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1
INVENTORY MANAGEMENT
2
Lead TimeLead Time(small introduction)(small introduction)
3
Estimated time from release of an order requesting the manufacture or procurement of an item until its delivery to the customer
Lead Time [LT]
4
SUPPLY CHAIN LEAD TIME AND ITS COMPONENTS
Commercial &Planning LT
Materials LΤ’s
ProductionWarehousing& Distribution
5
SUPPLY CHAIN LEAD TIME & ITS COMPONENTS
The longer the process the less the reaction in unforeseen changes
LT(days)
• Salesman• Supervisor• Head of Sales• DRP• Order
• Production abroad• Transportation to GR• Procurement of packing materials
• Warehousing• W/H Forwarder• Forwarder Customer
1 - 3 20 - 60 7 1 - 2 =30-70
• Production
Commercial &Planning LT
Materials LΤ’s
ProductionWarehousing& Distribution
6
The cycle “CASH-TO-CASH”
How long does it take to convert an order into cash?
CollectionCommercial &Planning LT
Materials LΤ’s
ProductionWarehousing& Distribution
7
Inventory managementInventory management
(small introduction, use material from (small introduction, use material from
operations management)operations management)
8
Factory Wholesaler Distributor Retailer Customer
Replenishment order
Replenishment order
Replenishment order
Customer order
Production Delay
WholesalerInventory
Shipping Delay
Shipping Delay
DistributorInventory
RetailerInventory
Item Withdrawn
Inventory Management
9
Definitions
• Inventory-A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.
• Inventory System- A set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be
10
Expensive Stuff
• The average carrying cost of inventory across all mfg.. in the U.S. is 30-35% of its value.
• What does that mean?
• Savings from reduced inventory result in increased profit.
11
Two Forms of Demand DependentDependent
Demand for items used to produce final products Demand for items used to produce final products Tires stored at a Goodyear plant are an example
of a dependent demand item
A
B(4) C(2)
D(2) E(1) D(3) F(2)
IndependentIndependent Demand for items Demand for items
used by external used by external customerscustomers
Cars, appliances, computers, and houses are examples of independent demand inventory
12
Independent Demand
• Demand from outside the organization
• Unpredictable usually forecasted
Demand for tables . . .
13
Dependent Demand
• Tied to the production of another item
• Relevant mostly to manufacturers
Once we decide how many tables we want tomake, how many legs do we need?
14
Arguments for Carrying Inventory
Balancing supply and demandBalancing supply and demand
Protection from uncertaintiesProtection from uncertainties
Buffer interfaceBuffer interface
Realizes economies of scale through reduction of fixed costs Realizes economies of scale through reduction of fixed costs
Allows quick response to customer demands
Allows quick response to customer demands
Keeps production line running Keeps production line running
Supports long production runsSupports long production runs
15
Disadvantages for Carrying Inventory
May become obsoleteMay become obsolete
Can be damaged or deteriorateCan be damaged or deteriorate
May be hazardous to storeMay be hazardous to store
May take up excessive W/H spaceMay take up excessive W/H space
Could be totally lost or hiddenCould be totally lost or hidden
Opportunity CostOpportunity Cost
Could be duplicated at different W/HCould be duplicated at different W/H
16
Financial Impact of Inventory [3]1. Inventory is often a company’s largest asset
2. Inventories can account for 20% of total assets
3. Inventory costs may run up to 40- 50% of the value of a product and ~ 40% of total integrated logistics costs
Inventory Management
17
Definitions
• Inventory accuracy refers to how well the inventory records agree with physical count
• Cycle Counting is a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year
Inventory Management
18
In our example of ABC classifications we used the monetary value of the annual usage of each item as a measure of inventory usage. Monetary value can also be used to measure the absolute level of inventory at any point in time. This would involve taking the number of each item in stock, multiplying it by its value (usually the cost of purchasing the item) and summing the value of all the individual items stored. This is a useful measure of the investment that an operation has in its inventories but gives no indication of how large that investment is relative to the total throughput of the operation. To do this we must compare the total number of items in stock against their rate of usage. There are two ways of doing this. The first is to calculate the amount of time the inventory would last, subject to normal demand, if it were not replenished. This is sometimes called the number of weeks’ (or days’, months’, years’ etc.) cover of the stock. The second method is to calculate how often the stock is used up in a period, usually one year. This is called the stock turn or turnover of stock and is the reciprocal of the stock-cover figure mentioned earlier.
