chap015 inventory control

8/12/2019 Chap015 Inventory Control

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Chapter 15

Inventory Control


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Inventory System Inventoryis the stock of any item or resource

used in an organization and can include: raw

materials, finished products, component parts,

supplies, and work-in-process

An inventory systemis the set of policies and

controls that monitor levels of inventory and

determines what levels should be maintained,

when stock should be replenished, and how

large orders should be


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Purposes of Inventory1. To maintain independence of operations

2. To meet variation in product demand

3. To allow flexibility in production scheduling

4. To provide a safeguard for variation in raw

material delivery time

5. To take advantage of economic purchase-order

size


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Inventory Costs Holding (or carrying) costs

Costs for storage, handling, insurance, etc

Setup (or production change) costs

Costs for arranging specific equipment

setups, etc

Ordering costs

Costs of someone placing an order, etc

Shortage costs

Costs of canceling an order, etc


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E(1

)

Independent vs. Dependent Demand

Independent Demand (Demand for the final end-

product or demand not related to other items)

Dependent

Demand

(Derived demand

items forcomponent

parts,

subassemblies,

raw materials,

etc)

Finished

product

Component parts


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7Inventory Systems Single-Period Inventory Model

One time purchasing decision (Example:

vendor selling t-shirts at a football game)

Seeks to balance the costs of inventory

overstock and under stock Multi-Period Inventory Models

Fixed-Order Quantity Models

Event triggered (Example: running out of

stock) Fixed-Time Period Models

Time triggered (Example: Monthly sales call

by sales representative)


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Single-Period Inventory Model

uo

u

CC

CP

soldbeunit willy that theProbabilit

estimatedunderdemandofunitperCostCestimatedoverdemandofunitperCostC

:Where

u

o

P

This model states that we

should continue to increasethe size of the inventory so

long as the probability of

selling the last unit added is

equal to or greater than theratio of: Cu/Co+Cu


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Single Period Model Example Our college basketball team is playing in a

tournament game this weekend. Based on ourpast experience we sell on average 2,400 shirtswith a standard deviation of 350. We make Rs100

on every shirt we sell at the game, but lose Rs50on every shirt not sold. How many shirts shouldwe make for the game?Cu=Rs100 and C

o= Rs50; P 100 / (100 + 50) = .667

Z.667= .432 (use NORMSDIST(.667) or Appendix E)therefore we need 2,400 + .432(350) = 2,551 shirts


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10Multi-Period Models:Fixed-Order Quantity Model ModelAssumptions Part 1)

Demand for the product is constant

and uniform throughout the period

Lead time (time from ordering to

receipt) is constant

Price per unit of product is constant


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Multi-Period Models:Fixed-Order Quantity Model ModelAssumptions Part 2)

Inventory holding cost is based on

average inventory

Ordering or setup costs are constant

All demands for the product will besatisfied (No back orders are allowed)

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12Basic Fixed-Order Quantity Modeland Reorder Point Behavior

R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Number

of unitson hand

1. You receive an order quantity Q.

2. Your start usingthem up over time. 3. When you reach down to

a level of inventory of R,

you place your next Q

sized order.

4. The cycle then repeats.


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Basic Fixed-Order QuantityEOQ) Model Formula

H2Q+S

QD+DC=TC

TotalAnnual =Cost

AnnualPurchase

Cost

AnnualOrdering

Cost

AnnualHolding

Cost+ +

TC=Total annual

cost

D =Demand

C =Cost per unit

Q =Order quantity

S =Cost of placing

an order or setup

costR =Reorder point

L =Lead time

H=Annual holding

and storage cost

per unit of inventory

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15Deriving the EOQUsing calculus, we take the first derivative of

the total cost function with respect to Q, andset the derivative (slope) equal to zero,

solving for the optimized (cost minimized)

value of QoptQ =

2D S

H =

2(Annual D emand )(Order or Setup C ost)

A nnual Ho lding CostO PT

R eorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

We also need areorder point to

tell us when to

place an order

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EOQ Example 1) Problem Data

Annual Demand = 1,000 unitsDays per year considered in average

daily demand = 365

Cost to place an order = Rs10

Holding cost per unit per year = Rs2.50Lead time = 7 days

Cost per unit = Rs15

Given the information below, what are the EOQ and

reorder point?

