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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter
Inventory Management
12
Slides prepared byLaurel DonaldsonDouglas College
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
Define the term inventory, list major reasons for holding inventory, and discuss the objectives of inventory management.
List the main requirements for effective inventory management, and describe A-B-C classification and perform it.
Describe the basic EOQ model, the economic production quantity model, the quantity discount model, and the planned shortage model and solve typical problems.
Describe how to determine the reorder point and solve typical problems.
Describe the fixed order interval model and solve typical problems.
Describe the single period model and solve typical problems.
LO 1
LO 3
LO 2
LO 4
LO 5
LO 6
2
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
IntroductionRequirements for Effective Inventory
ManagementFixed Order Quantity/Reorder Point Model
(FOQRP) FOQRP: Determining the Reorder PointFixed Order Interval ModelThe Single Period Model
3
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 1
What Is Inventory?
Stock of items kept to meet future demand
Decisions of inventory managementhow many units to orderwhen to order
4
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 1
Inventory
• Retail items,• finished goods, • supplies and parts, • some raw materials
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand• Manufactured parts
Independent demand is uncertain. Dependent demand is certain.
Independent Demand
5
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 1
Types of Inventories
Raw materials & purchased parts
Partially completed items called work in process (WIP)
Finished-goods (or merchandise)
Spare parts, tools, & supplies
6
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 1
Functions of Inventory
To wait while in transit
To protect against stock-
outs
To take advantage of
quantity discounts
To smooth production
requirements
To decouple operations
To hedge against price
increases
7
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 1
Objective of Inventory Control
Level of customer service (not understock)Fill rate
Costs of ordering and carrying inventory (not overstock) Inventory turnover
8
To achieve satisfactory levels of customer
service while keeping inventory costs within
reasonable bounds
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Effective Inventory Management
A reliable forecast of demandKnowledge of lead timesReasonable estimates of
Holding costsOrdering costsShortage costs
A classification systemA system to keep track of inventory
Quantity
Costs
Control
9
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Safely Storing Inventory Warehouse Management System (WMS)
computer software that controls the movement and storage of materials within a
warehouse, and processes the associated transactions
10
Warehouse/storeroom concernsSecurity Safety Obsolescenc
e
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Inventory Counting Systems
Periodic counting Physical count of items made at periodic intervals
Periodic counting Physical count of items made at periodic intervals
11
Perpetual (or continual) tracking keeps track of removals from and additions to inventory continuously, thus providing current levels of each item
Perpetual (or continual) tracking keeps track of removals from and additions to inventory continuously, thus providing current levels of each item
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Inventory Replenishment Fixed Order Quantity/Reorder Point Model
An order of a fixed size is placed when the amount on hand drops below a minimum quantity called the reorder point
Two-Bin System Two containers of inventory; reorder when the first is
empty Bar Code
A number assigned to an item or location, made of a group of vertical bars of different thickness that are readable by a scanner
Universal Product Code (UPC)Radio Frequency Identification (RFID)
technology that uses a RFID tag attached to the item that emits radio waves to identify items.
0
214800 232087768
12
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Forecasting Demand Lead time
time interval between ordering and receiving the order
Point of Sale (POS) systemSoftware for electronically recording
actual sales at the time and location of sale
13
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Inventory Costs
Inventory costs
Shortage costs
Ordering or Setup costs
Holding (carrying)
costs
14
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Inventory Costs Holding (carrying) costs
cost to carry an item in inventory Ordering costs
costs determining order quantity, preparing purchase orders, and fixed cost portion of receiving, inspection, and material handling
Setup costsTime spent preparing equipment for the job by
adjusting machine, changing tools, etc Shortage costs
costs when demand exceeds supply; often unrealized profit per unit
15
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
ABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A - very important
B - mod. important
C - least important Annual $ value of items
A
B
C
High(70-80)
Low(5-10)
Low(15-20)
High(50-60)
Percentage of Items16
A items should receive more attention!
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Example: A-B-C Classification
Item Numbe
r
Annual Deman
dx Unit
Cost =
Annual Dollar
Volume (ADV)
% of Total ADV
8 1,000 $ 90.00
$ 90,000 38.8%
10 500 154.00 77,000 33.2%
2 1,550 17.00 26,350 11.3%
5 350 42.86 15,000 6.4%
3 1,000 12.50 12,500 5.4%
1 600 14.17 8,500 3.7%
7 2,000 .60 1,200 .5%
9 100 8.50 850 .4%
6 1,200 .42 504 .2%
4 250 .60 150 .1% 17
72%
23%
5%
A
B
C
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 2
Cycle Counting
Cycle counting managementHow much accuracy is needed?
