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Chapter 13Inventory
Management
Management 3620 Chapter 13 Inventory Management 13-2
Independent Demand(Chapter 13)
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand(Chapter 15)
Independent demand is uncertainDependent demand is certain
Independent vs. Dependent Demand
Management 3620 Chapter 13 Inventory Management 13-3
Types of Inventories (1 of 2)
• Raw materials & purchased parts
• Partially completed goods called work in progress
• Finished-goods inventories – (manufacturing firms)
or merchandise (retail stores)
Management 3620 Chapter 13 Inventory Management 13-4
Types of Inventories (2 of 2)
• Replacement parts, tools, & supplies
• Goods-in-transit (pipeline) to warehouses or customers
Management 3620 Chapter 13 Inventory Management 13-5
Functions of Inventory• Meet anticipated demand
• Smooth production requirements
• Decouple components (areas) of the production-distribution
• Protect against stock-outs
• Take advantage of order cycles
• Help hedge against price increases or to take advantage of quantity discounts
• Permit operations (operation lead time)
Management 3620 Chapter 13 Inventory Management 13-6
Concerns ofInventory Management
• Level of customer service– have the right goods, in sufficient
quantities, in the right place, at the right time
– in other words, the customer gets what ever he/she wants when he/she wants it
• Inventory-related costs – ordering costs
– carrying costs
Management 3620 Chapter 13 Inventory Management 13-7
Objectives ofInventory Management (1 of 2)
• Achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
• Two fundamental decisions– how much to order
– when to place the order
Management 3620 Chapter 13 Inventory Management 13-8
Objectives ofInventory Management (2 of 2)
• Possible performance measures– customer satisfaction
• number of backorders/lost sales• number of customer complaints
– inventory turnover• ratio of annual cost of goods sold to
average inventory investment
– days of inventory• expected number of days of sales that
can be supplied from existing inventory
Management 3620 Chapter 13 Inventory Management 13-9
Requirements for Effective Inventory Management
• A system to keep track of the inventory on hand and on order
• A classification system for inventory items
• A reliable forecast of demand that includes an measure of forecast error
• Reasonable estimates of inventory holding costs, ordering costs, and shortage costs
• Knowledge of lead times and lead time variability
Management 3620 Chapter 13 Inventory Management 13-10
Inventory Counting Systems (1 of 2)
• Perpetual Inventory (Continual) System– Keeps track of removals
from and receipts into inventory continuously
• Periodic System– Physical count of items
made at periodic intervals
Management 3620 Chapter 13 Inventory Management 13-11
Inventory Counting Systems (2 of 2)
• Universal Product Code - Bar code printed on a label that hasinformation about the item to which it is attached
• Cycle counting - taking physical counts of items and reconciling with records on a continual rotating basis
0
214800 232087768
Management 3620 Chapter 13 Inventory Management 13-12
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
Figure 13-1
Annual $ volume of items
AA
BB
CC
High
Low
Few ManyNumber of Items
Management 3620 Chapter 13 Inventory Management 13-13
Demand Forecast andLead Time Information
• Reliable estimates of the amount and timing of demand
• Lead time - time interval between ordering and receiving the order
• Extent of variability in demand and lead time
Management 3620 Chapter 13 Inventory Management 13-14
Internal Order CycleOrder Request/RequisitionAuthorization signatures obtainedVerification by inventory controlPurchasing researches vendors, obtains quotes, etc.Order transferred to vendor
