Inventory models for production systems with constant/linear demand, time value of money, and perishable/non-perishable items

This research considers inventory systems for economic production models where the objective is to find the optimal cycle time, which minimizes the total cost, and optimal amount of shortage if it is allowed. Several aspects such as time value of money, inflation, constant and linear demand rates, shortages, and deterioration are considered in developing different models. Closed formulas are obtained for the optimal policy in one model. For others, more complex models where closed formulas cannot be obtained, search techniques are used to find the optimal solution.;First, a deterministic inventory control problem is considered for determination of optimal production quantities for an item with constant demand rate, while considering the effect of time value of money. Closed formulas are obtained to calculate the optimal cycle time and corresponding production quantity for the model without shortage. However, search procedures are used to find the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed.;In the next inventory control problem, a deterministic model for items with linear demand rate over time, for a finite planning horizon, while considering the effect of time value of money, is considered. Search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage.;A deterministic inventory control problem is also considered for items with constant rate of demand and exponentially decaying inventory over an infinite planning horizon, while considering the effect of time value of money. Two different search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage