Constrained integrated inventory model for multi-item under mixture of distributions
RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 3, pp. 849-893.

When the demand of different customers are not identical during the lead time, then one cannot use only a single distribution to describe the demand during that lead time. Hence, in this paper we have studied a mixture of normal distributions and a mixture of distribution free for several products under vendor-buyer integrated approach (coordination between both parties). Many integrated inventory models have proved that the integrated total cost is minimum when compared to sum of the total cost of the individuals. The inventory is continuously reviewed by the buyer and next order is placed when the inventory reaches some level called reorder level. The buyer has limited warehouse space capacity and also limited budget to purchase all products. The lead time of receiving all products from the vendor is a variable which is controlled by adding crashing cost. Shortages are allowed for all products and a fraction of shortages will be backordered and the remaining are lost. A mathematical model is developed and a solution procedure is employed in this study to obtain optimum order quantities, lead time and number of shipments in which the integrated total cost function attains its minimum subject to the floor space constraint and budget constraint. The expected integrated cost function is non-linear mixed integer with inequality constraints. Therefore, the proposed model have been solved by using Lagrangian multiplier technique. Finally numerical examples and sensitivity analysis were performed to illustrate the effectiveness of the proposed model.

DOI : 10.1051/ro/2018002
Classification : 90B05, 90C30, 78M50
Mots clés : Constrained non-linear programming problem, inventory control, Lagrangian multiplier, mixture distributions
Uthayakumar, R. 1 ; Ganesh Kumar, M. 1

1
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Uthayakumar, R.; Ganesh Kumar, M. Constrained integrated inventory model for multi-item under mixture of distributions. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 3, pp. 849-893. doi : 10.1051/ro/2018002. http://www.numdam.org/articles/10.1051/ro/2018002/

[1] K. Annadurai, Minimax distribution-free procedure for mixture inventory model with variable lead time and a service level constraint by reducing order cost. Am. J. Math. Manag. Sci. 35 (2016) 1–14.

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

[3] M. Ben-Daya and A. Raouf, On the constrained multi-item single-period inventory problem. Int. J. Oper. Prod. Manag. 13 (1993) 104–112. | DOI

[4] M. Ben-Daya and A. Raouf, Inventory models involving lead time as a decision variable. J. Oper. Res. Soc. 45 (1994) 579–582. | DOI | Zbl

[5] 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

[6] W.C. Benton, Quantity discount decisions under conditions of multiple items, multiple suppliers and resource limitations. Int. J. Prod. Res. 29 (1991) 1953–1961. | DOI | Zbl

[7] D.K. Bhattacharya, On multi-item inventory. Eur. J. Oper. Res. 162 (2005) 786–791. | DOI | MR | Zbl

[8] M. Braglia, D. Castellano and M. Gallo, Approximated closed-form minimum-cost solution to the (r, q) policy with complete backordering and further developments. Appl. Math. Model. 40 (2016) 8406–8423. | DOI | MR | Zbl

[9] M. Braglia, D. Castellano and M. Frosolini, Joint-replenishment problem under stochastic demands with backorders-lost sales mixtures,controllable lead times, and investment to reduce the major ordering cost. J. Oper. Res. Soc. 67 (2016) 1108–1120. | DOI

[10] M. Braglia, D. Castellano and D. Song, Distribution-free approach for stochastic Joint-Replenishment Problem with backorders-lost sales mixtures, and controllable major ordering cost and lead times. Comput. Oper. Res. 79 (2017) 161–173. | DOI | MR | Zbl

[11] O. Dey and B.C. Giri, Optimal vendor investment for reducing defect rate in a vendor-buyer integrated system with imperfect production process. Int. J. Prod. Econ. 155 (2014) 222–228. | DOI

[12] B.S. Everitt, Mixture Distributions – I. John Wiley & Sons, Inc. (1985).

