Inventory model with quantity discount, pricing and partial backlogging for a deteriorating items

Some products like fruits, vegetables, pharmaceuticals, volatile liquids, etc., deteriorate continuously due to evaporation, spoilage, obsolescence, etc. The objective of this study is to establish a deterministic inventory model with quantity discount, pricing and partial backordering when the product in stock deteriorates over time. Large number of retailers makes pricing decision of their products at certain times and these decisions affect demand. The demand rate is considered to be exponential price dependent. In this proposed model deterioration rate is taken as linear time dependent. Mathematical model is established to find optimal price, cycle and total profit. The second order approximation is used to obtain closed form optimal solution. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis is established with the variation of several parameters.