chapter 13 inventory management. management 3620chapter 13 inventory management13-2 independent...

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

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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)

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Types of Inventories (2 of 2)

• Replacement parts, tools, & supplies

• Goods-in-transit (pipeline) to warehouses or customers

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Cost Information

• Holding or carrying costs

• Ordering costs

• Shortage costs

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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

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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

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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

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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

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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

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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

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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

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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?

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Example 2, page 555

D=9,600 tires/yearH=$16/tire/yearS=$75/order

b. How many times per year does the store reorder?

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Example 2, page 555

D=9,600 tires/yearH=$16/tire/yearS=$75/order

c. What is the length of an order cycle?

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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?

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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

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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

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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

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Fixed Order Quantity Modelwith Incremental Replenishment• The optimization results in

u-p

p

H

2DS QO

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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

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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

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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

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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

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Discount ScheduleProblem 14, page 588

Quantity Price

1 - 399400 - 599

600+

$10$9

$8

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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

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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.

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Quantity Discount2 Using the appropriate price for the

for the EOQ found in Step 1, compute the TC

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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

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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

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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.

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Quantity Discount

3 Compute the TC for the feasible EOQ found in Step 2

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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

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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

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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

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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

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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

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Quantity Demanded

Distribution of DemandOver the Lead Time

Normal distribution with amean, , and a standard deviation,

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Quantity Demanded

If the ROP is set at the mean of the distribution, what would the order cycle service level be?

ROP

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Quantity Demanded

ROP

Servicelevel

What if management wanted the order cycle service level to be greater than 50%?

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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

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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

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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

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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

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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)

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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

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Lead Time Demand

Placeorder

Receiveorder

Lead Time

( )LTd

safety stock

Reorder point

Order cycle service level

Risk of shortage

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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

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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

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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

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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

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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

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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

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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

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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