Internal Order CycleOrder Request/RequisitionAuthorization signatures obtainedVerification by inventory controlPurchasing researches vendors, obtains quotes, etc.Order transferred to vendor
Vendor CycleReceives and enters orderManufactures or “picks” orderShips order
Vendor CycleReceives and enters orderManufactures or “picks” orderShips order
Internal Receiving CycleReceivingIncoming inspectionInventory control receives order, updates records, and notifies department
Internal Receiving CycleReceivingIncoming inspectionInventory control receives order, updates records, and notifies department
The Typical Procurement Cycle
Management 3620 Chapter 13 Inventory Management 13-15
Cost Information
• Holding or carrying costs
• Ordering costs
• Shortage costs
Management 3620 Chapter 13 Inventory Management 13-16
Holding or Carrying Costs
• Cost to carry a unit in inventory for a length of time
• Includes interest (opportunity cost), insurance, taxes, depreciation, obsolescence, deterioration
• May be expressed as a percentage of unit price or as a dollar amount per unit
Management 3620 Chapter 13 Inventory Management 13-17
Ordering Costs
• Cost of ordering and receiving inventory
• Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality
• Generally expressed as a fixed dollar amount, regardless of order size
Management 3620 Chapter 13 Inventory Management 13-18
Shortage Costs
• Result when demand exceeds the inventory on hand
• Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime
• Difficult to measure, thus may have be subjectively estimated
Management 3620 Chapter 13 Inventory Management 13-19
Basic Systems for Independent Demand
• Fixed-order-quantity systems– basic economic order quantity (EOQ)
model [purchasing model]– basic economic order quantity model
with incremental or noninstantaneous replenishment [production order quantity]
– quantity discount model
• Fixed-order-interval systems
Management 3620 Chapter 13 Inventory Management 13-20
Basic Model Assumptions• Only one product is involved• Annual demand requirements are known• Demand is spread evenly throughout the
year so that the demand rate is reasonable constant
• Lead time does not vary• Each order is received in a single
delivery• There are no quantity discounts, i.e., the
price is constant
Management 3620 Chapter 13 Inventory Management 13-21
Receive order
How the Basic Fixed-Order-Quantity Model Works
Lead time
Profile of Inventory Level Over Time
Quantityon hand
Q
Placeorder
Receive order
Placeorder
Receive order
Reorderpoint
Usage rate
Figure 13-2
Management 3620 Chapter 13 Inventory Management 13-22
Annualcarryingcost
Annualorderingcost
TotalAnnual =cost
+
Q
2H
D
QSTC = +
How Much to Order
Goal is to minimize total annual costs
Management 3620 Chapter 13 Inventory Management 13-23
Cost Minimization Goal
The Total Cost Curve is U-Shaped
AnnualOrdering Costs
QO
Order Quantity (Q)
An
nu
al C
os
t
(optimal order quantity)
AnnualCarrying Costs
SQ
DH
Q
2 TC
Management 3620 Chapter 13 Inventory Management 13-24
Minimum Total Cost The total cost curve reaches its minimum
where the carrying and ordering costs are equal.
Alternatively we can use calculus by taking the first derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Cost Holding Annual
Cost) Setup or derDemand)(Or 2(Annual =
H
2DS = QOPT
Management 3620 Chapter 13 Inventory Management 13-25
Example 2, page 555
D=9,600 tires/yearH=$16/tire/yearS=$75/order
a. What is the EOQ?
Management 3620 Chapter 13 Inventory Management 13-26
Example 2, page 555
D=9,600 tires/yearH=$16/tire/yearS=$75/order
b. How many times per year does the store reorder?
Management 3620 Chapter 13 Inventory Management 13-27
Example 2, page 555
D=9,600 tires/yearH=$16/tire/yearS=$75/order
c. What is the length of an order cycle?
Management 3620 Chapter 13 Inventory Management 13-28
Example 2, page 555D=9,600 tires/year H=$16/tire/yearS=$75/order
d. What is the total cost if the EOQ quantity is ordered?