When kind of counting cycle should be used?
Who should do it?
18
Regular actual count of the items in inventory on a cyclic schedule
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Fixed Order Quantity/Reorder Point Model: Determining Economic Order Quantity
basic economic order quantity (EOQ)
EOQ with
quantity discount
EOQ with
planned shortage
economic production quantity
(EPQ)
19
economic order quantity (EOQ) The order size that
minimizes total inventory control cost
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Assumptions of EOQ Model
1. Only one product is involved
2. Annual demand requirements known
3. Demand is even throughout the year
4. Lead time does not vary
5. Each order is received in a single delivery
6. There are no quantity discounts
7. Shortage is not allowed
20
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
R = Reorder pointQ = Economic order quantityLT = Lead time
LT LT
Q QQ
R
Time
Quantityon hand
1. You receive an order (size = Q)
2. Quantity decreases by demand rate (d) 3. When quantity reaches
reorder point quantity (R), place another order (size = Q).
4. Order received after lead time (LT) expires, when 0 on hand. The cycle then repeats.
21
Inventory Cycles with EOQ
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EOQ: Minimizing Total Costs
Ordering Costs
HoldingCosts
Order Quantity (Q)
ANNUAL
COST
Total Cost
QO
Total cost = Holding + Ordering Costs
Total cost is minimized at Q0 where holding = ordering cost
22
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Total Annual =Cost
AnnualOrdering
Cost
AnnualHolding
Cost+
TC = Total annual costQ = Order quantity (units)H = Annual holding cost
per unitD = Annual DemandS = Ordering (or setup) cost per order
Q0 = EOQ
23
TCQ
HD
QS
2
Basic Economic Order Quantity (EOQ)
Cost Holding Annual
Cost) Setupor (Order Demand) 2(Annual =
H
2DS = QO
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EOQ Example 1
H = $6 per unitS = $75D = 10,000 units
Qo =2(10,000) (75)
(6)
Qo = 500 units
TC = +
(10,000)(75)500
(500)(6)2
TC = $1500 + $1500= $3000
Orders per year = D/Qo
= 10,000/500= 20 orders/year
Length of order cycle = 250
days/(D/Qo)
= 250/20= 12.5 days 2
4
Qo =2DS
HTC = +
QH2
DSQ
A phone company has annual demand of 10,000. A component has annual holding cost of $6 per unit, and ordering cost of $75. Calculate EOQ, Total Cost, number of orders per year and the order cycle time.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Qo =2(15,000) (75)
(6)
Qo = 612 units
TC = +
(15,000)(75)612
(612)(6)2
TCmin = $1836 + $1838 = $3674
Orders per year = D/Qopt
= 15,000/612= 25 orders/year
Total cost is 22% more than
$3000
EOQ is 22% more than
500
25
Length of order cycle = 250
days/(D/Qo)
= 250/25= 10 days
EOQ Example 2a
H = $6 per unitS = $75D = 15,000 units
Qo =2DS
HTC = +
QH2
DSQ
A phone company has annual demand of 15,000. A component has annual holding cost of $6 per unit, and ordering cost of $75. Calculate EOQ, Total Cost, number of orders per year and the order cycle time.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Qo =2(15,000) (75)
(6)
Qo = 612 units
TC = +
(15,000)(75)500
(500)(6)2
TC = $1500 + $2250 = $375026
What if we still use
EOQ of 500? What is total
cost?