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EOQ Example 1) SolutionQ = 2DS

H = 2(1,000 )(10)

2.50 = 89.443 units orOPT 90 un its

d =1,000 units / year

365 days / year

= 2.74 units / day

R eo rder p oin t, R = d L = 2 .7 4u nits / d ay (7d ays) = 1 9.1 8 or_

20 un its

In summary, you place an optimal order of 90 units. Inthe course of using the units to meet demand, when

you only have 20 units left, place the next order of 90

units.

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EOQ Example 2) Problem Data

Annual Demand = 10,000 unitsDays per year considered in average daily

demand = 365

Cost to place an order = Rs10

Holding cost per unit per year = 10% of cost

per unit

Lead time = 10 days

Cost per unit = Rs15

Determine the economic order quantityand the reorder point given the following

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EOQ Example 2) SolutionQ = 2D S

H= 2(10,000 )(10)

1.50= 3 6 5 .1 4 8 un its , o rO PT 366 u nits

d =10,000 units / year

365 days / year

= 27.397 units / day

R = d L = 27.397 units / day (10 days) = 273.97 or_

274 u nits

Place an order for 366 units. When in the course of

using the inventory you are left with only 274 units,

place the next order of 366 units.

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20Fixed-Time Period Model with SafetyStock Formula

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

q = Average demand + Safety stock

Inventory currently on hand

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Multi-Period Models: Fixed-Time Period Model:Determining the Value of T+L

T+L di 1

T+L

d

T+L d

2

=

Since each day is independent and is constant,

= (T + L)

i

2

The standard deviation of a sequenceof random events equals the square

root of the sum of the variances

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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 the review period there are

200 units in inventory. The daily

demand standard deviation is 4 units.

Given the information below, how many units

should be ordered?

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23Example of the Fixed-Time PeriodModel: Solution Part 1) T+ L d 2 2 = (T + L) = 30 + 10 4 = 25.298

The value for z is found by using the Excel

NORMSINV function, or as we will do here, using

Appendix D. By adding 0.5 to all the values inAppendix D and finding the value in the table that

comes closest to the service probability, the z

value can be read by adding the column heading

label to the row label.

So, by adding 0.5 to the value from Appendix D of 0.4599,

we have a probability of 0.9599, which is given by a z = 1.75

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Example of the Fixed-Time PeriodModel: Solution Part 2)

or644.272,=200-44.272800=q

200-298)(1.75)(25.+10)+20(30=q

I-Z+L)+(Td=q L+T

units645

So, to satisfy 96 percent of the demand,

you should place an order of 645 units at

this review period

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Price-Break Model Formula

CostHoldingAnnual

Cost)SetuporderDemand)(Or2(Annual=

iC

2DS=QOPT

Based on the same assumptions as the EOQ model,the price-break model has a similar Qoptformula:

i = percentage of unit cost attributed to carrying inventory

C = cost per unit

Since C changes for each price-break, the formula

above will have to be used with each price-break cost

value

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Price-Break Example Problem DataPart 1)A company has a chance to reduce their inventoryordering costs by placing larger quantity orders using

the price-break order quantity schedule below. What

should their optimal order quantity be if this company

purchases this single inventory item with an e-mailordering cost of Rs4, 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(Rs)0 to 2,499 Rs1.202,500 to 3,999 1.004,000 or more .98

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Price-Break Example Solution Part 2)

units1,826=0.02(1.20)

4)2(10,000)(=

iC

2DS=QOPT

Annual Demand (D)= 10,000 unitsCost to place an order (S)= Rs4

First, plug data into formula for each price-break value of C

units2,000=0.02(1.00)

4)2(10,000)(=iC

2DS=QOP T

units2,020=0.02(0.98)

4)2(10,000)(=

iC

2DS=QOP T

Carrying cost % of total cost (i)= 2%Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, theQoptvalue is feasible

Interval from 2500-3999, theQoptvalue is not feasible

Interval from 4000 & more, theQoptvalue is not feasible

Next, determine if the computed Qoptvalues are feasible or not

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Price-Break Example Solution Part 3)Since the feasible solution occurred in the first price-break, it means that all the other true Qoptvalues occur

at the beginnings of each price-break interval. Why?

