Ch 15 Inventory Management

8/6/2019 Ch 15 Inventory Management

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Chapter 15. Inventory Management

InventoryInventory is the stock of any item or resource used in anorganization and can include: raw materials, finished products,component parts, supplies, and work-in-process

An inventory systeminventory system is the set of policies and controls thatmonitor levels of inventory and determines what levels should

be maintained, when stock should be replenished, and how largeorders should be

Firms invest 25-35 percent of assets in inventory but many donot manage inventories well


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Purposes of Inventory

1. To maintain independence of operations Provide optimal amount of cushion between work centers

Ensure smooth work flow

2. To allow flexibility in production scheduling

3. To meet variation in product demand4. To provide a safeguard for variation in raw material

or parts delivery time Protect against supply delivery problems (strikes, weather,

natural disasters, war, etc.)

5. To take advantage of economic purchase-order size


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Independent vs. Dependent Demand

Inventory costs

Single-Period Model

Multi-Period Models: Basic Fixed-Order Quantity Models

Event triggered (Example: running out of stock, or dropping below

a reorder point)

EOQ, EOQ with reorder point (ROP) , and with safety stock

Multi-

P

eriod Models: BasicF

ixed-TimeP

eriod Model EOQ with Quantity Discounts

ABC analysis

Inventory Control (Management)


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E(1

)

Independent vs. Dependent Demand

Independent Demand (Demand not related to otheritems or the final end-product)

Dependent Demand(Derived demand

items for componentparts,

subassemblies,raw materials, etc.)


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Inventory Costs

Holding (or carrying) costs. Costs for capital, taxes, insurance, etc.

(Dealing with storage and handling)

Setup (or production change) costs. (manufacturing)

Costs for arranging specific equipment setups, etc.

Ordering costs (services & manufacturing) Costs of someone placing an order, etc.

Shortage (backordering) costs. Costs of canceling an order, customer goodwill, etc.


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A Single-Period Model Sometimes referred to as the newsboy problem

Is used to handle ordering of perishables (fresh seafood, cutflowers, etc.) and items that have a limited useful life(newspaper, magazines, high fashion goods, some high techcomponents, etc)

The optimal stocking level uses marginal analysis is where theexpected profit (benefit from derived from carrying the nextunit) is less than the expected cost of that unit (minus salvagevalue)

Co = Cost/unit of overestimated demand (excess demand)Co = Cost per unit salvage value per unit

Cu = Cost/unit of underestimated demandCu = Price/unit cost/unit + cost of loss of goodwill per unit

Optimal order level is whereP


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Single Period Model Example

UNC Charlotte basketball team is playing in atournament game this weekend. Based on our pastexperience we sell on average 2,400 shirts with astandard deviation of 350. We make $10 on everyshirt we sell at the game, but lose $5 on every shirtnot sold. How many shirts should we make for thegame?

1. Determine Cu=$10 and Co = $5 (this time, these were directly given)

2. Compute P $10 / ($10 + $5) = 0.667 66.7%

3. Order up to ~ 66.7% of the demand4. How do you determine it?

5. Normal distribution, Z transformation,

6. Z0.667 = 0.432 (useNORMSDIST(.667) or Appendix E)

7. Therefore we need 2,400 +0.432(350) = 2,551 shirts


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Single Period Model, Marginal Analysis

Marginal analysis approach. Consider solved problem 1,p. 6171. Determine C

u= 100-70 = $30 and Co = 70-20 = $50

2. Compute P 30/(30+50) 0.3753. Develop a full marginal analysis table (Excel time!)4. Assume we purchase 35 units, compute the expected total cost

5. Repeat step 4, for 36,, 40

The optimal order (purchase) size is the no. of units with the minimum expectedtotal cost


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Fixed-Order Quantity Models: Assumptions

Demand for the product is constant and uniform throughout theperiod.

Inventory holding cost is based on average inventory.

Ordering or setup costs are constant.

All demands for the product will be satisfied. (No back ordersare allowed.)

Lead time (time from ordering to receipt) is constant (later, thisassumption is relaxed with safety stocks).

Price per unit of product is constant.


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Basic Fixed-Order Quantity Model and ReorderPoint Behavior

Receiveorder

Placeorder

Receiveorder

Placeorder

Receiveorder

Usagerate

Time

ROP

Lead time (L)

Q

ROP = Reorder pointQ = Economic order quantity

L = Lead time


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Cost Minimization Goal

Ordering Costs

HoldingCosts

QOPTIMAL Order Quantity (Q)

COST

Annual Cost of

Items (DC)

Total Cost

By adding the item, holding, and ordering costs together, wedetermine the total cost curve, which in turn is used to find theQoptimal (a.k.a. EOQ) inventory order point that minimizes totalcosts.