Total cost is only an extra 2% more if still use EOQ of
500
EOQ Example 2b
H = $6 per unitS = $75D = 15,000 units
Qo =2DS
HTC = +
QH2
DSQ
A phone company has annual demand of 15,000. A component has annual holding cost of $6 per unit, and ordering cost of $75.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Robust Model
The EOQ model is robustIt works even if all parameters
and assumptions are not metThe total cost curve is relatively flat near
the EOQ (especially to the right)
27
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Economic Production Quantity (EPQ)
Production done in batches or lotsproduction capacity > usage or demand
ratefor a part for the part
28
Assumptions of EPQsimilar to EOQexcept orders are received
incrementally during production
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Economic Production Quantity (EPQ)
29
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Economic Production Quantity (EPQ)
dpp
QI
p
Q
d
Q
SQ
DH
I
max
max
;lengthRun ;length Cycle
2Cost
Setup
Annual
Cost
Holding
Annual
TC
30
dp
p
H
DSQ
20TC = Total annual cost
Q = Order quantity (units)H = Annual holding cost
per unitD = Annual DemandS = Ordering (or setup) cost per order
Q0 = Optimal run or order quantityp = Production rated = Usage or demand rateImax = Maximum inventory level
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EPQ ExampleHoldit Inc. produces reusable shopping bags. Demand is 20,000 bags per day, 5 days per week, 50 weeks per year. Production is 50,000 per day. The setup cost is $200 and the annual holding cost rate is $.55 per bag. Calculate the EPQ, the total cost, the cycle length and optimal production run length.
H = $0.55 per bag S = $200 D = 20,000 bags x 50 wks x 5 daysd = 20,000 bags per day p = 50,000 bags per day
31
dp
p
H
DSQ
20
850,772050
50
55.
)200)(000,000,5(20
GG
GQ
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EPQ Example
H = $0.55 per bag S = $200 D = 20,000 bags x 50 wks x 5 daysd = 20,000 bags per day p = 50,000 bags per day
32
dpp
QIS
Q
DH
I
max
max 2
TC
bags 46,710 30000000,50
850,77max I
$25,690 002850,77
5)55(.
2
710,46TC
million
Holdit Inc. produces reusable shopping bags. Demand is 20,000 bags per day, 5 days per wk, 50 wks per yr. Production is 50,000 per day. Setup cost is $200 and annual holding cost rate is $.55 per bag. Calculate total cost.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EPQ ExampleHoldit Inc. produces reusable shopping bags. Demand is 20,000 bags per day, 5 days per week, 50 weeks per year. Production is 50,000 per day. The setup cost is $200 and the annual holding cost rate is $.55 per bag. Calculate cycle length and optimal production run length. H = $0.55 per bag S = $200 D = 20,000 bags x 50 wks x 5 daysd = 20,000 bags per day p = 50,000 bags per day
33
p
Q
d
Q lengthRun ;length Cycle
days 3.89every 000,20
850,77length Cycle
orderper days 56.1000,50
850,77lengthRun
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EOQ with Quantity Discounts Price reductions are often offered as incentive to
buy larger quantities Weigh benefits of reduced purchase price against
increased holding cost
R = per unit price of the itemD = annual demand
Annualholdingcost
PurchasingcostTC = +
Q2
H DQ
STC = +
+Annualorderingcost
RD +
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Total Cost with Purchase Cost
C
ost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing costdoesn’t change EOQ
35
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Total Cost with Quantity Discounts
36
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Best Purchase Quantity Procedure
begin with the lowest unit price
compute the EOQ for each price range
stop when find a feasible EOQ
Is EOQ for the lowest unit price
feasible?
Yes: it is the optimal order
quantity
No: compare total cost at all break quantities larger than feasible
EOQ
37
The quantity that yields the lowest total cost is optimum
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Example: Quantity DiscountsBelow is a quantity discount schedule for an item with
an annual demand of 10,000 units that a company orders regularly at an ordering cost of $4. The annual holding cost is 2% of the purchase price per year. Determine the optimal order quantity.
