# zbMATH — the first resource for mathematics

An inventory model with generalized type demand, deterioration and backorder rates. (English) Zbl 1208.90007
Summary: This study is motivated by the paper of K. Skouri, I. Konstantaras, S. Papachristos and I. Ganas [Eur. J. Oper. Res. 192, No. 1, 79–92 (2009; Zbl 1171.90326)]. We extend their inventory model from ramp type demand rate and Weibull deterioration rate to arbitrary demand rate and arbitrary deterioration rate in the consideration of partial backorder. We demonstrate that the optimal solution is actually independent of demand. That is, for a finite time horizon, any attempt at tackling targeted inventory models under ramp type or any other types of the demand becomes redundant. Our analytical approach dramatically simplifies the solution procedure.

##### MSC:
 90B05 Inventory, storage, reservoirs
##### Keywords:
inventory model; deteriorating item; backlog rate
Full Text:
##### References:
 [1] Abad, P.L., Optimal pricing and lot-sizing under conditions of perishability and partial backordering, Management science, 42, 1093-1104, (1996) · Zbl 0879.90069 [2] Abad, P.L., Optimal price and order size for a reseller under partial backordering, Computer and operations research, 28, 53-65, (2001) · Zbl 0976.90001 [3] Chu, P.; Yang, K.L.; Liang, S.K.; Niu, T., Note on inventory model with a mixture of back orders and lost sales, European journal of operational research, 159, 470-475, (2004) · Zbl 1065.90002 [4] Dave, U., A deterministic lot-size inventory model with shortages and a linear trend in demand, Naval research logistics, 36, 507-514, (1989) · Zbl 0672.90037 [5] Deng, P.S., Improved inventory models with ramp type demand and Weibull deterioration, International journal of information and management sciences, 16, 4, 79-86, (2005) · Zbl 1103.90014 [6] Deng, P.S.; Lin, R.; Peter Chu, P., A note on the inventory models for deteriorating items with ramp type demand rate, European journal of operational research, 178, 112-120, (2007) · Zbl 1110.90006 [7] Dye, C.-Y.; Chang, H.-J.; Teng, J.-U., A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging, European journal of operational research, 1172, 417-429, (2005) · Zbl 1168.90328 [8] Giri, B.C.; Jalan, A.K.; Chaudhuri, K.S., Economic order quantity model with Weibull deterioration distribution, shortage and ramp-type demand, International journal of systems science, 34, 4, 237-243, (2003) · Zbl 1074.90505 [9] Henery, R.J., Inventory replenishment policy for increasing demand, Journal of the operational research society, 30, 611-617, (1979) · Zbl 0424.90019 [10] Hill, R.M., Inventory models for increasing demand followed by level demand, Journal of the operational research society, 46, 10, 250-1259, (1995) · Zbl 0843.90039 [11] Mandal, B.; Pal, A.K., Order level inventory system with ramp type demand rate for deteriorating items, Journal of interdisciplinary mathematics, 1, 49-66, (1998) · Zbl 0911.90142 [12] Manna, S.K.; Chaudhuri, K.S., An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages, European journal of operational research, 171, 2, 557-566, (2006) · Zbl 1090.90068 [13] Padmanabhan, G.; Vrat, P., Inventory model with a mixture of back orders and lost sales, International journal of system science, 21, 1721-1726, (1990) · Zbl 0715.90038 [14] Panda, S.; Saha, S.; Basu, M., An EOQ model with generalized ramp-type demand and Weibull distribution deterioration, Asia – pacific journal of operational research, 24, 1, 93-109, (2007) · Zbl 1137.90321 [15] Panda, S.; Senapati, S.; Basu, M., Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand, Computers and industrial engineering, 54, 2, 301-314, (2008) [16] Papachristos, S.; Skouri, K., An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type-backlogging, Operations research letters, 27, 175-184, (2000) · Zbl 1096.90518 [17] Resh, M.; Friedman, M.; Barbosa, L.C., On a general solution of the deterministic lot size problem with time-proportional demand, Operations research, 24, 718-725, (1976) · Zbl 0363.90044 [18] Sachan, R.S., On policy inventory model for deteriorating items with time proportional demand, Journal of the operational research society, 35, 1013-1019, (1984) · Zbl 0563.90035 [19] Skouri, K.; Konstantaras, I.; Papachristos, S.; Ganas, I., Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate, European journal of operational research, 192, 1, 79-92, (2009) · Zbl 1171.90326 [20] Teng, J.T., A deterministic replenishment model with linear trend in demand, Operations research letters, 19, 33-41, (1996) · Zbl 0865.90038 [21] Teng, J.T.; Chang, H.J.; Dye, C.Y.; Hung, C.H., An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging, Operations research letters, 30, 387-393, (2002) · Zbl 1013.90006 [22] Wee, H.M., Joint pricing and replenishment policy for deteriorating inventory with declining market, International journal of production economics, 40, 163-171, (1995) [23] Wu, J.W.; Lin, C.; Tan, B.; Lee, W.C., An EOQ model with ramp type demand rate for items with Weibull deterioration, International journal of information and management sciences, 10, 41-51, (1999) · Zbl 0963.90009 [24] Wu, K.S.; Ouyang, L.Y., A replenishment policy for deteriorating items with ramp type demand rate, Proceeding of national science council ROC (A), 24, 279-286, (2000) [25] Wu, K.S., An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging, Production planning and control, 12, 787-793, (2001) [26] Wu, K.S.; Ouyang, L.Y.; Yang, C.T., Retailerâ€™s optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate, International journal of information and management sciences, 19, 245-262, (2008) · Zbl 1152.90327
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.