Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions LTD under finite capacity
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 4, pp. 1357-1384.

The significance of inflation and time value of money in inventory/production systems is indisputable for modern decision makers. Consequently, the paper aims to study the influence of inflationary condition on a stochastic continuous review integrated vendor–buyer inventory system in the presence of a multilevel reorder strategy for the system. It is considered that lead time components and ordering cost are controllable. Lead time is decomposed into its components: set-up time, production time and transportation time. Based on lead time components, demand during the lead time for different batches is assumed to be a mixture of normal distributions. The objective is to minimize joint inventory expected cost by simultaneously optimizing ordering quantity, reorder points of different batches, ordering cost, setup time, transportation time, production time and a number of deliveries under space constraint while the lead time demand follows a normal distribution. To minimize the expected inventory cost, a Lagrange multiplier method is applied in order to solve the problem, and an iterative algorithm is designed to find optimal values. The behavior of the model is illustrated in numerical examples. It was found that for a fixed value of transportation time, setup time and number of batches, with an augment in inflation rate, the two optimal reorder points for different batches were increased. Also, optimum joint expected annual cost with inflation for two kinds of customers’ demand is larger than one kind of customers’ demand. Furthermore, sensitivity analysis and managerial insights are given to show the applicability of the model.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2019060
Classification : 90B05, 90B30
Mots-clés : Controllable lead time, integrated vendor–buyer inventory model, nonlinear constrained stochastic optimization, mixture of normal distributions, inflation
Tahami, Hesamoddin 1 ; Mirzazadeh, Abolfazl 1 ; Gholami-Qadikolaei, Aref 1

1 
@article{RO_2019__53_4_1357_0,
     author = {Tahami, Hesamoddin and Mirzazadeh, Abolfazl and Gholami-Qadikolaei, Aref},
     title = {Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions {LTD} under finite capacity},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1357--1384},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {4},
     year = {2019},
     doi = {10.1051/ro/2019060},
     zbl = {1425.90011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2019060/}
}
TY  - JOUR
AU  - Tahami, Hesamoddin
AU  - Mirzazadeh, Abolfazl
AU  - Gholami-Qadikolaei, Aref
TI  - Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions LTD under finite capacity
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2019
SP  - 1357
EP  - 1384
VL  - 53
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2019060/
DO  - 10.1051/ro/2019060
LA  - en
ID  - RO_2019__53_4_1357_0
ER  - 
%0 Journal Article
%A Tahami, Hesamoddin
%A Mirzazadeh, Abolfazl
%A Gholami-Qadikolaei, Aref
%T Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions LTD under finite capacity
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2019
%P 1357-1384
%V 53
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2019060/
%R 10.1051/ro/2019060
%G en
%F RO_2019__53_4_1357_0
Tahami, Hesamoddin; Mirzazadeh, Abolfazl; Gholami-Qadikolaei, Aref. Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions LTD under finite capacity. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 4, pp. 1357-1384. doi : 10.1051/ro/2019060. http://www.numdam.org/articles/10.1051/ro/2019060/

A. Banerjee, Economic-lot-size model for purchaser and vendor. Decis. Sci. 17 (1986) 292–311. | DOI

M. Ben-Daya and M. Hariga, Lead-time reduction in a stochastic inventory system with learning consideration. Int. J. Prod. Res. 41 (2003) 571–579. | DOI | Zbl

M. Ben-Daya and M. Hariga, Integrated single vendor single buyer model with stochastic demand and variable lead time. Int. J. Prod. Econ. 92 (2004) 75–80. | DOI

H. Bierman and J. Thomas, Inventory decisions under inflationary conditions. Decis. Sci. 8 (1977) 151–155. | DOI

J.A. Buzacott, Economic Order Quantities with Inflation. J. Oper. Res. Soc. 26 (1975) 553–558. | DOI

H.C. Chang, L.Y. Ouyang, K.S. Wu and C.H. Ho, Integrated vendor–buyer cooperative inventory models with a controllable lead time and ordering cost reduction. Eur. J. Oper. Res. 170 (2006) 481–495. | DOI | MR | Zbl