Order Quantity(units) Price/unit($)0 to 2,499 $1.202,500 to 3,999 1.004,000 or more .98
38
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
units 1,826 = 0.02(1.20)
4)2(10,000)( =
H
2DS = QO
D = 10,000 units S = $4
units 2,000 = 0.02(1.00)
4)2(10,000)( =
H
2DS = QO
units 2,020 = 0.02(0.98)
4)2(10,000)( =
H
2DS = QO
H = .02R R = $1.20, 1.00, 0.98
Interval from 0 to 2499, the Qo value is feasible
Interval from 2500-3999, Qo value is NOT feasible
Interval from 4000 & up, Qo value is NOT feasible
39
Order Quantity Price/unit($)0 to 2,499 $1.202,500 to 3,999 1.004,000 or more .98
Example: Quantity Discounts
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Quantity Discount Models
2500 4000
An
nu
al cost
0 Quantity
EOQs (not feasible)
1st break quantity
2nd break quantity
1st range total cost
curve
40
2nd range total cost curve
3rd range total cost curve
EOQ
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
TC(0-2499) = (1826/2)(0.02*1.20) + (10000/1826)*4+(10000*1.20) = $12,043.82
TC(2500-3999)= $10,041
TC(4000&more)= $9,949.20
Therefore the optimal order quantity is 4000 units
41
Example: Quantity Discounts
Q2H D
QSTC = + RD +
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EOQ with Planned Shortages Assumptions:
all shorted demand is back-orderedback-orders incur shortage costsshortage cost is proportional to waiting timeall other basic EOQ assumptions
42
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
EOQ with Planned Shortages
orderper cost setup)(or ordering S
demand annual D
unitper cost holding annual H
cycleorder per ordered-backquantity
yearper unit per cost order back
2
22
Cost
OrderBack
Annual
Cost
Ordering
Annual
Cost
Holding
Annual
TC
22
b
bb
Q
B
B
BH
H
DSQ
BQ
QS
Q
DH
Q
QQTC
43
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Example: EOQ with Planned Shortage
Annual demand for a refrigerator is 50 units. Holding cost per unit per year is $200. Back-order cost per unit per year is estimated to be $500.Ordering cost from the manufacturer is $10 per order. Determine order quantity and back-order quantity per order cycle.
44
D = 50 H = $200 B = $500 S = $10
2 2(50)(10) 200 5002.65, round to 3 units.
200
2003 0.86, round to1.
200 500b
DS H BQ
H B B
HQ Q
H B
Allow inventory to drop to zero. When another unit is demanded, order 3 units.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Concept Check
Which of the following is FALSE about EOQ?
A. It determines how many to order.B. The EOQ always results in the lowest total
cost.C. The model minimizes total cost by
balancing carrying and order costs.D. The model is robust and works even if all
assumptions are not exact.
45
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Concept Check
Which is NOT a difference between EOQ and EPQ?
A. A different formula is used.B. EPQ is used mainly for producing batches,
and EOQ is for receiving orders.C. Quantity is received gradually in EPQ.D. Demand can be variable for EPQ but not
for EOQ.
46
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Concept Check
Which is NOT an assumption of both EOQ and EPQ?
A. Demand is known with certainty and is constant over time
B. No shortages are allowedC. Order quantity is received all at onceD. Lead time for the receipt of orders is
constant
47
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
What’s next?
EOQ models give HOW MANY to orderNow look at WHEN to order
Reorder Point (ROP)
48
d = Demand rate (units per day or week)LT = Lead time (in days or weeks)Note: Demand and lead time must have the same time units.
ROP = d LT
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 3
Annual Demand = 1,000 units
Days per year = 365Lead time = 7 days
units/day 2.74 = days/year 365
units/year 1,000 = d
units 20or 19.18=(7days)units/day 2.74=L =ROP d
When inventory level reaches 20 units, place the next order.
49
Example: ROP
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
Fixed Order Quantity/Reorder Point Model
Safety Stock
1. Variability of demand and lead time 2. Service Level
2a. Lead time service level
2b. Annual service level
50
Reorder Point = Expected demand + Safety Stock (ROP) during lead time
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
When to Reorder with EOQ Ordering Reorder Point – When inventory level drops to this
amount, the item is reordered.
Safety Stock - Stock that is held in excess of expected demand due to variability of demand and/or lead time.
Service Level – Probability demand will not exceed supply. Lead time service level: probability that demand will not
exceed supply during lead time. Annual service level: percentage of annual demand filled.
