# EPQ: Economic Production Quantity model In SCperf: Functions for Planning and Managing Inventories in a Supply Chain

## Description

Implements the Economic Production Quantity (EPQ) model.

## Usage

 `1` ```EPQ(d, p, k, h, b = 0) ```

## Arguments

 `d` Deterministic demant per time unit `p` Production rate `k` Ordering or fixed cost per order. `h` Holding cost per unit of product. `b` Shortage penalty cost per unit (default:0).

## Details

The EPQ model is an extension of the `EOQ` model. It considers finite production rate, that is, the inventory is replenished gradually as the order is produced. Note that this assumption requires the production rate to be greater than the demand rate (p>d) otherwise there would be no inventory at any time.

The model considers that a new order is produced incrementally when the inventory reaches zero. During the time that production run, t=Q/p, inventory is accumulated at rate p-d, which implies that when the production of the batch Q is finished the inventory will reach its maximum level I.

## Value

`EPQ()` returns a list containing:

 `Q` Order quantity `t` Time required to produce the batch quantity `T` Time between orders (cycle length or time) `I` Maximum inventory level `TC` Total cost

## References

- Gallego, G. "IEOR4000: Production Management" (Lecture 2), Columbia (2004).

 ```1 2 3 4 5 6 7 8``` ``` ## Not run: #Suppose k = 100, h = 5, d = 200, p = 1000. Then the production run at #t=0.1, the optimal order interval is T = 0.5, the optimal order quantity #is Q = 100, the maximum inventory level is I=80 and the total cost is #TC = \$400. ## End(Not run) EPQ(d=200,p=1000,k=100,h=5) ```