. Int. J. Process Manage. Benchmarking 10 (2020) 462–478. | DOI

[37] S. R. Singh, V. Gupta and P. Gupta, Three stage supply chain model with two warehouse, imperfect production, variable demand rate and inflation. Int. J. Ind. Eng. Comput. 4 (2013) 81–92.

[38] N. Singh, B. Vaish and S. R. Singh, Analysis of three level supply chain of inventory with deteriorating for muti-items. Int. J. Ind. Eng. Comput. 5 (2014) 417–430.

[39] S. R. Singh, S. Tayal and A. K. Attri, Two levels of storage model for deteriorating items stock dependent demand and partial backlogging with both rented warehouse. Int. J. Process Manage. Benchmarking 9 (2019) 485–498. | DOI

[40] A. A. Taleizadeh, An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Appl. Math. Modell. 38 (2014) 5357–5366. | MR | Zbl | DOI

[41] A. A. Taleizadeh and M. Nematollahi, An inventory control problem for deteriorating items with back-ordering and financial considerations. Appl. Math. Modell. 38 (2014) 93–109. | MR | Zbl | DOI

[42] A. A. Taleizadeh and A. Rasuli-Baghban, Pricing and lot sizing of a decaying item under group dispatching with time-dependent demand and decay rates. Sci. Iran. 25 (2018) 1656–1670.

[43] A. A. Taleizadeh, H. M. Wee and F. Jolai, Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math. Comput. Modell. 57 (2013) 1466–1479. | MR | DOI

[44] A. A. Taleizadeh, M. Noori-Daryan and L. E. Cárdenas-Barrón, Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items. Int. J. Prod. Econ. 159 (2015) 285–295. | DOI

[45] A. A. Taleizadeh, F. Satarian and A. Jamili, Optimal multi-discount selling prices schedule for deteriorating product. Sci. Iran. 22 (2015) 2595–2603.

[46] A. A. Taleizadeh, N. Pourmohammad-Zia and I. Konstantaras, Partial linked-to-order delayed payment and lifetime effects on decaying items ordering. Oper. Res. 21 (2021) 2077–2099.

[47] R. Tat, M. Esmaeili and A. Taleizadeh, Developing EOQ model with instantaneous deteriorating items for a vendor-managed inventory (VMI) system. J. Ind. Syst. Eng. 7 (2014) 21–42.

[48] S. Tavakoli and A. A. Taleizadeh, An EOQ model for decaying item with full advanced payment and conditional discount. Ann. Oper. Res. 259 (2017) 415–436. | MR | Zbl | DOI

[49] B. Sarkar, J. Joo, Y. Kim, H. Park and M. Sarkar, Controlling defective items in a complex multi-phase manufacturing system. RAIRO: Oper. Res. 56 (2022) 871–889. | MR | Zbl | Numdam | DOI

[50] R. Uthayakumar and S. Hemapriya, Integrated vendor buyer inventory model in a supply chain with variable lead time and setup cost reduction. Int. J. Process Manage. Benchmarking 9 (2019) 324–350. | DOI

[51] B. Sarkar, M. Ullah and M. Sarkar, Environmental and economic sustainability through innovative green products by remanufacturing. J. Clean. Prod. 332 (2022) 129813. | DOI

[52] Vandana, S. R. Singh, D. Yadav, B. Sarkar and M. Sarkar, Impact of energy and carbon emission of a supply chain management with two level trade credit policy. Energies 14 (2021) 1569. | DOI

[53] D. Yadav, R. Singh, A. Kumar and B. Sarkar, Reduction of pollution through sustainable and flexible production by controlling by-products. J. Env. Inform. (2022). http://www.jeionline.org/index.php?journal=mys&page=article&op=view&path%5B%5D=202200476

Cité par Sources :