0 1826 2500 4000 Order Quantity

Totalannualcosts So the candidates

for the price-

breaks are 1826,2500, and 4000

units

Because the total annual cost function isa u shaped function

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Price-Break Example Solution Part 4)

iC2

Q+S

Q

D+DC=TC

Next, we plug the true Qoptvalues into the total cost

annual cost function to determine the total cost under

each price-break

TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)= Rs12,043.82

TC(2500-3999)= Rs10,041TC(4000&more)= Rs9,949.20

Finally, we select the least costly Qopt, which is this

problem occurs in the 4000 & more interval. In summary,

our optimal order quantity is 4000 units

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Maximum Inventory Level, M

Miscellaneous Systems:Optional Replenishment System

MActual Inventory Level, I

q = M - I

I

Q = minimum acceptable order quantity

If q > Q, order q, otherwise do not order any.

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Miscellaneous Systems:Bin SystemsTwo-Bin System

Full Empty

Order One Bin of

Inventory

One-Bin System

Periodic Check

Order Enough toRefill Bin

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ABC Classification System Items kept in inventory are not of equal

importance in terms of:

Rupees invested

profit potential

sales or usage volume

stock-out penalties

0

30

60

30

60

A BC

% ofRs Value

% ofUse

So, identify inventory items based on percentage of total

dollar value, where A items are roughly top 15 %, B

items as next 35 %, and the lower 65% are the C items

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Inventory Accuracy and Cycle CountingInventory accuracyrefers to how

well the inventory records agree

with physical countCycle Countingis a physical

inventory-taking technique in which

inventory is counted on a frequentbasis rather than once or twice a

year

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Question BowlThe average cost of inventory in the

United States is which of the

following?

a. 10 to 15 percent of its cost

b. 15 to 20 percent of its costc. 20 to 25 percent of its cost

d. 25 to 30 percent of its cost

e. 30 to 35 percent of its costAnswer: e. 30 to 35 percent of its cost

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Question BowlWhich of the following is a reason why firms

keep a supply of inventory?

a. To maintain independence of operations

b. To meet variation in product demand

c. To allow flexibility in production scheduling

d. To take advantage of economic purchase

order size

e. All of the above

Answer: e. All of the above (Also can include to provide

a safeguard for variation in raw material delivery

time.)

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Question BowlAn Inventory System should include policies

that are related to which of the following?

a. How large inventory purchase orders should

beb. Monitoring levels of inventory

c. Stating when stock should be replenished

d. All of the abovee. None of the above

Answer: d. All of the above

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Question BowlWhich of the following is an Inventory Cost item

that is related to the managerial and clerical

costs to prepare a purchase or production order?

a. Holding costs

b. Setup costs

c. Carrying costs

d. Shortage costs

e. None of the above

Answer: e. None of the

above (Correct answer

is Ordering Costs.)


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Question BowlIf you are marketing a more expensive

independent demand inventory item, which

inventory model should you use?

a. Fixed-time period model

b. Fixed-order quantity model

c. Periodic system

d. Periodic review system

e. P-model

Answer: b. Fixed-order quantity model

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Question BowlIf the annual demand for an inventory item is5,000 units, the ordering costs are Rs100 per

order, and the cost of holding a unit is stock for a

year is Rs10, which of the following is

approximately the Qopt?a. 5,000 units

b. Rs5,000

c. 500 units

d. 316 units


Answer: d. 316

units(Sqrt[(2x1000x10

0)/10=316.2277)

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Question BowlThe basic logic behind the ABC Classificationsystem for inventory management is which of the

following?

a. Two-bin logic

b. One-bin logic

c. Pareto principle

d. All of the above


Answer: c. Pareto principle

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Question BowlA physical inventory-taking technique in

which inventory is counted frequently rather

than once or twice a year is which of the

following?

a. Cycle countingb. Mathematical programming

c. Pareto principle

d. ABC classification

e. Stockkeeping unit (SKU)

Answer: a. Cycle counting

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End of Chapter 15

chap015 inventory control

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