51
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
Determinants of the Reorder Point
Rate of demand Lead time
Demand and/or lead
time variability
Stockout risk (safety stock)
52
ROP Expected demandSafety stockduring lead time
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
Safety Stock
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qu
an
tity
Safety stock
Safety stock reduces risk ofstockout during lead time
53
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
Reorder Point
54
z = Safety factor; number of standard deviations above expected demanddLT = The standard deviation of demand during lead time
Safety Stock = z.dLT
The ROP based on a normalDistribution of lead time demand
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 4
Demand During Lead Time
55
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
ROP with Lead Time Service Level
variable demand during a lead time
ROP = expected demand during lead time + safety stock
56
z = Safety factor; number of standard deviations above expected demanddLT = The standard deviation of demand during lead time
ROP = + z.dLT
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
ROP with Lead Time Service Level
variable demand and constant lead time
ROP = (average demand x lead time) + z x st. dev. of demand
during lead time(demand and lead time measures in same time units)
sd = standard deviation of demand per day
sdLT = sd LT
57
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
ROP with Lead Time Service Level
both demand and lead time are variable
ROP = (avg. demand x avg. lead time) + z x st. dev. of demand
in lead time(demand and lead time measures in same time units)
sd= standard deviation of demand per day
sLT= standard deviation of lead time
sdLT = (average lead time x sd2)
+ (average daily demand) 2sLT2
58
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Example 1: ROP with Lead Time Service Level
Calculate the ROP required to achieve a 95% service level for a product with average demand of 350 units per week and a standard deviation of demand during lead time of 10. Lead time averages one week.
From Table 12-3 (p434), z for 95% = 1.65
ROP = 350 + ZsdLT
= 350 + 1.65 (10)
= 350 + 16.5 = 366.5 ≈ 367
A new order should be placed when inventory level reaches 367 units.
59
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Example 2: ROP with Lead Time Service Level
Calculate the ROP and amount of safety stock required to achieve a 90% service level for a product with variable demand that averages 15 units per day with a standard deviation of 5. Lead time is consistently 2 days.
From Table 12-3 (p434), z for 90% = 1.28
ROP = (15 units x 2 days) + ZsdLT
= 30 + 1.28 ( 2) (5)
= 30 + 8.96 = 38.96 ≈ 39
Safety stock is about 9 units and a new order should be placed when inventory level reaches 39 units. 60
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Example 3: ROP with Lead Time Service Level
Calculate the ROP for a product that has an average demand of 150 units per day and a standard deviation of 16. Lead time averages 5 days, with a standard deviation of 2. The company wants no more than 5% stockouts.
service level = 1 – 5% = 95%From Table 12-3 (p434), z for 95% =
1.65
Place a new order when inventory level reaches 1004 units
61
ROP = (150 units x 5 days) + 1.65sdlt
= (150 x 5) + 1.65 (5 days x 162) + (1502 x 12)
= 750 + 1.65 (154) = 1,004 units
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
ROP Using Annual Service Level1. Calculate
2. Use a table to find the z value associated with E(z)
3. Use the z value in the appropriate ROP formula,
62
dLT
annualSLQzE
)1(
)(
dLTzROP timeleadduringdemandexpected
SLannual = annual service level E(z) = standardized expected number of units short during an order cycle.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Min/Max model
similar to fixed order-quantity/reorder point (ROP) model
difference:if at order time, Q on hand < min (ROP),
then order quantity = max – Q on hand(max EOQ + ROP)
63
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Inventory Models
EOQ/ROP modelOrder size constant, time between orders
changes
Fixed Order Interval/Order up to Level Modelorders placed at fixed time intervalsdetermine how much to order to bring inventory
level up to a predetermined point (order up to level)
used widely for retailconsider expected demand during lead time,
safety stock, and amount on handdemand or lead time can be variable
64
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Comparing Inventory Models
65
EOQ/ROP
Fixed Interval/
Order up to
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Disadvantagesrequires a larger safety stockincreases carrying costcosts of periodic reviews
Fixed Order Interval: Benefits and Disadvantages
Benefitsgrouping items from same supplier
can reduce ordering/shipping costspractical when inventories
cannot be closely monitored
66
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Fixed Order Interval/Order up to Level Model
Determining the order interval
67
OI = order interval (in fraction of a year)S = fixed ordering cost per purchase orders = variable ordering cost per SKU included in the order (line item)
(assume s is the same for every SKU)n = n number of SKUs purchased from the supplierRj = unit cost of SKUj , j = 1, …, ni = annual holding cost rateDj = annual demand of SKUj , j = 1, …., n
Total Annual Inventory Cost:
TC =
Optimal Order Interval:
OInsSiR
OIDj
j 1)(.
