Transcript Inventory Management - Lyle School of Engineering

SMU
SYS 7340
NTU
SY-521-N
Logistics Systems Engineering
Inventory - Requirements, Planning and Management
Dr. Jerrell T. Stracener,
SAE Fellow
1
Inventory Requirements1
• Why hold inventory?
– Enables firm to achieve economics of scale
– Balances supply and demand
– Enable specialization in manufacturing
– Provides uncertainty in demand and order
cycle
– Acts as a buffer between critical interfaces
within the channel of distribution
2
Inventory Requirements
• Economics of scale
– Price per unit
– LTL movements
– Long production runs with few line changes
– Cost of lost sales
• Balancing supply and demand
– Holidays
– Raw material availability
• Specialization
– Manufacturing process
– Longer production runs
3
Inventory Requirements
• Protection from Uncertainties
– Future prices
– Shortages
– World conflicts
– Plant catastrophe
– Labor disputes
– Improve customer service
• Buffering
– See following graph
4
Inventory Requirements
5
Inventory Planning2
•
•
•
•
•
•
Cycle Stock
In transit
Safety Stock
Speculative Stock
Seasonal Stock
Dead Stock
6
Inventory Planning2
7
Inventory Planning2
8
Inventory Mangement3
• Economic Order Quantity (EOQ)
– Minimizes the inventory carrying cost
– Minimizes the ordering cost
Total Cost
Annual Cost
EOQ
Inventory
Carrying
Cost
Ordering
Cost
Size of Order
9
Inventory Management
• EOQ formula:
EOQ 
2PD
CV
where
P = the ordering cost (dollars/order)
D = Annual demand (number of units)
C = Annual inventory carrying cost (percent of
product cost or value)
V = Average cost per unit inventory
10
Inventory Management
• Note, if the number is 124 units and there are
20 units per order, then the order quantity
becomes 120 units
• Adjustments to the EOQ
– Includes volume transportation discounts
– Considers quantity discounts
rD
0
Q 2
 (1  r )Q
C
1
11
Inventory Management
• Adjustments to the EOQ (continue)
where
Q1 = the maximum quantity that can be
economically ordered
r = the percentage of price reduction if a larger
quantity is ordered
D = the annual demand in units
C = the inventory carrying cost percentage
Q0 = the EOQ based on current price
12
Safety Stock Requirements4
• Formula for calculating the safety stock
requirements:
sc 
2
R (sS )  S (sR 2 )
2
where
sc = units of safety stock needed to satisfy
68% of all probabilities
R = average replenishment cycle
sR = STD of replenishment cycle
S = average daily sales
sS = STD of daily sales
13
Calculating Fill Rate
• Formula for calculating the fill rate:
FR  1 
sc
EOQ
(I(K ))
where
FR = Fill rate
sc = combined safety stock required to consider
both variability in lead time and demand
EOQ = order quantity
I(K) = service function magnitude factor based
on desired number of STD
14
Calculating Fill Rate
• I(K) Table
15
References
1
2
3
4
5
Douglas M. Lambert and James R. Stock, “Strategic Logistics
Management”, third edition, (Boston, MA: Irwin, 1993), pp. 399 - 402
Ibid, pp. 403 - 406
Ibid, pp. 408 - 411
Ibid, pp. 415
Ibid, pp. 420
16
SMU
SYS 7340
NTU
SY-521-N
Logistics Systems Engineering
Mathematical Computations of Inventory
Dr. Jerrell T. Stracener,
SAE Fellow
17
Mathematical Computations
•
•
•
•
•
•
•
•
•
Problems with ordering too much
Items affecting ordering cost
Cost Trade-Offs Chart
Economic Order Quantity (EOQ)
EOQ considering discounts
Uncertainties
Basic Statistics
Safety Stock Requirements
Calculating Fill Rate
18
Problems with ordering too much
• Financial Statements
– Quick Ratio
– Inventory Turnover
– Debt Ratio
– Basic Earning Power (BEP)
– Return on Total Assets (ROA)
• Inventorying
• Warehousing
19
Problems with ordering too much
•
•
•
•
•
Obsolescence
Pricing
Obligation to Shareholders
Demotion
Market Share
20
Items affecting ordering cost