A. Charnes and W.W. Cooper, Chance-constrained programming. Manage. Sci. 6 (1959) 73–79. | DOI | MR | Zbl

B.K. Dey, B. Sarkar, M. Sarkar and S. Pareek, An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment. RAIRO: OR 53 (2018) 39–57. | DOI | Numdam | MR | Zbl

B.S. Everitt and D.J. Hand, Finite Mixture Distributions. 1st edition. Springer (1981). | MR | Zbl

A. Gholami-Qadikolaei, A. Mirzazadeh and R. Tavakkoli-Moghaddam, Lead time and ordering cost reductions in budget and storage space restricted prbabilistic inventory models with imperfect items. RAIRO: OR 49 (2014) 215–242. | DOI | Numdam | MR | Zbl

C. Glock, Lead time reduction strategies in a single-vendor–single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand. Int. J. Prod. Econ. 166 (2012) 37–44. | DOI

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

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

G. Hadley, A comparison of order quantities computed using the average annual cost and the discounted cost. Manage. Sci. 10 (2008) 472–476. | DOI

C. Haksever and J. Moussourakis, A model for optimizing multi-product inventory systems with multiple constraints. Int. J. Prod. Econ. 97 (2005) 18–30. | DOI

M.A. Hariga, A single-item continuous review inventory problem with space restriction. Int. J. Prod. Econ. 128 (2010) 153–158. | DOI

M.A. Hariga and P.L. Jackson, Time-variant lot sizing models for the warehouse scheduling problem. IIE Trans. (Institute Ind. Eng.) 27 (1995) 162–170.

Y.C. Hsiao, A note on integrated single vendor single buyer model with stochastic demand and variable lead time. Int. J. Prod. Econ. 114 (2008) 294–297. | DOI

S.J. Kim and B. Sarkar, Supply Chain model with stochastic lead time, trade-credit financing, and transportation discounts. Math. Probl. Eng. 2017 (2017) 1–14. | DOI | MR | Zbl

R. Landeros and D.M. Lyth, Economic-lot-size models for cooperative inter-organization. J. Bus. Logist. 10 (1989) 146–158.

W.C. Lee, J.W. Wu and W. Bin Hou, A note on inventory model involving variable lead time with defective units for mixtures of distribution. Int. J. Prod. Econ. 89 (2004) 31–44. | DOI

H.J. Lin, Reducing lost-sales rate on the stochastic inventory model with defective goods for the mixtures of distributions. Appl. Math. Model. 37 (2013) 3296–3306. | DOI | MR | Zbl

L. Lu, A one-vendor multi-buyer integrated inventory model. Eur. J. Oper. Res. 81 (1995) 312–323. | DOI | Zbl

A. Majumder, R. Guchhait and B. Sarkar, Manufacturing quality improvement and setup cost reduction in a vendor–buyer supply chain model. Eur. J. Ind. Eng. 11 (2017) 588. | DOI

A. Majumder, C.K. Jaggi and B. Sarkar, A multi-retailer supply chain model with backorder and variable production cost. RAIRO: OR 52 (2017) 943–954. | DOI | Numdam | MR | Zbl

R.B. Misra, Note on optimal inventory management under inflation. Nav. Res. Logist. Q 26 (1979) 161–165. | DOI | Zbl

A. Mirzazadeh, A comparison of the mathematical modeling methods in the inventory systems under uncertain conditions. Int. J. Eng. Sci. Technol. 3 (2011) 6131–6142.

