OPM 5339-1
Operations Operations ManagementManagement
Inventory ManagementInventory ManagementChapter 9Chapter 9
OPM 5339-2
Stock of materials Stored capacity Examples
© 1995 Corel Corp.© 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co.
© 1995 Corel Corp.
What is Inventory?
OPM 5339-3
The Functions of InventoryTo ”decouple” or separate various parts of the
production processTo provide a stock of goods that will provide a
“selection” for customersTo take advantage of quantity discountsTo hedge against inflation and upward price
changes
OPM 5339-4
Types of InventoryRaw material (RM)Work-in-progress (WIP)Maintenance/repair/operating supply (MRO)Finished goods (FG)
OPM 5339-5
Higher costs Item cost (if purchased) Ordering (or setup) cost
Costs of forms, clerks’ wages etc. Holding (or carrying) cost
Building lease, insurance, taxes etc.
Difficult to control Hides production problems
Disadvantages of Inventory
OPM 5339-6
Inventory
Process stage
Demand Type
Number & Value Other
Raw Material WIP
Finished Goods
Independent
Dependent
A Items
B Items
C Items
Maintenance Operating
© 1984-1994 T/Maker Co.
Inventory Classifications
OPM 5339-7
1 Run time: Job is at machine and being worked on2 Setup time: Job is at the work station, and the work station is
being "setup."3 Queue time: Job is where it should be, but is not being
processed because other work precedes it.4 Move time: The time a job spends in transit5 Wait time: When one process is finished, but the job is
waiting to be moved to the next work area.6 Other: "Just-in-case" inventory.
The Material Flow Cycle
Other WaitTime
MoveTime
Queue
Time
SetupTime
RunTime
Input
Cycle Time
Output
OPM 5339-8
Divides on-hand inventory into 3 classes A class, B class, C class
Basis is usually annual $ volume $ volume = Annual demand x Unit cost
Policies based on ABC analysis Develop class A suppliers more Give tighter physical control of A items Forecast A items more carefully
ABC Analysis
OPM 5339-9% of Inventory Items
Classifying Items as ABC
0
20
40
60
80
100
0 50 100
% Annual $ Usage
AA
BBCC
Class % $ Vol % Items
A 80 15B 15 30C 5 55
OPM 5339-10
Physically counting a sample of total inventory on a regular basis
Used often with ABC classification A items counted most often (e.g., daily)
Cycle Counting
OPM 5339-11
Advantages of Cycle Counting
Eliminates shutdown and interruption of production necessary for annual physical inventories
Eliminates annual inventory adjustmentsProvides trained personnel to audit the accuracy
of inventoryAllows the cause of errors to be identified and
remedial action to be takenMaintains accurate inventory records
OPM 5339-12
Techniques for Controlling Service Inventory Include:
Good personnel selection, training, and disciplineTight control of incoming shipmentsEffective control of all goods leaving the facility
OPM 5339-13
Independent versus Dependent Demand
Independent demand - demand for item is independent of demand for any other item
Dependent demand - demand for item is dependent upon the demand for some other item
OPM 5339-14
Inventory CostsHolding costs - associated with holding or
“carrying” inventory over time; e.g. obsolescence, insurance, extra staffing, interest, pilferage, damage, warehousing, etc.
Ordering costs - associated with costs of placing order and receiving goods; eg. Supplies, forms, order processing, clerical support, etc.
Setup costs - cost to prepare a machine or process for manufacturing an order; e.g. clean-up costs, re-tooling costs, adjustment costs, etc.
OPM 5339-15
Inventory Holding Costs(Approximate Ranges)
Category
Housing costs (building rent, depreciation, operating cost, taxes, insurance)
Material handling costs (equipment, lease or depreciation, power, operating cost)
Labor cost from extra handling
Investment costs (borrowing costs, taxes, and insurance on inventory)
Pilferage, scrap, and obsolescence
Overall carrying cost
Cost as a % of Inventory
Value6%
(3 - 10%)
3%(1 - 3.5%)
3%(3 - 5%)
11%(6 - 24%)
3% (2 - 5%)26%
OPM 5339-16
Fixed order-quantity modelsEconomic order quantityProduction order quantityQuantity discount
Probabilistic models
Fixed order-period models
Help answer the inventory planning questions!
