Inventory model with variable demand rate under stochastic inflation for deteriorating and ameliorating items with permissible delay in payment

In this paper, an inventory policy for the production units is presented with stochastic inflation, variable demand rate, deteriorating and ameliorating items in warehouse and permissible delay in payment. Shortages, backlogging and lost sale, are allowable. Also, inflation is constantly changing due to economic, political, social and cultural issues in the real world and we assume it uniform distribution. The demand rate is depended on selling price and permissible delay in payment and increases as delay in payment increases, however, decreases as selling price increases. The objective function considers optimal pricing policy, the number of production cycles and time fraction without shortage. So, the purpose is to derive the optimal replenishment policy that minimises the net present value of total cost per unit time. The study shows that the optimal solution not only exists but also is unique. Finally, some numerical examples and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.