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Basic Fixed-Order Quantity (EOQ) Model

AnnualHolding

CostTotal Annual Cost =

AnnualPurchase

Cost

AnnualOrdering

Cost+ +

S

Q

DH

QDCTC !

2A little bit of calculus

H

DSEOQ

2!

Ld=ROP_

A little bit of common sense

L

zWLd=ROP

_

ROPwith safety stock

TC = Total annual cost

D = Demand

C = Cost per unit

Q = Order quantity

S = Cost of placing an order or setup cost

H = Annual holding and storage cost per unit

of inventory

R orROP = Reorder pointL = Lead time (constant)

= average (daily, weekly, etc) demand

L = Standard deviation of demand during lead time

_

d


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Basic EOQ & ROP Example

Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10

Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15

Given the information below, what are the EOQ, reorder point, andtotal annual cost?

EOQ 89.44 89 or 90 unitsROP 2.74*7 19.18 19 or 20 units


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Another example

Days per year considered in average daily demand = 360Average daily demand is 3.5 unitsStandard deviation of daily demand is 0.95 unitsCost to place an order = $50Holding cost per unit per year = $7.25Lead time = 4 days

Compute the EOQ, and ROP is the firm wants tomaintain a 97% service levelservice level(probability of not stocking out)

2

d

1

2

constant,isandtindependenisdayeachSince

dL

L

i

dL

L

i

WW

W

WW

!

! !

LzWLd=ROP

_


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Fixed-Time Period Model with Safety Stock

order)onitems(includeslevelinventorycurrent=I

timeleadandreviewover thedemandofdeviationstandard=

yprobabilitservicespecifiedafordeviationsstandardofnumberthe=z

demanddailyaverageforecast=d

daysintimelead=L

reviewsbetweendaysofnumberthe=T

orderedbetoquantitiy=q

:Where

I-Z+L)+(Td=q

L+T

L+T

W

W

q = Average demand + Safety stock Inventory currently on hand

2

dL+T

d

L+T

1i

2

dL+T

L)+(T=

constant,isandtindependenisdayeachSince

=i

WW

W

WW !


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Example of the Fixed-Time Period Model

Average daily demand for a product is 20 units.The review period is 30 days, and lead time is 10 days.Management has set a policy of satisfying 96 percent of

demand from items in stock. At the beginning of thereview period there are 200 units in inventory. The dailydemand standard deviation is 4 units.

Given the information below, how many units should be ordered?

25.298=410+30=L)+(T= 22dL+T WW

q = 20(30+10) + 1.75(25.30) 200 644.27 units


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A special purpose model

Price-Break Model (Quantity discounts) Based on the same assumptions as the EOQ model, the price-

break model has a similar EOQ (Qopt) formula:

Annual holding cost, H, is calculated usingH = iC where

i = percentage of unit cost attributed to carrying inventory

C = cost per unit

Since C changes for each price-break, the formula above

must be applied to each price-break cost value. Determine the total cost for each price break

The lowest total cost suggests the optimal order size (EOQ)

CostHoldingAnnual

Cost)SetuporderDemand)(Or2(Annual=

iC

2DS=QOPT


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Price-Break Example

A company has a chance to reduce their inventory ordering costs byplacing larger quantity orders using the price-break order quantityschedule below. What should their optimal order quantity be if thiscompany purchases this single inventory item with an e-mail orderingcost of $4, a carrying cost rate of 2% of the inventory cost of the item,

and an annual demand of 10,000 units?

Order Quantity(units) Price/unit($)

0 to 2,499 $1.20

2,500 to 3,999 $1.00

4,000 ormore $0.98

Re-do the example with an order cost of $25 and an inventory carrying cost rate of 45%.


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0 1826 2500 4000 Order Quantity


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ABC Classification System

Items kept in inventory are not of equal importance in terms of:

dollars invested

profit potential

sales or usage volume

stock-out penalties

So, identify inventory items based on percentage of total dollar value,where A items are roughly top 15 %, B items as next 35 %, and thelower 65% are the C items

0

30

60

30

60

AB

C

% of

$ Value

% ofUse


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Inventory Accuracy and Cycle Counting

Inventory accuracy refers to how well the inventoryrecords agree with physical count Lock the storeroom

Hire the right personnel for as storeroom manager oremployees

Cycle Counting is aphysical inventory-taking technique in

which inventory is counted on a frequent basis rather than1-2 times a year Easier to conduct when inventories are low

Randomly (minimize predictability)

Pay more attention to A items, then B, etc.

Suggested problems: 3, 6, 12, 14, 17, 18, 21, 24

Case:Hewlett-Packard

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Ch 15 Inventory Management