# zbMATH — the first resource for mathematics

Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale. (English) Zbl 1208.90005
Summary: The paper describes an EOQ model of a perishable product for the case of price dependent demand, partial backordering which depends on the length of the waiting time for the next replenishment, and lost sale. The model is solved analytically to obtain the optimal price and size of the replenishment. In the model, the customers are viewed to be impatient and a fraction of the demand is backlogged. This fraction is a function of the waiting time of the customers. In most of the inventory models developed so far, researchers considered that inventory accumulates at the early stage of the inventory and then shortage occurs. This type of inventory is called IFS (inventory followed by shortage) policy. In the present model we consider that shortage occurs before the starting of inventory. We have proved numerically that instead of taking IFS, if we consider SFI (shortage followed by inventory) policy, we would get better result, i.e., a higher profit. The model is extended to the case of non-perishable product also. The optimal solution of the model is illustrated with the help of a numerical example.

##### MSC:
 90B05 Inventory, storage, reservoirs
Full Text:
##### References:
 [1] Montgomery, D.C.; Bazaraa, M.S.; Keswari, A.K., Inventory model with a mixture of backorders and lost sales, Naval research logistic quarterly, 20, 255-263, (1973) · Zbl 0262.90020 [2] Park, K.S., Another inventory model with a mixture of backorders and lost sales, Naval research logistic quarterly, 30, 397-400, (1983) · Zbl 0528.90017 [3] Mak, K.L., Determining optimal production inventory control policies for an inventory system with partial backlogging, Computers and operations research, 27, 299-304, (1986) · Zbl 0633.90015 [4] Chang, H.J.; Dye, C.Y., An EOQ model for deteriorating items with time varying demand and partial backlogging, International journal of operational research society, 50, 1176-1182, (1999) · Zbl 1054.90507 [5] Abad, P.L., Optimal lot size for a perishable goods under conditions of finite production and partial backordering and lost Sale, Computers and industrial engineering, 38, 457-465, (2000) [6] Abad, P.L., Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost Sale, European journal of operational research, 144, 677-685, (2003) · Zbl 1012.90002 [7] Ghosh, S.K.; Chaudhuri, K.S., An EOQ model for a deteriorating item with trended demand and variable backlogging with shortages in all cycles, International journal of advanced modeling and optimization, 7, 1, 57-68, (2005) · Zbl 1157.90311 [8] Raafat, F., Survey of literature on continuously deteriorating inventory models, Journal of the operational research society, 42, 27-37, (1991) · Zbl 0718.90025 [9] Rubin, P.A.; Dilts, D.M.; Barron, B.A., Economic order quantity with quantity discounts: grandma does it best, Decision sciences, 14, 270-279, (1983) [10] Das, C., A unified approach to the price break economic order quantity (EOQ) problem, Decision sciences, 15, 350-358, (1984) [11] Monahan, J.P., A quantity discount pricing model to increase vendor profits, Management sciences, 30, 720-726, (1984) [12] Tersine, R.J.; Toelle, R.A., Lotsize determination with quantity discounts, Production and inventory management, 27, 1-22, (1985) [13] Kim, K.H.; Hwang, H., An incremental discount pricing schedule with multiple customers and single price break, European journal of operational research, 35, 71-78, (1988) [14] Hwang, H.; Moon, D.H.; Shine, S.W., An EOQ model with quantity discounts for both purchasing price and freight cost, Computers and operations research, 17, 38-73, (1990) · Zbl 0682.90032 [15] Burwell, T.H.; Dave, D.S.; Fitzpatrick, K.E.; Roy, M.R., An inventory model with planned shortages and price-dependent demand, Decision sciences, 27, 1188-1191, (1991) [16] Giri, B.C.; Chakrabarti, T.; Chaudhuri, K.S., Retailerâ€™s optimal policy for a perishable product with shortages when supplier offers all-unit quantity and freight cost discount, Proceeding of the national Academy of science, 69, A, 315-326, (1999) · Zbl 1004.91023 [17] Jalan, A.K.; Chaudhuri, K.S., A note on a multi-product EOQ model for deteriorating items with pricing consideration and shortages, International journal of management and systems, 16, 183-194, (2000) [18] Mukhopadhyay, S.; Mukherjee, R.N.; Chaudhuri, K.S., Joint pricing and ordering policy for a deteriorating inventory, Computers and industrial engineering, 47, 339-349, (2004) [19] Sana, S.S., Optimal selling price and lot size with time varying deterioration and partial backlogging, Applied mathematics and computations, 217, 1, 185-194, (2010) · Zbl 1231.90055 [20] You, P.S.; Wu, M.T., Optimal ordering and pricing policy for an inventory system with order cancellation, OR spectrum, 4, 661-679, (2007) · Zbl 1168.90341 [21] Taleizadeh, A.A.; Wee, H.M.; Sadjadi, S.J., Multiproduct production quantity model with repair failure and partial backordering, Computers and industrial engineering, 59, 1, 45-54, (2010) [22] Goyal, S.K.; Gunasekaran, A., An integrated production-inventory-marketing model for deteriorating items, Computer and industrial engineering, 28, 755-762, (1995) [23] Luo, W., An integrated inventory system for perishable goods with backordering, Computer and industrial engineering, 34, 685-693, (1998) [24] Goyal, S.K.; Morin, D.; Nabebe, F., The finite horizon trended inventory replenishment problem with shortages, Journal of the operational research society, 43, 1173-1178, (1992) · Zbl 0762.90021 [25] Bazarra, M.; Sherali, H.; Shetty, C.M., Nonlinear programming, (1993), Wiley New York
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.