Formulas for Measuring Inventory
19
Time
QO
n-ha
nd I
nven
tory
Time
Q
On-
hand
Inv
ento
ryMany orders, low inventory level
Few orders, high inventory level
While carrying costs increase,
ordering costs fall and vice versa
20
OBJECTIVES: To determine the best ordering policy, i.e.
1. To decide how much, and
2. when to order
Economic Order Quantity [EOQ] model
•One of the oldest and most commonly used in inventory control
•Based on a number of assumptions
HOW MUCH?
Inventory Management
21
EOQ Model Cost Curves
Slope = 0 Total Costcurve
Ordering Cost = CoD/Q
Order Quantity, Q
Annualcost ($)
Minimumtotal cost
Optimal order Q*
(EOQ)
Carrying Cost = CcQ/2
Total Costs = Carrying Cost + Ordering CostCt = CcQ/2 + CoD/Q
EOQ, Q = 2 D Co
Cc
22
Inventory managementInventory management
(real thing ….)(real thing ….)
23
Production Quantity ModelProduction lot-size Model
Gradual replacement (or usage) modelEconomic batch quantity (EBQ)
EOQ model with noninstantaneous receipt
24
EOQ Assumptions
1. Continuous and known demand rate
2. Lead time/replenishment cycle is known and constant
3. Price to purchase is independent of the amount needed
4. Transportation costs remain constant
5. No stock outs (or shortages) are permitted
6. No inventory is in transit
7. The order quantity is received all at once
Inventory Management
25
Production Quantity Model
• An inventory system in which an order is received gradually, as inventory is simultaneously being depleted, i.e. assumption that Q is received all at once is relaxed
• p - daily rate at which an order is received over
time, i.e. production rate
• d - daily rate at which inventory is demanded, usage
rate
• P>= d, never the opposite so that …no shortages
26
Assumptions1. Only one item is involved
2. Annual demand is known
3. The usage rate is constant
4. Usage occurs continually, but production occurs periodically
5. Production rate is constant
6. Lead time not vary
7. There are no quantities discounts
8. No stock outs (or shortages) are permitted
Inventory Management
27
QQ(1-(1-d/pd/p))
Inventory level,Inventory level,unitsunits
TimeTime00
Replenishment order cycleReplenishment order cycle
Begin orderBegin orderreceiptreceipt
End orderEnd orderreceiptreceipt
MaximumMaximuminventory levelinventory level
Production Quantity Model
EPQ, the No. of units producedPr
oduc
tion
rate
= p
Usage rate = d
Inve
ntory
build
-up =
p-d
OrderOrderreceipt periodreceipt period Q/pQ/p
28
QQ(1-(1-d/pd/p))
InventoryInventoryLevel,Level,unitsunits
(1-(1-d/pd/p))QQ22
TimeTime00
OrderOrderreceipt periodreceipt period Q/pQ/p
BeginBeginorderorder
receiptreceipt
EndEndorderorder
receiptreceipt
MaximumMaximuminventory inventory levellevel
AverageAverageinventory inventory levellevel
Production Quantity Model
Slope = p - d
30
pp = production rate = production rate dd = demand rate = demand rate
Maximum inventory level =Maximum inventory level = QQ - - dd
== QQ 1 - 1 -
QQpp
ddpp
Average inventory level = Average inventory level = 1 - 1 -QQ22
ddpp
TCTC = + 1 - = + 1 -ddpp
CCooDD
CCccQQ
22
QQoptopt = =22CCooDD
CCcc 1 - 1 - ddpp
Production Quantity Model
31
Production Quantity ModelEXAMPLE 1
Assume that an outlet store has its own manufacturing facility in which it produces Supper Shag carpet. The ordering cost is $150 and the carrying cost $0.75 per yard and D=10,000 yards per year. The manufacturing facility operates the same days the store is open, i.e. 311 days and produces 150 yards of the carpet per day. Determine Qopt, total
inventory cost, the length of time to receive an order, the number of orders per year, and the maximum inventory level.
