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The Economic Order Quantity (EOQ) model, a fundamental concept in inventory management that helps organizations determine the optimal order quantity to minimize total costs. It covers the EOQ formula, its assumptions, and the trade-off between setup and holding costs. The document also explores the impact of demand, lead time, and production rate on inventory levels and the total cost curve. Additionally, it presents a quantity discount schedule and steps for analyzing it. Examples and figures are included to illustrate the concepts.
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A Items
B Items C Items Percent of annual dollar usage
80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 10 20 30 40 50 60 70
Percent of inventory items (^) Figure 12.
Figure 12.
Order quantity = Q (maximum inventory level)
Inventory level
Time
Usage rate Average inventory on hand Q 2
Minimum inventory
#
Table 11.
Annual cost
Order quantity
Curve for total cost of holding and setup
Holding cost curve
Setup (or order) cost curve
Minimum total cost
Optimal order quantity
$
_Q = Number of pieces per order Q = Optimal number of pieces per order (EOQ) D = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year_*
Annual setup cost = ( Number of orders placed per year ) x ( Setup or order cost per order )
Annual demand Number of units in each order
Setup or order = cost per order
= DQ ( S )
Annual setup cost = DQS
$
_Q = Number of pieces per order Q = Optimal number of pieces per order (EOQ) D = Annual demand in units for the Inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year_*
Annual holding cost = ( Average inventory level ) x ( Holding cost per unit per year )
Order quantity = 2 ( Holding cost per unit per year )
= Q 2 ( H )
Annual setup cost = DQS Annual holding cost = Q 2 H
%
Determine optimal number of needles to order D = 1,000 _units Q_* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year
Expected time between orders
Number of working days per year N
T = = 50 days between orders
%
Determine optimal number of needles to order D = 1,000 _units Q_* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost
TC = DS + H Q
&
The EOQ model is robust
It works even if all parameters and assumptions are not met
The total cost curve is relatively flat in the area of the EOQ
'
Number of working days in a year
'
_Q_*
ROP Inventory level (units)(units)
Figure 12.5^ Time (days) Lead time = L
Slope = units/day = d
' %
Demand = 8,000 DVDs per year 250 working day year Lead time for orders is 3 working days
ROP = d x L
d = D Number of working days in a year
= 8,000/250 = 32 units
= 32 units per day x 3 days = 96 units
'
Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days
inventory level^ Maximum^ =^^ Total produced duringthe production run – the production run^ Total used during = pt – dt However, Q = total produced = pt ; thus t = Q/p
Maximum inventory level = p^ – d^ = Q^ 1 –
Q p
Q p
d p
Holding cost = Maximum inventory level 2 ( H ) = Q 2 1 – dp H
'
Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate D = Annual demand
Setup cost = ( D / Q ) S Holding cost = 1/2 HQ [1 - ( d / p )]
( D / Q ) S = 1/2 HQ [1 - ( d / p )]
Q^2 =
H [1 - ( d / p )]
Q *** =** (^) H [1 - (^2 DSd / p )]
'
%
D = 1,000 units p = 8 units per day S = $10 d = 4 units per day H = $0.50 per unit per year
H [1 - ( d / p )]
= 282.8 or 283 hubcaps
'
When annual data are used the equation becomes
annual demand rate annual production rate
(
Total cost = Setup cost + Holding cost + Product cost
(
5
4 4 7 4 &6( &(
4 8 1
Table 12.
3
"
7
4 8 1
Table 12. Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit
