# Deterministic Inventory Models

## Abstract

In this chapter, we discuss mathematical models to manage inventory of a single item whose demand is known and is constant. We start our discussion with the most fundamental of inventory models – the Economic Order Quantity (EOQ) model – which assumes that the demand for the item is constant, the order is filled instantaneously, and there are no shortages. We derive an expression for the total annual inventory cost (TIC) comprising the ordering cost, carrying cost, and the cost of procurement, and determine the optimal order quantity that minimizes the TIC. We also discuss computation of the reorder level when lead time is assumed to be constant and known. Later in this chapter, we discuss extensions of the EOQ model to other situations where supply is not instantaneous (i.e., supply is gradual), and another where planned shortages are allowed. Toward the end of this chapter, we also discuss a periodic review model under certainty.

## Keywords

Economic order quantity Total inventory cost Replenishment policy Gradual replenishment Planned shortages## References

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