Management 3620 Chapter 13 Inventory Management 13-29
Fixed Order Quantity Model with Incremental Replenishment• Used to determine the order size,
production lot, if an item is produced at one stage of production and then sent to the next stage or the customer
• Differs from the basic model because orders are assumed to be supplied or produced at a uniform rate (p) rather than the order being received all at once
Management 3620 Chapter 13 Inventory Management 13-30
Fixed Order Quantity Model with Incremental Replenishment
Profile of Inventory Level Over Time
Quantityon hand
Q
Start toreceive order
Placeorder
Start toreceive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
TimeFinishreceiving order
Production rate- usage rate
Management 3620 Chapter 13 Inventory Management 13-31
Fixed Order Quantity Modelwith Incremental Replenishment• It is also assumed that the supply
rate, p, is greater than the usage rate, u
• The change in maximum inventory level requires modification of the TC equation
SQ
D + H
p
u-p
2
Q = TC
O
O
Management 3620 Chapter 13 Inventory Management 13-32
Fixed Order Quantity Modelwith Incremental Replenishment• The optimization results in
u-p
p
H
2DS QO
Management 3620 Chapter 13 Inventory Management 13-33
Example 4, page 558
D=48,000 wheels/yearH=$1/wheel/yearS=$45/setup
p=800 wheels/day
y wheels/da200=u
days/year 240
ar wheels/ye48,000=u
a. Optimal run size
Management 3620 Chapter 13 Inventory Management 13-34
Example 4, page 558
D=48,000 wheels/yearH=$1/wheel/yearS=$45/setup
p=800 wheels/day
b. Minimum total annual cost for carrying and setup
u=200 wheels/day
Management 3620 Chapter 13 Inventory Management 13-35
Example 4, page 558
D=48,000 wheels/yearH=$1/wheel/yearS=$45/setup
p=800 wheels/day
c. Cycle time for the optimal run size
u=200 wheels/day
Management 3620 Chapter 13 Inventory Management 13-36
Example 4, page 558
D=48,000 wheels/yearH=$1/wheel/yearS=$45/setup
p=800 wheels/day
d. Run time
u=200 wheels/day
Management 3620 Chapter 13 Inventory Management 13-37
Quantity Discount Model• This model differs from the basic model
because the price per unit (P) may vary with the quantity ordered
• The supplier offers a lower unit price if larger quantities are ordered at one time
• This is presented as a price or discount schedule, i.e., a certain unit price covers a certain order quantity range
Management 3620 Chapter 13 Inventory Management 13-38
Discount ScheduleProblem 14, page 588
Quantity Price
1 - 399400 - 599
600+
$10$9
$8
Management 3620 Chapter 13 Inventory Management 13-39
Quantity Discount
• Under this condition, annual product cost becomes an incremental cost and must be considered in the determination of the EOQ
• The total annual costs (TC) = Annual holding cost + annual setup cost + annual product cost
