SCperf (version 1.1.1)

EPQ: Economic Production Quantity model

Description

Implements the Economic Production Quantity (EPQ) model.

Usage

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).

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

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.

References

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

See Also

EOQ, newsboy, WW

Examples

# NOT RUN {
 
# }
# 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.
# }
# NOT RUN {
 
EPQ(d=200,p=1000,k=100,h=5)

# }