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Logistics Systems EngineeringInventory - Requirements, Planning and Management
NTUSY-521-N
SMUSYS 7340
Dr. Jerrell T. Stracener, SAE Fellow
2
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
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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
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Inventory Requirements
• Protection from Uncertainties– Future prices– Shortages– World conflicts– Plant catastrophe– Labor disputes– Improve customer service
• Buffering– See following graph
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Inventory Requirements
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Inventory Planning2
• Cycle Stock• In transit• Safety Stock• Speculative Stock• Seasonal Stock• Dead Stock
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Inventory Planning2
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Inventory Planning2
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Inventory Mangement3
• Economic Order Quantity (EOQ)– Minimizes the inventory carrying cost– Minimizes the ordering cost
InventoryCarrying
Cost
OrderingCost
Total Cost
EOQAnnual Cost
Size of Order
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Inventory Management
• EOQ formula:
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
CV
PD2EOQ
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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
01 Q)r1(C
rD2Q
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Inventory Management
• Adjustments to the EOQ (continue)where
Q1 = the maximum quantity that can be economically orderedr = the percentage of price reduction if a larger quantity is orderedD = the annual demand in unitsC = the inventory carrying cost percentageQ0 = the EOQ based on current price
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Safety Stock Requirements4
• Formula for calculating the safety stock requirements:
wherec = units of safety stock needed to satisfy 68% of all probabilitiesR = average replenishment cycleR = STD of replenishment cycleS = average daily salesS = STD of daily sales
)R(S)S(Rc 222
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Calculating Fill Rate
• Formula for calculating the fill rate:
whereFR = Fill rate
c = combined safety stock required to consider both variability in lead time and demandEOQ = order quantityI(K) = service function magnitude factor based on desired number of STD
))K(I(EOQ
c1FR
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Calculating Fill Rate
• I(K) Table
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1 Douglas M. Lambert and James R. Stock, “Strategic Logistics Management”, third edition, (Boston, MA: Irwin, 1993), pp. 399 - 402
2 Ibid, pp. 403 - 4063 Ibid, pp. 408 - 4114 Ibid, pp. 4155 Ibid, pp. 420
References
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Logistics Systems EngineeringMathematical Computations of Inventory
NTUSY-521-N
SMUSYS 7340
Dr. Jerrell T. Stracener, SAE Fellow
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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
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Problems with ordering too much
• Financial Statements– Quick Ratio– Inventory Turnover– Debt Ratio– Basic Earning Power (BEP)– Return on Total Assets (ROA)
• Inventorying• Warehousing
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Problems with ordering too much
• Obsolescence• Pricing• Obligation to Shareholders• Demotion• Market Share
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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
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Cost Trade-Offs: Most Economical OQ
Total Cost
InventoryCarry Cost
Ordering Cost
Lowest Total Cost(EOQ)
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Inventory Management
• EOQ formula:
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
CV
PD2EOQ
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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?
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Inventory Management
• At what rate should the company order skates?– Solution:
P = $10 per shipmentD = 16,000 units per yearC = 0.25V = $9.00, and
CV
PD2EOQ
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Inventory Management
• Solution:
• Note, if the number is 377 units and there are 20 units per order, then the order quantity becomes 380 units
00.9$25.0
000,1610$2EOQ
380377EOQ
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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)
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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
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Inventory Management
• Adjustments to the EOQ formula must be made to address– Volume transportation discounts– Quantity discounts
• Thus, the formula becomes:
01 Q)r1(C
rD2Q
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Inventory Management
• where,Q1 = the maximum quantity that can be economically orderedr = the percentage of price reduction if a larger quantity is orderedD = the annual demand in unitsC = the inventory carrying cost percentageQ0 = the EOQ based on current price
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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?
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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:
01 Q)r1(C
rD2Q
380)01.01(25.0
000,1601.02Q1
660,1656,1376280,1Q1
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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
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Uncertainties
• What drives managers to consider safety stocks of the product?– Raw material– Suppliers not responding– Work stoppage
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Basic Statistics
• Properties of a Normal Distribution– Resembles a bell shape curve– Measures central tendency– Probabilities are determined by its mean,
and standard deviation, , where
– and the theoretically infinite range is
n
X i
n
1i
n
)X( 2i
n
1i2
)X(
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Basic Statistics
2 323
Normal Curve
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Safety Stock Requirements
• Example: Given
=
Number Xi (Xi - u)2
1 80 2252 85 1003 90 254 95 05 100 256 105 1007 110 225
Totals 665 700
957
665
n
X i
n
1i
107
700n
)X(
2
2i
n
1i2
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Safety Stock Requirements
• Formula for calculating the safety stock requirements:
wherec = units of safety stock needed to satisfy 68% of all probabilitiesR = average replenishment cycleR = STD of replenishment cycleS = average daily salesS = STD of daily sales
)R(S)S(Rc 222
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Safety Stock Requirements
• And where:
• Example– Calculate the Safety Stock Requirements
based on the two following tables:
1n
fdS
2
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Safety Stock Requirements
• Given: Sales History for Market Area
Sales SalesDay in Cases Day in Cases1 100 14 802 80 15 903 70 16 904 60 17 1005 80 18 1406 90 19 1107 120 20 1208 110 21 709 100 22 10010 110 23 13011 130 24 11012 120 25 9013 100
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Safety Stock Requirements
• Solution: Calculation of STD of Sales
• Where S= 100, and n= 25, and fd2 = 10,000
Daily Sales Frequency Deviation Deviation
in Cases (f) (d) (d) 2 fd 2
60 1 -40 1,600 1,60070 2 -30 900 1,80080 3 -20 400 1,20090 4 -10 100 400
100 5 0 0 0110 4 10 100 400120 3 20 400 1,200130 2 30 900 1,800140 1 40 1,600 1,600100 25 10,000
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Safety Stock Requirements
• Solution: Given - Replenishment Cycle
• Where R = 10, and n = 16, and fd2 = 40
Lead Time Frequency Deviation Deviation
in Days (f) (d) (d) 2 fd 2
7 1 -3 9 98 2 -2 4 89 3 -1 1 3
10 4 0 0 011 3 1 1 312 2 2 4 813 1 3 9 910 16 40
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Safety Stock Requirements
• Solution:
1n
fdS
2
125
000,10S
20S
1n
fdR
2
116
40R
634.1R
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Safety Stock Requirements
• Solution(continue):Finally, we have
)R(S)S(Rc 222
222 )634.1()100()20(10c
cases175c
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Calculating Fill Rate
• Formula for calculating the fill rate:
whereFR = Fill rate
c = combined safety stock required to consider both variability in lead time and demandEOQ = order quantityI(K) = service function magnitude factor based on desired number of STD
))K(I(EOQ
c1FR
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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.
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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,
))K(I(EOQ
c1FR
)0236.0(000,1
1751FR
9959.0FR
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Calculating Fill Rate
Insert table 10-8, p 422
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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.
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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.