TC = (Q/2)H + (D/Q)S + DP
Management 3620 Chapter 13 Inventory Management 13-40
Total Cost Curvefor Price 3
Total Cost Curvefor Price 1
Total Cost Curvefor Price 2
Costs FunctionsUnder Quantity Discount
Order Quantity
$ co
st
Figure 13-8
Management 3620 Chapter 13 Inventory Management 13-41
Total Cost Curvefor Price 3
Total Cost Curvefor Price 1
Total Cost Curvefor Price 2
Costs FunctionsUnder Quantity Discount
Order Quantity
$ co
st
Quantity at whichprice 1 ends andprice 2 begins
Management 3620 Chapter 13 Inventory Management 13-42
Total Cost Curvefor Price 3
Total Cost Curvefor Price 1
Total Cost Curvefor Price 2
Costs FunctionsUnder Quantity Discount
Order Quantity
$ co
st
Quantity at whichprice 2 ends andprice 3 begins
Management 3620 Chapter 13 Inventory Management 13-43
Costs FunctionsUnder Quantity Discount
Order Quantity
$ co
st
TOTAL COST CURVE
Management 3620 Chapter 13 Inventory Management 13-44
Quantity Discount
To find the EOQ, the following procedure is used
1 Compute the basic EOQ.
Management 3620 Chapter 13 Inventory Management 13-45
Quantity Discount2 Using the appropriate price for the
for the EOQ found in Step 1, compute the TC
Management 3620 Chapter 13 Inventory Management 13-46
Quantity Discount3 Compute the TC for all quantities
greater than Step 1’s EOQ where a discount begins. Select the quantity with the lowest TC as the EOQ
Management 3620 Chapter 13 Inventory Management 13-47
Problem 14a, page 588
Order Quantity
$ co
st
400 600
P=$10
P=$9
P=$8
$41,000
Management 3620 Chapter 13 Inventory Management 13-48
Problem 14b, page 588
Order Quantity
$ co
st
400 600
P=$10
P=$9
P=$8
D=25 stones/day x 200 days/year = 5,000stones/yearH=.30 x PS=$48/order
Management 3620 Chapter 13 Inventory Management 13-49
Quantity Discount
To find the EOQ, the following procedure is used
1 Compute the basic EOQ using the lowest unit price and H=IP where I is an interest rate. If the resulting EOQ is feasible, i.e., that quantity can be purchased at the price used, it is optimal. Otherwise, go on to Step 2
Management 3620 Chapter 13 Inventory Management 13-50
Problem 14b, page 588
D=5,000 stones/yearH=.30 x $8 = $2.40/year/stoneS=$48/order Compute the basic EOQ
Management 3620 Chapter 13 Inventory Management 13-51
Quantity Discount2 Using the EOQ from Step 1 and the
discount schedule, find the price that should have been used and compute a new EOQ using this price. This new EOQ should be feasible.
Management 3620 Chapter 13 Inventory Management 13-52
Quantity Discount
3 Compute the TC for the feasible EOQ found in Step 2
Management 3620 Chapter 13 Inventory Management 13-53
Quantity Discount4 Compute the TC for all quantities
greater than Step 2’s EOQ where a discount begins. Select the quantity with the lowest TC as the EOQ
Management 3620 Chapter 13 Inventory Management 13-54
The Reorder Point• In the fixed quantity system, the question
of “when to order” is answered by setting a reorder point (ROP), an inventory level
• When the inventory drops to this level, the activities involved in the ordering or replenishment process are triggered.
• The time that it takes to complete these activities is the lead time
• The lead time period ends when the order is received
Management 3620 Chapter 13 Inventory Management 13-55
The Reorder Point• During this lead time, customer
demand continues and the inventory continues to decrease
• This is the only time you can run out of inventory (stockout)
• Management wants to set the reorder point sufficiently high to serve most of the customers, but not so high that carrying costs are excessive; a tradeoff
Management 3620 Chapter 13 Inventory Management 13-56
The Reorder Point• One way to handle this tradeoff is for
management to specify the customer service level they want their inventory management system to maintain– order cycle service level is the
probability that demand will not exceed the reorder point during the lead time
– annual service level is the percentage of demand filled directly from inventory
Management 3620 Chapter 13 Inventory Management 13-57
Setting the Reorder Point• If the demand during the lead time is
constant, the reorder point would be set equal to that demand
• If the demand during the lead time is not constant, i.e., there is variability, the demand is assumed to follow some distribution
• Typically the distribution is assumed to be a normal distribution
Management 3620 Chapter 13 Inventory Management 13-58
Quantity Demanded
Distribution of DemandOver the Lead Time
Normal distribution with amean, , and a standard deviation,
Management 3620 Chapter 13 Inventory Management 13-59
Quantity Demanded
If the ROP is set at the mean of the distribution, what would the order cycle service level be?
ROP
Management 3620 Chapter 13 Inventory Management 13-60
Quantity Demanded
ROP
Servicelevel
What if management wanted the order cycle service level to be greater than 50%?