[13] X. Feng, I. Moon and K. Ryu, Warehouse capacity sharing via transshipment for an integrated two-echelon supply chain. Transp. Res. Part E: Logist. Transp. Rev. 104 (2017) 17–35. | DOI

[14] G. Gallego and I. Moon, The distribution free newsboy problem: review and extensions. J. Oper. Res. Soc. 44 (1993) 825–834. | DOI | Zbl

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

[16] S.K. Goyal, A one-vendor multi-buyer integrated inventory model: a comment. Eur. J. Oper. Res. 82 (1995) 209–210. | DOI | Zbl

[17] K. Güler, E. Körpeoğlu and A. Şen, Design and analysis of mechanisms for decentralized joint replenishment. Eur. J. Oper. Res. 259 (2017) 992–1002. | DOI | MR | Zbl

[18] D. Ha and S.L. Kim, Implementation of JIT purchasing: an integrated approach. Prod. Plan. Control 8 (1997) 152–157. | DOI

[19] R.M. Hill, The optimal production and shipment policy for the single-vendor singlebuyer integrated production-inventory problem. Int. J. Prod. Res. 37 (1999) 2463–2475. | DOI | Zbl

[20] M.S.J. Hossain, M.M. Ohaiba and B.R. Sarker, An optimal vendor-buyer cooperative policy under generalized lead-time distribution with penalty cost for delivery lateness. Int. J. Prod. Econ. 188 (2017) 50–62. | DOI

[21] C.K. Huang, An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration. Int. J. Prod. Econ. 91 (2004) 91–98. | DOI

[22] S.H. Huang and P.C. Lin, A modified ant colony optimization algorithm for multi-item inventory routing problems with demand uncertainty. Transp. Res. Part E: Logist. Transp. Rev. 46 (2010) 598–611. | DOI

[23] L.I.N. Hsien-Jen, An integrated supply chain inventory model with imperfect-quality items, controllable lead time and distribution-free demand. Yugosl. J. Oper. Res. 23 (2013) 87–109. | DOI | MR | Zbl

[24] P.N. Joglekar, Note – Comments on “A quantity discount pricing model to increase vendor profits”. Manag. Sci. 34 (1988) 1391–1398. | DOI

[25] F. Kangi, S. Javanmard and S.H.R. Pasandideh, Economic production quantity model with imperfect products and random order frequency under due date and limited storage capacity. J. Ind. Prod. Eng. 34 (2017) 344–361.

[26] W.C. Lee, J.W. Wu and W.B. 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

[27] W.C. Lee, J.W. Wu and J.W. Hsu, Computational algorithm for inventory model with a service level constraint, lead time demand with the mixture of distributions and controllable negative exponential backorder rate. Appl. Math. Comput. 175 (2006) 1125–1138. | MR | Zbl

[28] Y.J. Lin, An integrated vendor-buyer inventory model with backorder price discount and effective investment to reduce ordering cost. Comput. Ind. Eng. 56 (2009) 1597–1606. | DOI

[29] L.Y. Ouyang, N.C. Yeh and K.S. Wu, Mixture inventory model with backorders and lost sales for variable lead time. J. Oper. Res. Soc.47 (1996) 829–832. | DOI | Zbl

[30] L.Y. Ouyang, K.S. Wu and C.H. Ho, An integrated vendor-buyer inventory model with quality improvement and lead time reduction. Int. J. Prod. Econ. 108 (2007) 349–358. | DOI

[31] 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

[32] E.L. Porteus, Investing in reduced setups in the EOQ model. Manag. Sci. 31 (1985) 998–1010. | DOI | Zbl

[33] S. Priyan and R. Uthayakumar, Mathematical modeling and computational algorithm to solve multi-echelon multi-constraint inventoryproblem with errors in quality inspection. J. Math. Model. Algorithm Oper. Res. 14 (2015) 67–89. | DOI | MR | Zbl

[34] S. Priyan and R. Uthayakumar, Two-echelon multi-product multi-constraint product returns inventory model with permissible delay in payments and variable lead time. J. Manuf. Syst. 36 (2015) 244–262. | DOI

[35] S. Priyan and P. Manivannan, Optimal inventory modeling of supply chain system involving quality inspection errors and fuzzy defective rate. Opsearch 54 (2017) 21–43. | DOI | MR | Zbl

[36] M. Rabbani, N.P. Zia and H. Rafiei, Joint optimal dynamic pricing and replenishment policies for items with simultaneous quality and physical quantity deterioration. Appl. Math. Comput. 287 (2016) 149–160. | MR | Zbl

[37] M. Rabbani, H. Rezaei, M. Lashgari and H. Farrokhi-Asl, Vendor managed inventory control system for deteriorating items using metaheuristic algorithms. Decis. Sci. Lett. 7 (2018) 25–38. | DOI

[38] A.A. Taleizadeh, S.T.A. Niaki and F. Barzinpour, Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: a harmony search algorithm. Appl. Math. Comput. 217 (2011) 9234–9253. | MR | Zbl

[39] R.J. Tersine, Principles of Inventory and Materials Management (1994). | MR

[40] 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

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