32
CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards
dd = 10,000/311 = 32.2 yards = 10,000/311 = 32.2 yards//dayday pp = 150 yards = 150 yards//dayday
QQoptopt = = = 2,256.8 yards = = = 2,256.8 yards
22CCooDD
CCcc 1 - 1 - ddpp
2(150)(10,000)2(150)(10,000)
0.75 1 - 0.75 1 - 32.232.2150150
TCTC = + 1 - = $1,329 = + 1 - = $1,329ddpp
CCooDD
CCccQQ
22
Production run = = = 15.05 days per orderProduction run = = = 15.05 days per orderQQpp
2,256.82,256.8150150
Production Quantity Model
33
Number of production runs = = = 4.43 runs/yearDQ
10,0002,256.8
Maximum inventory level = Q 1 - = 2,256.8 1 -
= 1,772 yards
dp
32.2150
Production Quantity Model
34
EXAMPLE 2
A toy manufacturer uses 48,000 rubber wheels peryear for its popular dump truck series. The firmmakes its own wheels, which it can produce at a rateof 800 per day. The toy trucks are assembleduniformly over the entire year. Carrying cost is €1per wheel a year. Set-up cost for a production run ofwheels is €45. The firm operates 240 days peryear. Determine each of the following :(i) Optimal run size(ii) Minimum total annual cost for carrying and set-up(iii) Cycle time for optimal run size(iv) Run time
Production Quantity Model
35
ANSWER
D = 48,000 wheels per yearCCοο = = €45
CCcc = = €1 per wheel per yearp = 800 wheels per dayd = 48,000 wheels/240 days, or 200 wheels/day
Production Quantity Model
36
QQoptopt = = = 2, = = = 2,400 400 wheelswheels
22CCooDD
CCcc 1 - 1 - ddpp
2(2(4545)()(4848,000),000)
1 1 1 - 1 - 220000800800
TCTC = + 1 - = = + 1 - = € 900 + €900 = €1800€ 900 + €900 = €1800ddpp
CCooDD
CCccQQ
22
Production run = = = 12 days for every run of wheelsProduction run = = = 12 days for every run of wheelsQQpp
2,2,400400800800
Production Quantity Model
Cycle time = = = Cycle time = = = 3 3 days per rundays per runQQdd
2,2,400400220000
37
EXAMPLE 3a
The manager of a bottle-filling plant which bottles soft drinks needs to decide how long a run of each type of drink to process. Demand for each type of drink is reasonably constant at 80,000 per year (a year has 160 production hours). The bottling lines fill at a rate of 3000 bottles per hour, but take an hour to clean and reset between different drinks. The cost of (labour and lost production capacity) of each of these changeovers has been calculated at €100 per hour. Stock-holding costs are counted at €0.1 per bottle per month.
Determine the Optimal run size, EBQ
Production Quantity Model
38
ANSWER
D = 80,000 per year
CCοο = = €100
CCcc = = €0.1 per bottle per month
p = 3000 bottles per hour
d = 80,000 per year = 500 per hour
Production Quantity Model
39
ANSWER
Production Quantity Model
QQoptopt = = = 13,856 = = = 13,856 bottlesbottles
22CCooDD
CCcc 1 - 1 - ddpp
2(100)(80,000)2(100)(80,000)
0.0.1 1 1 - 1 - 55000030300000
TCTC = + 1 - = = + 1 - =ddpp
CCooDD
CCccQQ
22
Production run = = = Production run = = = QQpp
138561385630300000
Cycle time = = = Cycle time = = = QQdd
1385613856550000
40
EXAMPLE 3b
The manager of a bottle-filling plant which bottles soft drinks needs to decide how long a run of each type of drink to process. Demand for each type of drink is reasonably constant at 80,000 per year (a year has 160 production hours). The bottling lines fill at a rate of 3000 bottles per hour, but take an hour to clean and reset between different drinks. The cost of (labour and lost production capacity) of each of these changeovers has been calculated at €100 per hour. Stock-holding costs are counted at €0.1 per bottle per month.
Determine the Optimal run size, EBQ
The staff who operates the lines have devised a method of reducing the changeover time from 1 hour to 30 minutes. How would that change the EBQ?