A. Mirzazadeh, M.M. Seyyed Esfahani and S.M.T. Fatemi Ghomi, An inventory model under uncertain inflationary conditions, finite production rate and inflation-dependent demand rate for deteriorating items with shortages. Int. J. Syst. Sci. 40 (2009) 21–31. | DOI | MR | Zbl

I. Moon and B.-H. Ha, Inventory systems with variable capacity. Eur. J. Ind. Eng. 6 (2012) 68–86. | DOI

I. Moon, B.C. Giri and B. Ko, Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting. Eur. J. Oper. Res. 162 (2005) 773–785. | DOI | MR | Zbl

I. Moon, E. Shin and B. Sarkar, Min-max distribution free continuous-review model with a service level constraint and variable lead time. Appl. Math. Comput. 229 (2014) 310–315. | MR | Zbl

L.Y. Ouyang, K.S. Wu and C.H. Ho, Integrated vendor–buyer cooperative models with stochastic demand in controllable lead time. Int. J. Prod. Econ. 92 (2004) 255–266. | DOI

J.C.-H. Pan and J.-S. Yang, A study of an integrated inventory with controllable lead time. Int. J. Prod. Res. 40 (2002) 1263–1273. | DOI | Zbl

B. Sarkar and A.S. Mahapatra, Periodic review fuzzy inventory model with variable lead time and fuzzy demand. Int. Trans. Oper. Res. 24 (2017) 1197–1227. | DOI | MR | Zbl

B. Sarkar and A. Majumder, Integrated vendor–buyer supply chain model with vendor’s setup cost reduction. Appl. Math. Comput. 224 (2013) 362–371. | MR | Zbl

B. Sarkar and I. Moon, Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process. Int. J. Prod. Econ. 155 (2014) 204–213. | DOI

B. Sarkar, K. Chaudhuri and I. Moon, Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint. J. Manuf. Syst. 34 (2015) 74–82. | DOI

B. Sarkar, B. Mandal and S. Sarkar, Quality improvement and backorder price discount under controllable lead time in an inventory model. J. Manuf. Syst. 35 (2015) 26–36. | DOI

B. Sarkar, A. Majumder, M. Sarkar, B. Koli Dey and G. Roy, Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction. J. Ind. Manag. Optim. 13 (2016) 1085–1104. | DOI | MR | Zbl

B. Sarkar, S. Saren, M. Sarkar and Y.W. Seo, A Stackelberg game approach in an integrated inventory model with carbon-emission and setup cost reduction. Sustainability 8 (2016) 1–23. | DOI

B. Sarkar, R. Guchhait, M. Sarkar, S. Pareek and N. Kim, Impact of safety factors and setup time reduction in a two-echelon supply chain management. Robot. Comput. Integr. Manuf. 55 (2019) 250–258. | DOI

D. Shin, R. Guchhait, B. Sarkar and M. Mittal, Controllable lead time, service level constraint, and transportation discounts in a continuous review inventory model. RAIRO: OR 50 (2015) 921–934. | DOI | Numdam | MR | Zbl

H.N. Soni, B. Sarkar and M. Joshi, Demand uncertainty and learning in fuzziness in a continuous review inventory model. J. Intell. Fuzzy Syst. 33 (2017) 2595–2608. | DOI | Zbl

H.N. Soni, B. Sarkar, A.S. Mahapatra and S.K. Mazumder, Lost sales reduction and quality improvement with variable lead time and fuzzy costs in an imperfect production system. RAIRO: OR 52 (2018) 819–837. | DOI | Numdam | MR | Zbl

H. Tahami, A. Mirzazadeh, A. Arshadi-Khamseh and A. Gholami-Qadikolaei, A periodic review integrated inventory model for buyer’s unidentified protection interval demand distribution. Cogent Eng. 3 (2016). | DOI

A. Veinott, Optimal policy for a multi-product, dynamic, nonstationary inventory problem. Manage. Sci. 12 (1965) 206–222. | DOI | MR | Zbl

J.W. Wu and H.Y. Tsai, Mixture inventory model with back orders and lost sales for variable lead time demand with the mixtures of normal distribution. Int. J. Syst. Sci. 32 (2001) 259–268. | DOI | MR | Zbl

K. Xu and M.T. Leung, Stocking policy in a two-party vendor managed channel with space restrictions. Int. J. Prod. Econ. 117 (2009) 271–285. | DOI

H. Yang, J. Teng and M. Chern, Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand. Nav. Res. Logist. 48 (2001) 144–158. | DOI | MR | Zbl

Cité par Sources :