Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1691-1708.

Advance payment has a great influence on making the optimal decision in an inventory system. Two-warehouse inventory system is another imperative factor in inventory analysis. Due to competitive marketing situation, the position of a warehouse performs a significant role in business strategy. Generally, retailers want to find a shop in a popular marketing place. So, they need an additional store room due to insufficient space in a popular marketplace. Also, we have considered the advance payment scheme which is made by equal installment up to n times before receiving the products. Using all of these concepts in together, we have developed a two-warehouse inventory model for deteriorating items with advanced payment scheme. Shortages are allowed with a constant partial backlogging rate. Demand of the product is dependent on selling price. We have presented this physical problem in mathematically and solved. Also, we proved the optimality mathematically as well as graphically and proposed one theorem in order to show the optimality in theoretically. We have supplied a numerical example to illustrate the proposed inventory model. To validate the numerical result of the proposed model, we have plotted 2D and 3D graphs by using MATLAB and observed these satisfy the numerical result. Finally, we have performed sensitivity analysis changing one parameter and keeping others the same.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2018093
Classification : 90B05
Mots-clés : EOQ, two-warehouse, advance payment, deterioration, partial backlogging
Al-Amin Khan, Md. 1 ; Shaikh, Ali Akbar 1 ; Panda, Gobinda Chandra 1 ; Konstantaras, Ioannis 1

1 
@article{RO_2019__53_5_1691_0,
     author = {Al-Amin Khan, Md. and Shaikh, Ali Akbar and Panda, Gobinda Chandra and Konstantaras, Ioannis},
     title = {Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1691--1708},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {5},
     year = {2019},
     doi = {10.1051/ro/2018093},
     zbl = {1430.90023},
     mrnumber = {4016531},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2018093/}
}
TY  - JOUR
AU  - Al-Amin Khan, Md.
AU  - Shaikh, Ali Akbar
AU  - Panda, Gobinda Chandra
AU  - Konstantaras, Ioannis
TI  - Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2019
SP  - 1691
EP  - 1708
VL  - 53
IS  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2018093/
DO  - 10.1051/ro/2018093
LA  - en
ID  - RO_2019__53_5_1691_0
ER  - 
%0 Journal Article
%A Al-Amin Khan, Md.
%A Shaikh, Ali Akbar
%A Panda, Gobinda Chandra
%A Konstantaras, Ioannis
%T Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2019
%P 1691-1708
%V 53
%N 5
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2018093/
%R 10.1051/ro/2018093
%G en
%F RO_2019__53_5_1691_0
Al-Amin Khan, Md.; Shaikh, Ali Akbar; Panda, Gobinda Chandra; Konstantaras, Ioannis. Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1691-1708. doi : 10.1051/ro/2018093. http://www.numdam.org/articles/10.1051/ro/2018093/

H.K. Alfares and A.M. Ghaithan, Inventory and pricing model with price-dependent demand, time-varying holding cost and quantity discounts. Comput. Ind. Eng. 94 (2016) 170–177. | DOI

T. Avinadav, A. Herbon and U. Spiegel, Optimal inventory policy for a perishable item with demand function sensitive to price and sale. Int. J. Prod. Eng. 144 (2013) 497–506. | DOI

A.K. Bhunia and A.A. Shaikh, An Application of PSO in a two ware house inventory model for deteriorating item under permissible delay in payment with different inventory policies. Appl. Math. Comput. 256 (2015) 831–850. | MR | Zbl

A.K. Bhunia and A.A. Shaikh, Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm optimization. Math. Comp. Model. Dyn. 22 (2016) 160–179. | DOI | MR | Zbl

A.K. Bhunia, A.A. Shaikh, A.K. Maiti and M. Maiti, A two ware house deterministic inventory model for deteriorating items with a linear trend in time dependent demand over finite time horizon by Elitist Real-coded Genetic Algorithm. Int. J. Ind. Eng. Comput. 4 (2013) 241–258.

A.K. Bhunia, A.A. Shaikh and R.K. Gupta, A study on two ware house partially backlogged deteriorating inventory models under inflation via particle swarm optimization. Int. J. Syst. Sci. 46 (2015) 1036–1050. | DOI | MR | Zbl

A.K. Bhunia, A.A. Shaikh, G. Sharma and S. Pareek, A two storage inventory model for deteriorating items with variable demand and partial backlogging. J. Ind. Prod. Eng. 32 (2015) 263–272.

A.K. Bhunia, A.A. Shaikh and L.N. Sahoo, A two ware house inventory model for deteriorating item under permissible delay in payments via particle swarm optimization. Int. J. Logist. Syst. Manag. 24 (2016) 45–69.

D. Das, M.B. Kar, A. Roy and S. Kar, Two storage inventory model of a deteriorating item with variable demand under partial trade credit. Cent. Eur. J. Oper. Res. 20 (2012) 251–280.