Production Quantity Model
41
ANSWER 3b
D = 80,000 per year
CCοο = = €50
CCcc = = €0.1 per bottle per month
p = 3000 bottles per hour
d = 80,000 per year = 500 per hour
Production Quantity Model
42
Quantity discounts are price reductions for large orders offered to customers to induce them to buy in large quantities.
For example, a box supplier publishes the price list shown in table for boxes of ½ Kg. Note that the price per box decreases as order quantity increases.
Quantity Discounts
43
Total Costs with Purchasing Cost
Annualcarryingcost
PurchasingcostTC = +
Q2
Cc DQ
CoTC = +
+Annualorderingcost
PD +
EOQ models with constant purchase price:
Quantity Discounts
Where P = Unit price
44
Adding PD doesn’t change the EOQ.
The rationale for not including unit price in the EOQ is that under the assumption of no quantity discounts, price per unit is the same for all order sizes.
Quantity Discounts
45
The total-cost curve with quantity discounts is composed of a portion of the total-cost curve for each price.
Including unit prices merely raises each curve by a constant amount. However, because the unit prices are different, each curve is raised by a different amount, i.e. smaller unit prices will raise the a total-curve less than larger unit prices.
Quantity Discounts
46
Quantity Discounts
47
A. When carrying costs are constant, all curves have their minimum points at the same quantity.
B. When carrying costs are stated as a percentage of unit price, the minimum points do not line up.
Quantity DiscountsComparison of TC curves for constant carrying costs and carrying costs that are a percentage of unit costs
48
For carrying costs that are constant, the procedure is as follows:
1. Compute the common minimum point.
2. Only one of the unit prices will have the minimum point in its feasible range since the ranges do not overlap. Identify that range.
a. If the feasible minimum point is on the lowest price range, that is the optimal order quantity.
b. If the feasible minimum point is in any other range, compute the total cost for the minimum point and for the price breaks of all lower unit costs. Compare the total costs; the quantity (minimum point or price break) that yields the lowest total cost is the optimal order quantity.
Quantity Discounts with constant carrying cost
49
QQoptopt
Carrying cost Carrying cost
Ordering cost Ordering cost
Inve
ntor
y co
st (
$)In
vent
ory
cost
($)
QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200
TC TC ((dd2 2 = $6 ) = $6 )
TCTC ( (dd1 1 = $8 )= $8 )
TC TC = ($10 )= ($10 ) ORDER SIZE PRICE
0 - 99 $10
100 – 199 8 (d1)
200+ 6 (d2)
Quantity Discounts
50
EXAMPLE [PCs]
Annual carrying cost is $190/pc, ordering cost = $2,500 and annual demand is estimated to be 200 PCs. Should it take the advantage of this discount or order EOQ?
Quantity Discounts with constant carrying cost
ORDER SIZE PRICE
1 – 49 $1,400
50 – 89 1,100
90+ 900
51
QUANTITYQUANTITY PRICEPRICE
1 - 491 - 49 $1,400$1,400
50 - 8950 - 89 1,1001,100
90+90+ 900900
CCoo = = $2,500 $2,500
CCcc = = $190 per computer $190 per computer
DD = = 200200
QQoptopt = = = 72.5 PCs = = = 72.5 PCs22CCooDD
CCcc
2(2500)(200)2(2500)(200)190190
TCTC = + + = + + P P D D = $233,784 = $233,784 CCooDD
QQoptopt
CCccQQoptopt
22
For For QQ = 72.5 = 72.5
TCTC = + + = + + P P D D = $194,105= $194,105CCooDD
CCccQQ
22
For For QQ = 90 = 90
$ 1100
$ 900
Quantity Discounts with constant carrying cost
52
QUANTITYQUANTITY PRICEPRICE
1 - 491 - 49 $1,400$1,400
50 - 8950 - 89 1,1001,100
90+90+ 900900
TCTC = $233,784 = $233,784 For For QQ = 72.5 = 72.5
TCTC = $194,105 = $194,105For For QQ = 90 = 90
Quantity Discounts with constant carrying cost
Since this total cost is lower (194,105 < 233,784), the max discount price should be taken, and 90 units should be ordered.
53
Example
The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost.
