Supply Chain Logistics

1. Supply Chain : Logistics
Week 5
Inventory Management Problem

2. Introduction
• Inventory is an idle resources (idle resources)
whose existence is awaiting further
processing.
• further processing here can be found in
production activities such as manufacturing
activities, marketing activities were found in
the distribution system, or consumption
activities such as found in household
systems, offices, and so on.

3. Introduction
Two Problems on the Inventory System:
• Policy Issues Inventory (inventory policy) is a
problem in the system supplies related to how to
ensure that every user requests can be met with
minimal costs.
• Operational issues, more qualitative and principally
related to the issue smoothness and efficiency
mechanisms and operating procedures inventory
system

4. Basic EOQ model
• Receive an order
• Use the inventory at a constant rate
• Reorder same amount
• Instantaneously receive the order

5. Economic Order Quantity
On-hand
inventory
(units)
Time

6. Economic Order Quantity
On-hand
inventory
(units)
Time

7. Economic Order Quantity
On-hand
inventory
(units)
Time
Receive
order
Q

8. Economic Order Quantity
On-hand
inventory
(units)
Time
Receive
order
Q
1 cycle

9. Economic Order Quantity
On-hand
inventory
(units)
Time
Receive
order
Q
1 cycle

10. Economic Order Quantity
On-hand
inventory
(units)
Time
Receive
order
Inventory depletion
(demand rate)
Q
1 cycle

11. Economic Order Quantity
On-hand
inventory
(units)
Time
Receive
order
Inventory depletion
(demand rate)
Q
1 cycle

12. Economic Order Quantity
On-hand
inventory
(units)
Time
Average
cycle
inventory
Q
Q
—
2
1 cycle
Receive
order
Inventory depletion
(demand rate)

13. Total Cost = Holding Cost + Order Cost

14. Total Cost = Holding Cost +
Order Cost
Annual
cost
(dollars)
Lot Size (Q)

15. Annual
cost
(dollars)
Lot Size (Q)
Holding cost (HC)
Total Cost = Holding Cost + Order Cost

16. • More units must be stored if more are ordered
Purchase Order
Description Qty.
Microwave 1
Order quantity
Purchase Order
Description Qty.
Microwave 1000
Order quantity
Why Holding Costs Increase

17. Annual
cost
(dollars)
Lot Size (Q)
Holding cost (HC)
Ordering cost (OC)
Total Cost = Holding Cost + Order Cost

18. • If we order more when we place an
order, then we order fewer times over
the year.
• Example: You expect to order 10
microwave ovens over a year for a retail
store like Sears. It cost $10 to place an
order.
Why Order Costs Decrease
Order Cost $10
Purchase Order
Description Qty.
Microwave 10
Order cost $10
Purchase Order
Description Qty.
1
Microwave
 If you order 1 microwave, how many
orders will you place over the year?
what is the ordering cost? What is the
ordering cost per microwave?
 If you order 10 microwaves, how many
orders will you place over the year?
What is the ordering cost? What is the
ordering cost per microwave?

19. Annual
cost
(dollars)
Lot Size (Q)
Ordering cost (OC)
Holding cost (HC)
Total cost = HC + OC
Total Cost = Holding Cost + Order Cost

20. Gift Shop
• A museum of natural history is having
problems managing their inventories. Low
inventory turnover is squeezing profit margins
and causing cash-flow problems.
• A Class A item, a birdfeeder is also a top-
selling item.
– Sales: 18 units/week
– Purchase cost: $60
– Order cost: $45
– Annual holding cost: 25% of purchase cost
– 52-week year
• Management has been ordering in lots of 390
units.

21. • Q – order quantity
• TC – Total cost
– Annual
– Monthly
– ??
What is the annual cost
of the current policy?
Time
Q

22. Holding Cost
H
Q
Cost
Holding
Annual 






2
)
/
/
)(
( year
unit
Cost
Holding
Inventory
Ave
Cost
Holding
Annual 

23. Holding cost
| | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Holding cost = (H)
Q
2
Annual
cost
(dollars)

24. Ordering cost
)
(OrderCost
ity
OrderQuant
nd
AnnualDema
rCost
AnnualOrde 
S
Q
D
rCost
AnnualOrde 

25. Holding & Ordering Cost
| | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Holding cost = (H)
Q
2
Ordering cost = (S)
D
Q
Annual
cost
(dollars)

26. Total Cost
| | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) + (S)
D
Q
Q
2
Holding cost = (H)
Q
2
Ordering cost = (S)
D
Q
Annual
cost
(dollars)

27. Total cost:
H
Q
S
Q
D
TC
2


Cost
Holding
Total
Cost
Order
Total
Cost
Total 


28. What is the annual cost of the
current policy?
H
Q
S
Q
D
TC
2


D – Total demand
Q – Order quantity
S – Setup/order cost
H – Holding cost

29. What is the annual cost of the current
policy?
H
Q
S
Q
D
TC
2


D – Total demand
936/year
Q – Order quantity
390/order
S – Setup/order cost
$45/order
H – Holding cost
= 0.25*60
= $15/unit/year
15
2
390
45
390
936


