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Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging. (English) Zbl 1255.90019
Summary: We consider a joint pricing and inventory control model for non-instantaneously deteriorating items with permissible delay in payments. We adopt a demand function which is dependent on the price and time. Shortage is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that the total profit is maximized. On the basis of the aforementioned assumptions, for any given selling price, we first establish conditions for an optimal replenishment schedule to exist and be unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm for finding the optimal solution. Finally, to illustrate the solution procedure and the algorithm, we solve a numerical example.

##### MSC:
 90B05 Inventory, storage, reservoirs
Full Text:
##### References:
 [1] Wee, H.M., Economic production lot size model for deteriorating items with partial back-ordering, Computers and industrial engineering, 24, 449-458, (1993) [2] Ghare, P.M.; Schrader, G.H., A model for exponentially decaying inventory system, International journal of production research, 21, 449-460, (1963) [3] Covert, R.P.; Philip, G.C., An EOQ model for items with Weibull distribution deterioration, AIIE transactions, 5, 323-326, (1973) [4] Goyal, S.K.; Giri, B.C., Recent trends in modeling of deteriorating inventory, European journal of operational research, 134, 1-16, (2001) · Zbl 0978.90004 [5] Geetha, K.V.; Uthayakumar, R., Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments, Journal of computational and applied mathematics, 223, 2492-2505, (2010) · Zbl 1183.90019 [6] Abad, P.L., Optimal pricing and lot sizing under conditions of perishability and partial backordering, Management science, 42, 1093-1104, (1996) · Zbl 0879.90069 [7] Abad, P.L., Optimal price and order size for a reseller under partial backordering, Computers and operations research, 28, 53-65, (2001) · Zbl 0976.90001 [8] Dye, C.Y., Joint pricing and ordering policy for a deteriorating inventory with partial backlogging, Omega, 35, 184-189, (2007) [9] Chang, H.J.; Teng, J.T.; Ouyang, L.Y.; Dye, C.Y., Retailerâ€™s optimal pricing and lot-sizing policies for deteriorating items with partial backlogging, European journal of operational research, 168, 51-64, (2006) · Zbl 1077.90002 [10] Wu, K.S.; Ouyang, L.Y.; Yang, C.T., An optimal replenishment policy for non-instantaneous deteriorating items with stock dependent demand and partial backlogging, International journal of production economics, 101, 369-384, (2006) [11] Yang, C.T.; Ouyang, L.Y.; Wu, H.H., Retailers optimal pricing and ordering policies for non-instantaneous deteriorating items with price-dependent demand and partial backlogging, Mathematical problems in engineering, 2009, (2009) · Zbl 1177.90030 [12] Ouyang, L.Y.; Wu, K.S.; Yang, C.T., A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments, Computers & industrial engineering, 51, 637-651, (2006) [13] Chung, K.-J., A complete proof on the solution procedure for non-instantaneous deteriorating items with permissible delay in payment, Computers & industrial engineering, 56, 267-273, (2009) [14] Tsao, Y.C.; Sheen, G.J., Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments, Computers & operations research, 35, 3562-3580, (2008) · Zbl 1140.91358
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