In this study, a volume flexible inventory system for deteriorating items with stock & time dependent demand has been developed over a finite planning horizon. Shortages are permitted with partial backorder. Uncertainties are inherent in real inventory problems due to complexities of market situation. This uncertainty can be handled by the concept of randomness. As a result, backorder rate is taken as random and follows a probability distribution. All the costs are influenced by the learning effect. The optimal number of production cycles that minimize the total cost is considered. Numerical illustrations together with sensitivity analysis are given to elucidate the model. Furthermore, the numerical results of the finite planning horizon model have been plotted graphically.