TC
2925
108

TC
3033

TC

30. Total Cost for Q = 390
Annual
cost
(dollars)
| | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Current
cost
Current
Q
Total cost = (H) + (S)
D
Q
Q
2
Holding cost = (H)
Q
2
Ordering cost = (S)
D
Q

31. Can the gift shop do
better?
Annual
cost
(dollars)
| | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Current
cost
Current
Q
Total cost = (H) + (S)
D
Q
Q
2
Holding cost = (H)
Q
2
Ordering cost = (S)
D
Q

32. Economic Order Quantity – Q*
Annual
cost
(dollars)
| | | | | | | |
50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Q*
Setup cost = Holding Cost

33. Economic Order Quantity
(EOQ) – Q*
H
DS
Q
2
* 
15
)
45
)(
936
(
2
* 
Q order
units/
75
94
.
74 


34. Total Cost of Economic Order
Quantity (EOQ) – Q*
15
2
75
45
75
936


TC
H
Q
S
Q
D
TC
2
*
*


10
.
1124

TC
3033

TC
When Q = 390

35. When to order?
• Reorder point (ROP)
– Lead time – amount of time from order
placement to receipt of goods
– Lead time demand – the demand the occurs
during the lead time

36. Reorder point
Order
received
OH
On-hand
inventory

37. Reorder point
Order
received
OH
TBO
On-hand
inventory
Time between orders

38. Reorder point
Order
received
OH
TBO
L
On-hand
inventory
Lead time

39. Reorder point
Order
received
OH
Order
placed
TBO
L
R
On-hand
inventory

40. Gift shop reorder point
• Demand: 18 birdfeeders/week
• Lead time: 2 weeks
• Lead time demand: 36 birdfeeders
• ROP: 36 birdfeeders

41. Gift shop order policy
• Place order when the on-hand inventory is
36 birdfeeders.
• Order 75 birdfeeders
• Order received in 2 weeks
• Place next order when the on-hand
inventory is 36 birdfeeders

42. Gift shop order policy
Order
received
OH
Order
placed
2 wks
36
On-hand
inventory
75

43. Distribution Game
• What is the EOQ for
the central warehouse
in the distribution
game?
– Order cost: S =
– Holding cost: H =
– Demand: D =
$200
$14.70/unit/year
2190

44. Distribution Game
H
DS
Q
2
* 
7
.
14
)
200
)(
2190
(
2
* 
Q
units
Q 244
1
.
244
* 


45. Production Order
Quantity

46. On-hand
inventory
Time
Production Order
Quantity

47. Production quantity
On-hand
inventory
Q
Time
Production Order
Quantity

48. Production quantity
On-hand
inventory
Q
Time
Demand during
production interval
p – d
Production Order
Quantity

49. Production quantity
Demand during
production interval
On-hand
inventory
Q
Time
p – d
Production Order
Quantity

50. Production quantity
Demand during
production interval
On-hand
inventory
Q
Time
p – d
Production
and demand
Demand
only
TBO
Production Order
Quantity

51. Production quantity
Demand during
production interval
Production
and demand
Demand
only
TBO
On-hand
inventory
Q
Time
p – d
Production Order
Quantity

52. Production quantity
Demand during
production interval
Maximum inventory
Production
and demand
Demand
only
On-hand
inventory
Q
Time
p – d
Production Order Quantity
(POQ Model)

53. POQ model
• Assumptions
– Known and constant demand
– Known and constant lead time
– Partial receipt of material
– No quantity discounts
– Only order (setup) cost and holding cost
– No stockouts

54. POQ model
• Producing and shipping product simultaneously
until production quantity is reached.
• Ship the inventory at a constant rate (no
production)
• Reorder same amount
• Begin production and shipping product
simultaneously

55. POQ Model
)
/
1
(
2
*
p
d
H
DS
Qp


D – annual demand
S – Setup cost
H – Holding cost
d – daily demand rate
p – daily production rate

56. Chemical Plant
A plant manager of a chemical plant must determine
the lot size for a particular chemical that has a
steady demand of 30 barrels/day. The production
rate is 190 barrels/day, annual demand is 10,500
barrels, setup cost is $200, annual holding cost is
$0.21/barrel, and the plant operates 350
days/year. Determine the production order
quantity.

57. Chemical Plant
Demand:
Setup cost:
Holding cost:
Production:
d = 30 barrels/day
D = 10,500 barrels/year
$200/setup
$0.21/barrel/year
190 barrels/day

58. Chemical Plant
)
/
1
(
2
*
p
d
H
DS
Qp


)
190
/
30
1
(
21
.
0
)
200
)(
10500
(
2
*


p
Q
barrels
Qp 4873
4
.
4873
*



59. Thank You
Thank You
Thank You