Quantity Discounts with constant carrying cost
54
D = 816 cases per year
Co = $12
Cc = $4 per case per year
Quantity Discounts with constant carrying cost
55
Compute the common EOQ:
The 70 cases can be bought at $18 per case because 70 falls in the range of 50 to 79 cases. The total cost to purchase 816 cases a year, at the rate of 70 cases per order, will be
TC = Carrying cost + Order cost + Purchase cost
TC = (Q/2)Cc + (D/Q0)Co + PD
TC70 = (70/2)4 + (816/70)12 + 18(816) = $14,968
TC80 = (80/2)4 + (816/80)12 + 17(816) = $14,154
TC100 = (100/2)4 + (816/100)12 + 16(816) = $13,354
Quantity Discounts with constant carrying cost
56
When carrying costs are expressed as a percentage of price, determine the best purchase quantity with the following procedure:
1. Beginning with the lowest unit price, compute the minimum points for each price range until you find a feasible minimum point (i.e., until a minimum point falls in the quantity range for its price).
2. If the minimum point for the lowest unit price is feasible, it is the optimal order quantity. If the minimum point is not feasible in the lowest price range, compare the total cost at the price break for all lower prices with the total cost of the feasible minimum point. The quantity that yields the lowest total cost is the optimum.
Quantity Discounts when carrying cost are % of price
57
Homework - ExampleSurge Electric uses 4,000 toggle switches a year.
Switches are priced as follows: 1 to 499, 90 cents each; 500 to 999, 85 cents each; and 1,000 or more, 80 cents each. It costs approximately $30 to prepare an order and receive it, and carrying costs are 40 percent of purchase price per unit on an annual basis. Determine the optimal order quantity and the total annual cost.
Quantity Discounts when carrying cost are % of price
58
Quantity Discounts when carrying cost are % of price
59
D = 4,000 switches per year
S = $30
H = .40P
Quantity Discounts when carrying cost are % of price
60
This is feasible; it falls in the $0.85 per switch range of 500 to 999.
Now compute the total cost for 840, and compare it to the total cost of the minimum quantity necessary to obtain a price of $0.80 per switch.
Thus, the minimum-cost order size is 1,000 switches.
Quantity Discounts when carrying cost are % of price
61
Company ABC has about 5000 items in its inventory. After hiring a bright SC manager, the firm determined that it has 500 A items, 1750 B items and 2750 C items.Company policy is to count all A items every month (every 20 working days), all B items every quarter (every 60 working days), and C items every 6 months (every 120 working days). How many items should be counted each day?
Company ABC has about 5000 items in its inventory. After hiring a bright SC manager, the firm determined that it has 500 A items, 1750 B items and 2750 C items.Company policy is to count all A items every month (every 20 working days), all B items every quarter (every 60 working days), and C items every 6 months (every 120 working days). How many items should be counted each day?
Cycle Counting
62
Cycle Counting
ITEM
CLASS
QUANTITY CYCLE COUNTING
POLICY
NO. OF ITEMS COUNTED PER
DAY
A 500 Each month (20 working days
500/20 = 25/day
B 1750 Each quarter (60 working days
1750/60 = 29/day
C 2750 Every month (120 working days
52750/120 = 23/day
5000 77/day
63
Quantity Discounts
Price per unit decreases as order quantity increasesPrice per unit decreases as order quantity increases
TCTC = + + = + + PDPDCCooDD
CCccQQ
22
wherewhere
PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand
64
Reorder Point
Level of inventory at which a new order Level of inventory at which a new order is placed is placed
RR = = dLdL
wherewhere
dd = demand rate per period = demand rate per periodLL = lead time = lead time
65
Reorder Point: Example
Demand = 10,000 yards/yearDemand = 10,000 yards/year
Store open 311 days/yearStore open 311 days/year
Daily demand = 10,000 / 311 = 32.154 Daily demand = 10,000 / 311 = 32.154 yards/dayyards/day
Lead time = L = 10 daysLead time = L = 10 days
R = dL = (32.154)(10) = 321.54 yardsR = dL = (32.154)(10) = 321.54 yards
66
CASE STUDY: The UK National Blood Service
67
CASE STUDYManor Bakeries
68
CASE STUDY: Trans – European Pastics