2
.
jj RDi
nsSOI
)(2*
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Fixed Order Interval/Order up to Level Model
Determining the Order up to Level
LTOIzLTOId d
Stock
Safety
interval
protection during
demand Expected
I
handon Amount IQ
max
max
68
= Average daily or weekly or monthly demand OI = Order interval (length of time between ordersLT = Lead time in days or weeks or monthsz = Safety factor; # of standard deviations above expected demandd = Standard deviation of daily or weekly or monthly demand
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
= 20 (30 + 10) + (2.32) (4) 30 + 10 = 800 + 2.32 (25.298) = 858.7 or 859 units stock up to level
Average daily demand for a product is 20 units, with a standard deviation of 4 units. The order interval is 30 days, and lead time is 10 days. Desired service level is 99%. If there are currently 200 units on hand, how many should be ordered?
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LTOIzLTOId d maxI
maxI
Amount to order = 859 – 200 = 659 units
Example: Fixed Order Interval Model
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 5
Coordinated Periodic Review Modeldetermines an order interval (OI) and order up to
level for reviewing every stock keeping unit (SKU)calculate a multiple (mi ) of OI for each SKUi
use this to determine the optimal OI for each SKUi
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To use:Compare on hand inventory of each SKU to its ROP
(forecast demand for next OI + lead time + safety stock)
if on hand is less: order a quantity that brings the on hand level to SKU’s order up-to levelthe order up-to level is enough for the next OI + LT.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 6
Single Period Model Single period model
model for ordering of perishables and other items with limited useful lives
Shortage cost Cs
generally the unrealized profits per unitRevenue per unit – Cost per unit
Excess cost Ce cost per unit - salvage per unit
for items left over at the end of a period
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GOAL = find order quantity (stock level) that minimizes total excess and shortage costs.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 6
Single Period Model
Continuous stocking levelsIdentifies optimal stocking levelsOptimal stocking level balances unit
shortage and excess cost
Discrete stocking levelsDesired service level is equaled or
exceededCompare service level to cumulative probability of
demand
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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 6
Optimal Stocking Level
Service Level
So
Quantity
Ce
Cs
Balance point
Service level (SL) =Cs
Cs + CeCs = Shortage cost per unitCe = Excess cost per unit
73So = Optimum stocking level (i.e., order quantity
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 6
Example 1: Single Period ModelCe = $0.20 per unitCs = $0.60 per unitService level = Cs/(Cs+Ce) =
.6/(.6+.2)Service level = .75
Service Level = 75%
Quantity
Ce
Cs
Stockout risk = 1.00 – 0.75 = 0.2574
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
LO 6
Example 2: Single Period Model
The Poisson table (App. B, Table C) Cs is unknown Ce = $500
provides these values for a mean of 2.0: Number of FailuresCumulative Probability0 .1351 .4062 .6773 .8574 .9475 .983
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s.406, so .406($500 )$500s
ss
CC C
C
Optimum stock level = 2, then
SL between
Cs = $343.17
The range of shortage cost is $343.17 to $1,047.99.
.677, so .677($500 )$500s
s ss
CC C
C
Cs = $1,047.99.
A company usually carries 2 units of a spare part that costs $500 and has no salvage value. Part failures can be modeled by a Poisson distribution with a mean of 2 failures during the useful life of the equipment. Estimate the range of shortage cost for which stocking 2 units of this spare part is optimal.
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Review: Inventory Models
EOQ models used to determine order sizeSimple model for many types of inventoryTrade-off between carrying and ordering costsQuantity discount model adds purchasing costs
and compares total cost for various order sizes (that is still a feasible EOQ)
EPQ models used to determine production lot sizeUsed when producing and depleting items at
same timeTrade-off between carrying and setup costsConsider production and usage rate
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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Review: Inventory Models ROP (reorder point)
Determines at what quantity (when) to re-order Consider expected demand during lead time and
safety stock Trade-off cost of carrying safety stock & risk of
stockout Fixed Order Interval Model
Used when orders placed at fixed time intervals – determine how much to order
Used widely for retailConsider expected demand during lead time, safety
stock, and amount on handDemand or lead time can be variable Need more safety stock, but not continuous
monitoring Single-Period Model
Determines at what quantity (when) to re-order Used when can’t carry goods to next period (e.g..
perishables)Trade-off cost of shortages & of excess (wasted)
inventory
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Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Checklist
Define the term inventory and list the major reasons for holding inventories.
Discuss the objectives of inventory management.
List the main requirements for effective inventory management.
Describe the A-B-C approach and perform it.Describe Basic Inventory Control SystemsBe able to describe and solve problems
using: EOQ, EPQ, ROP, Fixed Order Interval Model, Single Period Model.
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