Management 3620 Chapter 13 Inventory Management 13-61
Basis for Setting the Reorder Point
• Determinants of the reorder point– The parameters (mean and standard
deviation) of the distribution of demand over the entire lead time
– The probability that demand will not exceed the reorder point during the lead time acceptable to management, order cycle service level
Management 3620 Chapter 13 Inventory Management 13-62
Developing the Demand Distribution Parameters
• We assume that the demand for each time period (usually a day) comes from a normal distribution with a mean of and a standard deviation of
• We also assume the lead time is constant at some number of time periods (usually days)
ddσ
Management 3620 Chapter 13 Inventory Management 13-63
Lead Time Demand
Placeorder
Receiveorder
Lead Time
To determine the parameters of the distribution of demand over the entire lead time period, we need to add together the demand distributions for each day of the lead time
Management 3620 Chapter 13 Inventory Management 13-64
SummationLead Time Demand
Placeorder
Receiveorder
Lead Time
+
++
+Since the daily demand distributions are assumed to be identical, the distribution has a mean of and a standard deviation of
( )LTd( )LTσd
Management 3620 Chapter 13 Inventory Management 13-65
Lead Time Demand
Placeorder
Receiveorder
Lead Time
( )LTdGiven the order cycle service level, the proper safety stock is calculated using the normal table.
safety stock
Reorder point
Given the order cycle service level, the proper safety stock is calculated using the normal table. The reorder point is found by adding this safety stock amount to the mean (expected demand)
Management 3620 Chapter 13 Inventory Management 13-66
Lead Time Demand
Placeorder
Receiveorder
Lead Time
( )LTd
safety stock
Reorder point
The safety stock is where is found in the normal table based on the specified order cycle service level
z LTdz
Management 3620 Chapter 13 Inventory Management 13-67
Lead Time Demand
Placeorder
Receiveorder
Lead Time
( )LTd
safety stock
Reorder point
Order cycle service level
Risk of shortage
Management 3620 Chapter 13 Inventory Management 13-68
Risk ofa stockout
Order cycle service level
Probability ofno stockout
Mean or expected demand =
Safetystock
Quantity
Reorder Point Calculation
( )LT dStandard deviation = LTσd
( ) LTσz + LT d = ROP d
Management 3620 Chapter 13 Inventory Management 13-69
Administration of the System• Using the perpetual counting system, a signal is given
when the records indicate that the inventory reaches the ROP
• Using the periodic counting system, a two-bin system could be used– two bins of inventory– bin A holds an amount equal to the reorder point– bin B holds the remainder of the order– customers are supplied out of bin B– when bin B is empty, it is time to reorder– customers are then supplied out of bin A until the order
arrives
Fixed-Order-Interval Model
Management 3620 Chapter 13 Inventory Management 13-71
Basic Fixed-Order-Interval System
Time
Inve
nto
ry L
evel
Target Maximum
Minimum Inventory
OrderQuantity
OI
OrderQuantity
OrderQuantity
OrderQuantity
OI OI OI
When to order
How muchto order
Inventory Level Over Time
Figure 13-15
Management 3620 Chapter 13 Inventory Management 13-72
Operation ofFixed-Order-Interval Systems
• As demand for the inventoried item occurs, the inventory level drops
• When a prescribed period of time has elapsed, the ordering process is triggered, i.e., the time between orders is fixed or constant
• At that time the order quantity is determined using order quantity = target maximum level - current inventory level
Management 3620 Chapter 13 Inventory Management 13-73
Operation ofFixed-Order-Interval Systems
• After the lead time elapses, the ordered quantity is received, and the inventory level increases
• The maximum inventory level is expected demand during protection interval + safety stock, or
LTOIz LTOId d
Management 3620 Chapter 13 Inventory Management 13-74
Administration of the System
• Using the periodic counting system, the inventory is reviewed (counted) at the end of each order interval
• Using the perpetual counting system, an item’s inventory level is checked in the inventory at the end of each order internal
Management 3620 Chapter 13 Inventory Management 13-75
Reasons to Use
• Supplier’s policy might encourage use
• Some situations do not lend themselves to continuous monitoring
• Used where it is desirable to physically count inventory each time an order is placed
Management 3620 Chapter 13 Inventory Management 13-76
Benefits/Advantages• Benefits
– results in tight control needed for A items in a A-B-C classification
– grouping ordering to one supplier may result in savings• Ordering• Packing• Shipping costs
• Disadvantages– larger amount of safety stock needed for
the same service level– cost of periodic reviews