L. Feng, Y.L. Chen and L.E. Cardenas-Barron, Pricing and lot-sizing policies for perishable goods when the demand depends on selling price, displayed stocks and expiration date. Int. J. Prod. Econ. 185 (2017) 11–20. | DOI

M. Gayen and A.K. Pal, A two ware house inventory model for deteriorating items with stock dependent demand rate and holding cost. Oper. Res. Int. J. 9 (2009) 153–165. | DOI | Zbl

P. Guchhait, M.K. Maiti and M. Maiti, Two storage inventory model of deteriorating item with variable demand under partial trade credit. Appl. Soft Comput. 13 (2013) 428–448. | DOI

C.K. Jaggi, S. Tiwari and S.K. Goel, Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities. Ann. Oper. Res. 248 (2017) 253–280. | DOI | MR | Zbl

M. Lashgari, A.A. Taleizadeh and A. Ahmadi, A partial-up-stream advance payment and partial-down-stream delayed payments in a three level supply chain. Ann. Oper. Res. 238 (2016) 329–354. | DOI | MR | Zbl

Y. Liang and F. Zhou, A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment. Appl. Math. Model. 35 (2011) 2221–2231. | DOI | MR | Zbl

R. Maihami and I.K. Kamalabadi, Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand. Int. J. Prod. Econ. 136 (2012) 116–122. | DOI

A.K. Maiti, M.K. Maiti and M. Maiti, Inventory model with stochastic lead time and price dependent demand incorporating advance payment. Appl. Math. Model. 33 (2009) 2433–2443. | DOI | MR | Zbl

D. Panda, M.K. Maiti and M. Maiti, Two ware house inventory model for single vendor multiple retailers with price and stock dependent demand. Appl. Math. Model. 34 (2010) 3571–3585. | DOI | MR | Zbl

S. Saha and S.K. Goyal, Supply chain co-ordination contracts with inventory level and retailer price dependent demand. Int. J. Prod. Econ. 161 (2015) 140–152. | DOI

S.S. Sana, Price-sensitive demand for perishable items-an EOQ model. Appl. Math. Comput. 217 (2011) 6248–6259. | MR | Zbl

B. Sarkar, P. Mandal and S. Sarkar, An EMQ model with price and sensitive time dependent demand under the effect of reliability and inflation. Appl. Math. Comput. 231 (2014) 414–421. | MR | Zbl

A.A. Shaikh, A two ware house inventory model for deteriorating items with variable demand under alternative trade credit policy. Int. J. Logist. Syst. Manag. 27 (2017) 40–61.

S.R. Singh, N. Kumar and R. Kumari, Two-ware house fuzzy inventory model under the conditions of permissible delay in payments. Int. J. Oper. Res. 11 (2011) 78–99. | DOI | MR | Zbl

G. Sridevi, K.N. Deve and K.S. Rao, Inventory model for deteriorating items with Weibull rate of replenishment and selling price dependent demand. Int. J. Oper. Res. 9 (2010) 329–349. | DOI | MR | Zbl

A.A. Taleizadeh, D.W. Pentico, M.S. Jabalamali and M. Aryanezhad, An economic order quantity model with multiple partial prepayment and partial back ordering. Math. Comput. Model. 57 (2013) 311–323. | DOI | MR | Zbl

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

A.A. Taleizadeh, An EOQ model with partial backordering and advance payments for an evaporating item. Int. J. Prod. Econ. 155 (2014) 185–193. | DOI

S. Tavakoli and A.A. Taleizadeh, An EOQ model for decaying items with full advance payment and conditional discount. Ann. Oper. Res. 259 (2017) 1–22. | DOI | MR

J.T. Teng, L.E. Cardenas-Barron, H.J. Chang, J. Wu and Y. Hu, Inventory lot size policies for deteriorating items with expiration date and advance payments. Appl. Math. Model. 40 (2016) 8605–8616. | DOI | MR | Zbl

A. Thangam, Dominants retailers’ optimal policy in a supply chain under advance payment scheme and trade credit. Int. J. Math. Oper. Res. 3 (2011) 658–679. | DOI | MR | Zbl

A. Thangam, Optimal price discounting and lot-sizing policies for perishable items in a supply chain under advance payment scheme and two-echelon trade credits. Int. J. Prod. Econ. 139 (2012) 459–472. | DOI

S. Tiwari, L.E. Cárdenas-Barrón, M. Goh and A.A. Shaikh, Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. Int. J. Prod. Econ. 200 (2018) 16–36. | DOI

S. Tiwari, C.K. Jaggi, A.K. Bhunia, A.A. Shaikh and M. Goh, Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization. Ann. Oper. Res. 254 (2017) 401–423. | DOI | MR | Zbl

S. Tiwari, C.K. Jaggi, M. Gupta and L.E. Cárdenas-Barrón, Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity. Int. J. Prod. Econ. 200 (2018) 278–290. | DOI

Y.C. Tsao, Retailer’s optimal ordering and discounting policies under advance sales discount and trade credits. Comput. Ind. Eng. 56 (2009) 208–215. | DOI

Y.C. Tsao, Designing a supply chain network for deteriorating inventory under preservation effort and trade credits. Int. J. Prod. Res. 54 (2016) 3837–3851. | DOI

N.P. Zia and A.A. Taleizadeh, A lot-sizing with backordering under hybrid linked to order multiple advance payment and delay payments. Transport. Res. E-Log. 82 (2015) 19–37. | DOI

Cité par Sources :