Help answer the inventory planning questions!
© 1984-1994 T/Maker Co.
Inventory Models
OPM 5339-17
Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts Only order (setup) cost and holding cost No stockouts
1. EOQ Assumptions
OPM 5339-18
Inventory Usage Over Time
Time
Inve
ntor
y Le
vel
AverageInventory
(Q*/2)
0
Minimum inventory
Order quantity = Q (maximum inventory level)
Usage Rate
OPM 5339-19
EOQ ModelHow Much to Order?
Order quantity
Annual Cost
Holding Cost CurveTotal Cost Curve
Order (Setup) Cost Curve
Optimal Order Quantity (Q*)
Minimum total cost
OPM 5339-20
More units must be stored if more are ordered
Purchase OrderDescription Qty.Microwave 1
Order quantity
Purchase OrderDescription Qty.Microwave 1000
Order quantity
Why Holding Costs Increase
OPM 5339-21
Cost is spread over more units
Example: You need 1000 microwave ovens
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
Purchase OrderDescription Qty.Microwave 1
1 Order (Postage $ 0.33) 1000 Orders (Postage $330)
Order quantity
Purchase Order
Description Qty.Microwave 1000
Why Order Costs Decrease
OPM 5339-22
Deriving an EOQ1. Develop an expression for setup or ordering
costs
2. Develop an expression for holding cost
3. Set setup cost equal to holding cost
4. Solve the resulting equation for the best order quantity
OPM 5339-23
Optimal Order Quantity
Expected Number of Orders
Expected Time Between Orders Working Days / Year
Working Days / Year
= =× ×
= =
= =
=
= ×
Q*D S
H
ND
Q*
TN
dD
ROP d L
2
D = Demand per year
S = Setup (order) cost per order
H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
EOQ Model Equations
OPM 5339-24
The Reorder Point (ROP) Curve
Q*
ROP (Units)
Slope = units/day = d
Lead time = L
Time (days)
Inve
ntor
y le
vel
(uni
ts)
OPM 5339-25
Answers how much to order and when to order Allows partial receipt of material
Other EOQ assumptions apply Suited for production environment
Material produced, used immediately Provides production lot size
Lower holding cost than EOQ model
2. Production Order Quantity Model
OPM 5339-26
Reasons for Variability in Production
Most variability is caused by waste or by poor management. Specific causes include: employees, machines, and suppliers produce
units that do not conform to standards, are late or are not the proper quantity
inaccurate engineering drawings or specifications production personnel try to produce before
drawings or specifications are complete customer demands are unknown
OPM 5339-27
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per day
POQ Model Equations
Optimal Order Quantity
Setup Cost
Holding Cost
= =
-
= *
= *
=
Q
H*d
p
Q
D
QS
p*
1
(
0.5 * H * Q -d
p1
)-d
p1
( )
2*D*S
( )Maximum inventory level
OPM 5339-28
Answers how much to order & when to order
Allows quantity discounts Reduced price when item is purchased in larger
quantities Other EOQ assumptions apply
Trade-off is between lower price & increased holding cost
3. Quantity Discount Model
Inventory Usage Over Time
29Figure 12.3Figure 12.3
Order Order quantity = Q quantity = Q (maximum (maximum inventory inventory
level)level)
Inve
nto
ry le
vel
Inve
nto
ry le
vel
TimeTime
Usage rateUsage rate Average Average inventory inventory on handon hand
QQ22
Minimum Minimum inventoryinventory
Minimizing Costs
30
Objective is to minimize total costsObjective is to minimize total costs
Table 11.5Table 11.5
An
nu
al c
ost
An
nu
al c
ost
Order quantityOrder quantity
Curve for total Curve for total cost of holding cost of holding
and setupand setup
Holding cost Holding cost curvecurve
Setup (or order) Setup (or order) cost curvecost curve
Minimum Minimum total costtotal cost
Optimal Optimal order order
quantityquantity
The EOQ Model
31
QQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per year
Annual setup cost Annual setup cost == ((Number of orders placed per yearNumber of orders placed per year) ) x (x (Setup or order cost per orderSetup or order cost per order))
Annual demandAnnual demand
