Inventory model of deteriorating items with two-warehouse and stock dependent demand using genetic algorithm in fuzzy environment

Authors

  • Dharmendra Yadav Department of Mathematics, Keshav Mahavidyalaya, Delhi, India
  • S.R. Singh Department of Mathematics, D.N (P.G.) College, Meerut (U.P) India
  • Rachna Kumari Department of Mathematics, Meerut College, Meerut (U.P) India

DOI:

https://doi.org/10.2298/YJOR100219005Y

Keywords:

possibility/necessity measures, inflation, time value of money, deterioration, genetic algorithm

Abstract

Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example.

References

Roy, A., Maiti, M.K., Kar, S., and Maiti, M., “Two storage inventory model with fuzzy deterioration over a random planning horizon”, Mathematical and Computer Modelling, 46 (2007) 1419-1433.

Giri, B.C., and Chaudhuri, K.S., “Deterministic models of perishable inventory with stock dependent demand rate and non-linear holding cost”, European Journal of Operational Research, 19 (1998) 1267–1274.

Mandal, B.N., and Maiti, M., “An inventory model for deteriorating items and stock dependent consumption rate”, Journal of the Operational Research Society, 40 (1989) 483-488.

Giri, C., Pal, S., Goswami, A., and Chaudhuri, K.S., “An inventory model for deteriorating items with stock dependent demand rate”, European Journal of Operational Research, 95 (1996) 604-610.

Dubois, D., and Prade, H., “Ranking fuzzy numbers in the setting of possibility theory”, Information Sciences, 30 (1983) 183-224.

Dubois, D., and Prade, H., “The three semantics of fuzzy sets”, Fuzzy Sets and Systems, 90 (1997) 141-150.

Yadav, D., Singh, S.R., and Kumari, R., “A fuzzy multi-item production model with reliability and flexibility under limited storage capacity with deterioration via geometric programming”, International Journal of Mathematics in Operational Research, 3 (1) (2011) 78-98.

Schrader, G.P., and Ghare, P.M., “A model for exponentially decaying inventory”, Journal of Industrial Engineering, 14 (1963) 238–243.

Katagiri, H., Sakawa, M., Kato, K., and Nishizaki, I., “A fuzzy random multiobjective 0-1 programming based on the expectation optimization model using possibility and necessity measures”, Mathematical and Computer Modelling, 40 (2004) 411-421.

Liao, H.C., Tsai, C.H., and Su, C.T., “An inventory model with deteriorating items under inflation when a delay in payment is permissible”, International Journal of Production Economics, 63 (2000) 207-214.

Yang, H.L., “Two-Warehouse inventory models for deteriorating items with shortages under inflation”, European Journal of Operational Research, 157 (2004) 344-356.

Buzacott, J.A., “Economic order quantities with inflation”, Operational Research Quarterly, 26 (1975) 553–558.

Maity, K., and Maity, M., “Production inventory system for deteriorating multi-item with inventory-dependent dynamic demands under inflation and discounting”, Tamsui Oxford Journal of Management Sciences, 21 (2005) 1-18.

Chung, K.J., and Lin, C.N., “Optimal inventory replenishment models for deteriorating items taking account of time discounting”, Computers and Operations Research, 28 (2001) 67-83.

Chung, K.J., and Liao, J.J., “The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity”, International Journal of Production Economics, 100 (2006) 116-130.

Benkherouf, L.A., “Deterministic order level inventory model for deteriorating items with two storage facilities”, International Journal of Production Economics, 48 (1997) 167–175.

Zadeh, L.A., “Fuzzy sets as a basis for a theory of possibility”, Fuzzy Sets and Systems, 1 (1978) 3-28.

Ouyang, L.Y., Teng, J.T., Goyal, S.K., and Yang, C.T., “An economic order quantity model for deteriorating items with partially permissible delay in payment linked to order quantity”, European Journal of Operational Research, 194 (2009) 418-431.

Hariga, M.A., “Effects of inflation and time value of money on an inventory model with time dependent demand rate and shortage”, European Journal of Operational Research, 81 (1995) 512-520.

Mandal, M., and Maiti, M., “Inventory of damageable items with variable replenishment and stock-dependent demand”, Asia Pacific Journal of Operational Research, 17 (2000) 41-54.

Rang, M., Mahapatra, N.K., and Maiti, M., “A two warehouse inventory model for a deteriorating item with partially/fully backlogged shortage and fuzzy lead time”, European Journal of Operational Research, 189 (2008) 59-75.

Maiti, M.K., and Maiti, M., “Fuzzy inventory model with two warehouse under possibility constraints”, Fuzzy Sets and Systems, 157 (2006) 52-73.

Maiti, M.K., and Maiti, M., “Two storage inventory model with lot size dependent fuzzy lead time under possibility constraints via genetic algorithm”, European Journal of Operational Research, 179 (2007) 352-371.

Chen, M.S., Yang, H.L., Teng, J.T., and Papachristos, S., “Partial backlogging inventory lot size models for deteriorating items with fluctuating demand under inflation”, European Journal of Operational Research, 191 (2008) 127-141.

Mandal, N.K., Roy, T.K., and Maiti, M., “Multi-objective fuzzy inventory model with three constraints: A geometric programming approach”, Fuzzy Sets and Systems, 150 (2005) 87-106.

Misra, R.B., “Optimum production lot-size model for a system with deteriorating inventory”, International Journal of Production Research, 13 (1975) 495–505.

Misra, R.B., “A note on optimal inventory management under inflation”, Naval Research Logistics, 26 (1979) 161–165.

Levin, R.I., McLaughlin, C.P., Lamone, R.P., and Kottas, J.F., Production/Operation Management: Contemporary Policy for Managing Operation System, McGraw-Hill, New York, 1972.

Covert, R.P., and Philip, G.C., “An EOQ model for item with Weibull distribution deterioration”, AIIE Transactions, 5 (1973) 323–326.

Kar, S., Bhunia, A.K., and Maiti, M., “Inventory of multi-deteriorating items sold from two shops under single management with constraints on space and investment”, Computers & Operations Research, 28 (2001) 1203–1221.

Mandal, S., Maity, K., Mondal, S., and Maiti, M., “Optimal production inventory policy for defective items with fuzzy time period”, Applied Mathematical Modelling, 34 (2010) 810-822.

Goyal, S.K., and Gunasekaran, A., “An integrated production inventory marketing model for deteriorating item”, Computers & Industrial Engineering, 28 (1995) 755–762.

Goyal, S.K., and Chang, C.T., “Optimal ordering and transfer policy for an inventory with stock-dependent demand”, European Journal of Operational Research, 196 (1) (2009) 177-185.

Goyal, S.K., and Giri, B.C., “Recent trends in modeling of deteriorating inventory”, European Journal of Operational Research, 134 (2001) 1–16.

Urban, T.L., “An inventory model with an inventory level dependent rate and related terminal conditions”, Journal of Operational Research Society, 43 (1992) 721-724.

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Published

2012-03-01

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Research Articles