Lead time and ordering cost reductions in budget and storage space restricted probabilistic inventory models with imperfect items

Gholami-Qadikolaei, Aref; Mirzazadeh, Abolfazl; Tavakkoli-Moghaddam, Reza

RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 2, pp. 215-242.

Regarding today’s business environment restrictions, one of significant concern of inventory manager is to determine optimal policies of inventory/production systems under some restrictions such as budget and storage space. Therefore here, a budget constraint on total inventory investment and a maximum permissible storage space constraint are added simultaneously to a stochastic continuous review mixed backorder and lost sales inventory system. This study also assumes that the received lot may contain some defective units with a beta-binomial random variable. Two lead time demand (LTD) distribution approach are proposed in this paper, one with normally distributed demand and another with distribution free demand. For each approach, a Lagrange multiplier method is applied in order to solve the discussed constrained inventory models and a solution procedure is developed to find optimal values. This study, also, shows that the respective budget and storage space constrained inventory models to be minimized are jointly convex in the decision variables. Numerical examples are also presented to illustrate the models.

Classification : 90B05, 90C15, 90C30, 90C47
Mots clés : Stochastic inventory system, lead time, inventory constraints, minimax distribution free procedure, imperfect items, ordering cost reduction, Lagrange multiplier method

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 S.M. Noman, Integrated inventory and inspection policies for stochastic demand. Euro. J. Oper. Res. 185 (2008) 159–169. | DOI | Zbl

P. Billington, The classic economic production quantity model with set up cost as a function of capital expenditure. Decision Sci. 18 (1987) 25-42. | DOI

R.G. Brown and G. Gerson, Decision rules for inventory management, Holt, Rinehart and Winston, New York (1967).

U.K. Bera, M. Rong, N.K. Mahaparta and M. Maiti, A multi-item mixture inventory model involving random lead time and demand with budget constraint and surprise function. Appl. Math. Model. 33 (2009) 4337–4344. | DOI | Zbl

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

C. Chandra and J. Grabis, Inventory management with variable lead-time dependent procurement cost. Omega 36 (2008) 877–887. | DOI

H.C. Chang, An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput. Oper. Res. 31 (2004) 2079–2092. | DOI | Zbl

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

B.R. Chaung, L.Y. Ouyang and K.W. Chaung, A note on periodic review inventory model with controllable setup cost and lead time. Comput. Oper. Res. 31 (2004) 549–561. | DOI | Zbl

G. Gallego and I. Moon, The distribution of free news boy problem: review and extension. J. Oper. Res. Soc. 44 (1993) 825–834. | DOI | Zbl

C.H. 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. 136 (2012) 37–44. | DOI

R.W. Hall, Zero inventories, Dow Jones Irwin, Homewood, Illinois (1983).

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

M. Hariga and M. Ben-Daya, Some stochastic inventory models with deterministic variable lead time. Eur. J. Oper. Res. 113 (1999) 42–51. | DOI | Zbl

C.J. Liao and C.H. Shyu, An analytical determination of lead time with normal demand. Int. J. Prod. Manage. 11 (1991) 72–78.

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

S.W. Lin, Y.W. Wou and P. Julian, Note on minimax distribution free procedure for integrated inventory model with defective goods and stochastic lead time. Appl. Math. Model. 35 (2011) 2087–2093. | DOI | Zbl

I. Moon and G. Gallego, Distribution free procedures for some inventory models. J. Oper. Res. Soc. 45 (1994) 651–658. | DOI | Zbl

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

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

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

M.J. Paknejad, F. Nasri and J.F. Affiso, Defective units in a continuous review (s,Q) system. Int. J. Prod. Res. 33 (1995) 2767–2777. | DOI | Zbl

K.L. Kim and J.C. Haya, Setup reduction in economic quantity production model. Decision Sci. 23 (1992) 500–508. | DOI

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

B.R. Sarker, E.R. Coates, Manufacturing setup cost reduction under variable lead times and finite opportunities for investment. Int. J. Prod. Econ. 49 (1997) 237–247. | DOI

K.S. Wu, I.C. Lin, Extend (Q,r) inventory model under lead time and ordering cost reductions when receiving quantity is different from the ordered quantity. Quality and Quantity 38 (2004) 771–786. | DOI

J.W. Wu, W.C. Lee and H.Y. Tsai, Computational algorithmic procedure of optimal inventory policy involving a negative exponential crashing cost and variable lead time. Appl. Math. Comput. 184 (2007) 798–808. | Zbl

S.M. Ross, Stochastic processes. 2$nd$ edition, Wiley, New York (1996). | Zbl

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

D.A. Schrady and U.C. Choe, Models for multi-item inventory continuous review inventory policies subject to constraints. Nav. Rese. Logist. 18 (1971) 451–464. | DOI | Zbl

J. Taheri-Tolgari, A. Mirzazadeh and F. Jolai, An inventory model for imperfect items under inflationary conditions with considering inspection errors. Comput. Math. Appl. 63 (2012) 1007–1019. | DOI | Zbl

R.J. Tersine, Principle of Inventory and Material Management. 4th edition, Prentice-Hall, USA (1994).