Number of units in each orderNumber of units in each orderSetup or order Setup or order cost per ordercost per order
==
= (= (SS))DDQQ
Annual setup cost = SDQ
The EOQ Model
32
QQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per year
Annual holding cost Annual holding cost == ((Average inventory levelAverage inventory level) ) x (x (Holding cost per unit per yearHolding cost per unit per year))
Order quantityOrder quantity
22= (= (Holding cost per unit per yearHolding cost per unit per year))
= (= (HH))QQ22
Annual setup cost = SDQ
Annual holding cost = HQ2
The EOQ Model
33
QQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup cost Optimal order quantity is found when annual setup cost equals annual holding costequals annual holding cost
Annual setup cost = SDQ
Annual holding cost = HQ2
DDQQ
SS = = HHQQ22
Solving for Q*Solving for Q*22DS = QDS = Q22HHQQ22 = = 22DS/HDS/H
Q* = Q* = 22DS/HDS/H
An EOQ Example
34
Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units unitsS S = $10= $10 per order per orderH H = $.50= $.50 per unit per year per unit per year
Q* =Q* =22DSDS
HH
Q* =Q* =2(1,000)(10)2(1,000)(10)
0.500.50= 40,000 = 200= 40,000 = 200 units units
An EOQ Example
35
Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q* Q* = 200= 200 units unitsS S = $10= $10 per order per orderH H = $.50= $.50 per unit per year per unit per year
= N = == N = =Expected Expected number of number of
ordersorders
DemandDemandOrder quantityOrder quantity
DDQ*Q*
N N = = 5= = 5 orders per year orders per year 1,0001,000200200
An EOQ Example
36
Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q*Q* = 200= 200 units unitsS S = $10= $10 per order per order NN = 5= 5 orders per year orders per yearH H = $.50= $.50 per unit per year per unit per year
= T == T =Expected Expected
time between time between ordersorders
Number of working Number of working days per yeardays per year
NN
T T = = 50 = = 50 days between ordersdays between orders250250
55
An EOQ Example
37
Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q*Q* = 200= 200 units unitsS S = $10= $10 per order per order NN = 5= 5 orders per year orders per yearH H = $.50= $.50 per unit per year per unit per year TT = 50= 50 days days
Total annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding cost
TC = S + HTC = S + HDDQQ
QQ22
TC TC = ($10) + ($.50)= ($10) + ($.50)1,0001,000200200
20020022
TC TC = (5)($10) + (100)($.50) = $50 + $50 = $100= (5)($10) + (100)($.50) = $50 + $50 = $100
An EOQ Example with safety stock
38
Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 units units Q*Q* = 200= 200 units unitsS S = $10= $10 per order per order NN = 5= 5 orders per year orders per yearH H = $.50= $.50 per unit per year per unit per year TT = 50= 50 days daysSafety Stock (ss) = 10 unitsSafety Stock (ss) = 10 unitsTotal annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding cost
TC = S + TC = S + (( + ss + ss))HHDDQQ
QQ22
TC TC = ($10) + (100 + )($.50)= ($10) + (100 + )($.50)1,0001,000200200
20020022
TC TC = (5)($10) + (200)($.50) = $50 + $100 = $150= (5)($10) + (200)($.50) = $50 + $100 = $150
Reorder Points
39
EOQ answers the “how much” questionEOQ answers the “how much” question
The reorder point (ROP) tells when to The reorder point (ROP) tells when to orderorder
ROP ROP ==Lead time for a Lead time for a
new order in daysnew order in daysDemand Demand per dayper day
== d x L d x L
d = d = DDNumber of working days in a yearNumber of working days in a year
Reorder Point Curve
40
Q*Q*
ROP ROP (units)(units)In
ven
tory
lev
el (
un
its)
Inve
nto
ry l
evel
(u
nit
s)
Time (days)Time (days)Figure 12.5Figure 12.5 Lead time = LLead time = L
Slope = units/day = dSlope = units/day = d
Reorder Point Example
41
Demand Demand = 8,000= 8,000 DVDs per year DVDs per year250250 working day year working day yearLead time for orders is Lead time for orders is 33 working days working days
ROP =ROP = d x L d x L
d =d = DD
