Reorder Level
`
Additional assumption:
Lead time is known and constant
`
No need to carrying stock from one cycle to the next
`
So each order should be scheduled to arrive as existing stock runs
out
Reorder level = demand during lead time = lead time x demand per unit time
ROL = LT x D
Revisit Ex 1: Carpet Sell. Given that product lead time is 5 days. Calculate reorder
level
1 (ROL)
Reorder Level with Longer Lead Time
When lead time is longer than the stock cycle
There is always one order outstanding.
Example:
`
`
`
when it is time to place order B, there is one order, A
outstanding and due to arrive before B.
` The stock on hand plus the outstanding order must be enough
to last until B arrive or equal the lead time demand
`
ROL
Stock on hand
ROL
2
=
+
LT x D
Stock on order
-
Stock on order
=
LT x D
Reorder Level with Longer Lead Time
When lead time is very long
Several orders are outstanding at anytime
When lead time is between n and n+1 cycle length
`
`
`
n x T < LT < (n+1) x T
ROL
3
There are n orders
outstanding
=
Lead time demand
-
Stock on order
=
LT x D
-
n x Qo
Ex 2
Demand for an item is steady at 1,200 units a year
with an ordering cost of $16 and holding cost of
$0.24 per unit per year. Describe a appropriate
ordering policy if the lead time is constant at
(a)
(b)
(c)
4
3 months
9 months
18 months
Discussion Questions
What are the benefit of short lead times? How can
these be achieved in practice?
5
IM 322
Inventory Management
Chapter 4 Models for Known Demand
-6-
Textbook:
Donald Waters, Inventory Control and Management, 2nd
ed
Chapter Outline
Extension of EOQ by relaxing
some assumptions
1.
2.
3.
4.
7
Discount in the unit cost /
price from suppliers
Increasing cost with higher
quantity
Finish replenishment rate
Back orders
Price Discount from Suppliers
Costs vary with the quantity ordered (Q)
8
Price Discount from Suppliers
Price discount for higher
quantity orders
`
P = Unit price of item
`
Example:
Quantity (Q)
0 - 100
101 - 200
201 or more
Unit Price
$10
$8
TC (P1 = $10 )
TC (P2 = $8 )
Inventory cost ($)
`
TC (P3 = $6 )
holding cost
$6
Reordering cost
Q(P2 ) = 100 Qopt Q(P3 ) = 200
9
Start
1. Take the next lowest
unit cost
2. Find the lowest point
using EOQ equation
4. Calculate the cost at
the break point
NO
3. Is this point
valid?
YES
5. Calculate the cost at
this valid minimum
6. Compare the costs of
all the points considered
7. Find the lowest cost
and corresponding Q
10
End
Procedure for Finding
Best Order Size
Price Discount from Suppliers:
Finding the lowest valid cost
Case 1: All costs are constant except the unit cost (or
unit price from supplier)
`
Qo will be calculated using EOQ formula
`
Qo could be either
Qo =
2 × RC × D
HC
`
Valid minimum: within the range of valid order quantities for this
particular unit cost
`
Invalid minimum: falls outside the valid order range for this particular
unit cost
11
Ex 1a: Sweatshirt in Bookstore
The university bookstore purchases sweatshirts with school
logo from a vendor. The vendor sells the sweatshirts to the
store for $38 a piece. The cost to bookstore for placing an
order is $120, and the annual carrying cost is estimated as
$9.5 per unit. 1700 sweatshirts are estimated to be sold
during the year. The vendor has offered the bookstore the
following volume discount:
Order Size
Discount
1-299
300-499
500-799
800 and up
0%
2%
4%
5%
What is an optimal order quantity?
12
Price Discount from Suppliers:
Finding the lowest valid cost
Case 2: All costs are constant except the unit cost (or
unit price from supplier) and holding cost
`
Holding cost can be expressed a
proportion of the unit cost (I)
`
For each unit cost (UCi), the minimum
point of the cost curve comes with Qoi
`
Qoi for each curve could be either
`
Valid minimum: within the range of valid
order quantities for this particular unit cost
`
Invalid minimum: falls outside the valid order
range for this particular unit cost
13
Qo =
Qo i =
2 × RC × D
HC
2 × RC × D
I × UCi
Ex 1b: Sweatshirt in Bookstore
The university bookstore purchases sweatshirts with school
logo from a vendor. The vendor sells the sweatshirts to the
store for $38 a piece. The cost to bookstore for placing an
order is $120, and the annual carrying cost is 25% of the
cost of sweatshirt. 1700 sweatshirts are estimated to be sold
during the year. The vendor has offered the bookstore the
following volume discount:
14
Order Size
Discount
1-299
300-499
500-799
800 and up
0%
2%
4%
5%
What is an optimal order quantity?
Rising cost with larger quantity
15
Ex 2 Rising delivery cost
Kwok Cheng Ho makes a range of high
quality garden ornaments. On average
day he uses 4 tons of fine grain sand.
This sand costs $20 a ton to buy, and
$1.90 a ton to store for a day.
Deliveries are made by modified lorries that
carry up to 15 tons, and each delivery of
a load or part load costs $200.
Find the cheapest way to ensure
continuous supplies of sand
16
Inventory Level
Finish
replenishment
rate
Production quantity
Q
Demand during
production interval
Imax
Maximum inventory
D
P–D
Time
17
Production
and demand
(PT)
T
Demand
only
(DT)
CASE 1
CASE 3
CASE 3
CASE 3
CASE 1, CASE 2, CASE 3
EX 2