• Ordering Cost
– Transmitting the order
– Receiving the order
– Placing in storage
– Processing invoice
• Restocking Cost
– Transmitting & processing inventory transfers
– Handling the product
– Receiving at field location
– Cost associated with documentation
21
Cost Trade-Offs: Most Economical OQ
Total Cost
Lowest Total Cost
(EOQ)
Inventory
Carry Cost
Ordering Cost
22
Inventory Management
• EOQ formula:
EOQ 
2PD
CV
where
P = the ordering cost (dollars/order)
D = Annual demand (number of units)
C = Annual inventory carrying cost (percent of
product cost or value)
V = Average cost per unit inventory
23
Inventory Management
• Example
– A company purchased a line of relay for use
in its air conditioners from a manufacturer in
the Midwest. It ordered approximately 300
cases of 24 units each 54 times per year.
The annual volume was about 16,000 cases.
The purchase price was $8.00 per case, the
ordering cost were $10.00 per order, and the
inventory carrying cost was 25 percent. The
delivered cost of a case of product would be
$9.00 ($8.00 plus $1.00 transportation).
What is the EOQ?
24
Inventory Management
• At what rate should the company order skates?
– Solution:
P = $10 per shipment
D = 16,000 units per year
C = 0.25
V = $9.00, and
EOQ 
2PD
CV
25
Inventory Management
• Solution:
EOQ 
2  $10 16 ,000
0.25  $9.00
EOQ  377  380
• Note, if the number is 377 units and there are
20 units per order, then the order quantity
becomes 380 units
26
Inventory Management
• Assumptions:
– A continuous, constant and known rate of
demand
– A constant and known replenishment or lead
time
– A constant purchase price that is independent
of the order quantity or time
– A constant transportation cost that is
independent of the order quantity or time
– The satisfaction of all demand (no stock-outs
are permitted)
27
Inventory Management
• Assumptions:
– No inventory in transit
– Only one item in inventory, or at least no
interaction
– An infinite planning horizon
– No limit on capital availability
28
Inventory Management
• Adjustments to the EOQ formula must be made
to address
– Volume transportation discounts
– Quantity discounts
• Thus, the formula becomes:
rD
Q 2
 (1  r )Q 0
C
1
29
Inventory Management
• where,
Q1 = the maximum quantity that can be
economically ordered
r = the percentage of price reduction if a larger
quantity is ordered
D = the annual demand in units
C = the inventory carrying cost percentage
Q0 = the EOQ based on current price
30
Inventory Management
• Example
– Using the same example as previous, assume
that the relays weighed 25 pounds per case.
The freight rate was $4.00 per 100 lbs. on
shipments of less than 15,000 lbs., and $3.90
per 100 lbs on shipments of 15,000 to
39,000 lbs. Lastly, on shipments of more
than 39,000 lbs, the cost is $3.64 per 100
lbs. The relays were shipped on pallets of 20
cases. What is the cost if the company
shipped in quantities of 40,000 pounds or
more?
31
Inventory Management
• Solution:
– Cost per case: $3.64/100 lbs x25 lbs= $0.91.
– r = [($9.00 - $8.91) / $9.00] x 100 = 1.0%
– And Q1 is:
rD
0
Q 2
 (1  r )Q
C
0.01 16 ,000
1
Q 2
 (1  0.01)  380
0.25
1
Q1  1,280  376  1,656  1,660
32
Uncertainties
• What drives managers to consider safety stocks
of the product?
– Economic conditions
– Competitive actions
– Change in government regulation
– Market shifts
– Consumer buying patterns
– Transit times
– Supplier lead times
33
Uncertainties
• What drives managers to consider safety stocks
of the product?
– Raw material
– Suppliers not responding
– Work stoppage
34
Basic Statistics
• Properties of a Normal Distribution
– Resembles a bell shape curve
– Measures central tendency
– Probabilities are determined by its mean, u
and standard deviation, s, where
n