Number of working days in a yearNumber of working days in a year
= 8,000/250 = 32= 8,000/250 = 32 units units
= 32= 32 units per day x units per day x 33 days days = 96= 96 units units
Reorder point with Safety Stock
42
Annual Demand = 25,000 units Annual Demand = 25,000 units Number of working days in a year 250 daysNumber of working days in a year 250 daysLead time = 5 daysLead time = 5 daysSafety stock (ss) = 2 days usageSafety stock (ss) = 2 days usage
ROP = d x l + ssROP = d x l + ss
d= D / Number of days work in a yeard= D / Number of days work in a year
d= 25,000 / 250 = 100 units d= 25,000 / 250 = 100 units
ss= 2 days x 100 = 200ss= 2 days x 100 = 200
ROP = 100 x 5 + 200 = 700 unitsROP = 100 x 5 + 200 = 700 units
Quantity Discount Models
43
Reduced prices are often available when Reduced prices are often available when larger quantities are purchasedlarger quantities are purchased
Trade-off is between reduced product cost Trade-off is between reduced product cost and increased holding costand increased holding cost
Total cost = Setup cost + Holding cost + Product costTotal cost = Setup cost + Holding cost + Product cost
TC = S + + PDTC = S + + PDDDQQ
QHQH22
Quantity Discount Models
44
Discount Number Discount Quantity Discount (%)
Discount Price (P)
1 0 to 999 no discount $5.00
2 1,000 to 1,999 4 $4.80
3 2,000 and over 5 $4.75
Table 12.2Table 12.2
A typical quantity discount scheduleA typical quantity discount schedule
Quantity Discount Models
45
1.1. For each discount, calculate Q*For each discount, calculate Q*
2.2. If Q* for a discount doesn’t qualify, If Q* for a discount doesn’t qualify, choose the smallest possible order size choose the smallest possible order size to get the discountto get the discount
3.3. Compute the total cost for each Q* or Compute the total cost for each Q* or adjusted value from Step 2adjusted value from Step 2
4.4. Select the Q* that gives the lowest total Select the Q* that gives the lowest total costcost
Steps in analyzing a quantity discountSteps in analyzing a quantity discount
Quantity Discount Models
46
1,0001,000 2,0002,000
To
tal
cost
$T
ota
l co
st $
00
Order quantityOrder quantity
Q* for discount 2 is below the allowable range at point a Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point band must be adjusted upward to 1,000 units at point b
aabb
1st price 1st price breakbreak
2nd price 2nd price breakbreak
Total cost Total cost curve for curve for
discount 1discount 1
Total cost curve for discount 2Total cost curve for discount 2
Total cost curve for discount 3Total cost curve for discount 3
Figure 12.7Figure 12.7
Quantity Discount Example
47
Calculate Q* for every discountCalculate Q* for every discount Q* =2DSIP
QQ11* * = = 700= = 700 cars order cars order2(5,000)(49)2(5,000)(49)
(.2)(5.00)(.2)(5.00)
QQ22* * = = 714= = 714 cars order cars order2(5,000)(49)2(5,000)(49)
(.2)(4.80)(.2)(4.80)
QQ33* * = = 718= = 718 cars order cars order2(5,000)(49)2(5,000)(49)
(.2)(4.75)(.2)(4.75)
Quantity Discount Example
48
Calculate Q* for every discountCalculate Q* for every discount Q* =2DSIP
QQ11* * = = 700= = 700 cars order cars order2(5,000)(49)2(5,000)(49)
(.2)(5.00)(.2)(5.00)
QQ22* * = = 714= = 714 cars order cars order2(5,000)(49)2(5,000)(49)
(.2)(4.80)(.2)(4.80)
QQ33* * = = 718= = 718 cars order cars order2(5,000)(49)2(5,000)(49)
(.2)(4.75)(.2)(4.75)
1,0001,000 — adjusted — adjusted
2,0002,000 — adjusted — adjusted
Quantity Discount Example
49
Discount Number
Unit Price
Order Quantity
Annual Product
Cost
Annual Ordering
Cost
Annual Holding
Cost Total
1 $5.00 700 $25,000 $350 $350 $25,700
2 $4.80 1,000 $24,000 $245 $480 $24,725
3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50
Table 12.3Table 12.3
Choose the price and quantity that gives Choose the price and quantity that gives the lowest total costthe lowest total cost
Buy Buy 1,0001,000 units at units at $4.80$4.80 per unit per unit
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