 Xi
i1
n
n
s
2

 (X i  u )
2
i 1
n
– and the theoretically infinite range is
(  X  )
35
Basic Statistics
Normal Curve
3s
2s
s

s
2s
3s
36
Safety Stock Requirements
• Example: Given
Number
1
2
3
4
5
6
7
Totals
Xi
80
85
90
95
100
105
110
665
s=
(Xi - u)2
225
100
25
0
25
100
225
700
n

 Xi
i 1
n
665

 95
7
n
s2 
s
2
 (X i  u ) 2
i 1
n
700

 10
7
37
Safety Stock Requirements
• Formula for calculating the safety stock
requirements:
sc 
2
R (sS )  S (sR 2 )
2
where
sc = units of safety stock needed to satisfy
68% of all probabilities
R = average replenishment cycle
sR = STD of replenishment cycle
S = average daily sales
sS = STD of daily sales
38
Safety Stock Requirements
• And where:
sS 
fd
n 1
2
• Example
– Calculate the Safety Stock Requirements
based on the two following tables:
39
Safety Stock Requirements
• Given: Sales History for Market Area
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
Sales
in Cases
100
80
70
60
80
90
120
110
100
110
130
120
100
Day
14
15
16
17
18
19
20
21
22
23
24
25
Sales
in Cases
80
90
90
100
140
110
120
70
100
130
110
90
40
Safety Stock Requirements
• Solution: Calculation of STD of Sales
Daily Sales Frequency Deviation Deviation
(d) 2
in Cases
(f)
(d)
60
70
80
90
100
110
120
130
140
100
1
2
3
4
5
4
3
2
1
25
-40
-30
-20
-10
0
10
20
30
40
1,600
900
400
100
0
100
400
900
1,600
fd 2
1,600
1,800
1,200
400
0
400
1,200
1,800
1,600
10,000
• Where S= 100, and n= 25, and fd2 = 10,000
41
Safety Stock Requirements
• Solution: Given - Replenishment Cycle
Lead Time
Frequency
Deviation
in Days
7
8
9
10
11
12
13
10
(f)
1
2
3
4
3
2
1
16
(d)
-3
-2
-1
0
1
2
3
Deviation
(d) 2
9
4
1
0
1
4
9
fd 2
9
8
3
0
3
8
9
40
• Where R = 10, and n = 16, and fd2 = 40
42
Safety Stock Requirements
• Solution:
sS 
fd 2
n 1
sS 
10 ,000
25  1
sS  20
sR 
fd 2
n 1
sR 
40
16  1
sR  1.634
43
Safety Stock Requirements
• Solution(continue):
Finally, we have
sc 
2
R (sS )  S (sR 2 )
2
sc  10 (20 )  (100 ) (1.634 )
2
2
2
sc  175 cases
44
Calculating Fill Rate
• Formula for calculating the fill rate:
FR  1 
sc
EOQ
(I(K ))
where
FR = Fill rate
sc = combined safety stock required to consider
both variability in lead time and demand
EOQ = order quantity
I(K) = service function magnitude factor based
on desired number of STD
45
Calculating Fill Rate
• Example
– Using the data from the previous example,
what will the fill rate be if a manager wants
to hold 280 units as safety stock? Assume
EOQ = 1,000.
46
Calculating Fill Rate
• Solution:
– The safety stock determined by the manager
is 280 units. Thus, K is equal to 280 / 175 =
1.60. From the table in the end, we see that
I(K) = 0.0236. Hence,
FR  1 
sc
(I(K ))
EOQ
175
FR  1 
(0.0236 )
1,000
FR  0.9959
47
Calculating Fill Rate
Insert table 10-8, p 422
48
Calculating Fill Rate
• Differences
– Safety Stock: policy of customer service and
inventory availability
– Fill Rate: represents the percent of units
demanded that are on hand to fill customer
orders. The magnitude of stock-out.
49
Calculating Fill Rate
• Conclusion
– K (the safety factor) is the safety stock the
manager decides to hold divided by EOQ
– Therefore:
The average fill rate is 99.59%. That is, of
every 1,000 units of product XYZ
demanded, 99.59 will be on hand to be
sold if the manager uses 280 units of
safety stock and orders 1,000 units each
time.
50