unit08 - inventory management

7/31/2019 Unit08 - Inventory Management

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Dr. Rameez Khalid, PMPAssociate Professor

NED University of Engineering and Technology

Learning Objectives

Objectives of inventory management

Periodic and Perpetual review systems

A-B-C approach

EOQmodel

Economic Production Quantity model

Quantity Discount model

Reorder Point model


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Independent Demand

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand

Independent demand is uncertain.Dependent demand is certain.

Inventory: a stock or store of goods

Inventory

Typesof Inventories

Raw materials & purchased parts

Partially completed goods calledwork in progress (WIP)

Finished-goods inventories (manufacturingfirms)

or merchandise

(retail stores)


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Typesof Inventories

Replacement parts, tools, & supplies

Goods-in-transit to warehouses or customers

Functionsof Inventory To meet anticipated demand

To smooth production requirements

To decouple operations

To protect against stock-outs

To take advantage of order cycles

To help hedge against price increases To permit operations

To take advantage of quantity discounts


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Objectiveof Inventory Control

To achieve satisfactory levels of customer servicewhile keeping inventory costs within reasonablebounds

Level of customer service

Costs of ordering and carrying inventory

Inventory turnover is the ratio of:average cost of goods sold toaverage inventory investment.

A system to keep track of inventory

A reliable forecast of demand

Knowledge of lead times

Reasonable estimates of

Holding costs

Ordering costs

Shortage costs

A classification system

Effective Inventory Management


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Inventory Counting Systems

Periodic System (Tor PSystem)

Physical count of items made at periodicintervals

Perpetual Inventory System (QSystem)System that keeps trackof removals from inventorycontinuously, thusmonitoringcurrent levels ofeach item

Lead time: time interval between ordering andreceiving the order

Holding (carrying) costs: cost to carry an item ininventory for a length of time, usually a year

Ordering costs: costs of ordering and receivinginventory

Shortage costs: costs when demand exceedssupply

Key Inventory Terms


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ABCClassification System

Classifying inventory according to some measure ofimportance and allocating control effortsaccordingly.

AA - very important

BB- mod. important

CC- least important

0

20

40

60

80

100

0 50 100% of Inventory Items

%A

nnu

al$Usage

AA

BB CC

Class % $ Vol % Items

A 80 15

B 15 30

C 5 55

Inventory

Processstage

DemandType

Number& Value

Other

Raw Material WIPFinished Goods Independent

Dependent

A ItemsB ItemsC Items

MaintenanceDependentOperating

Inventory Classifications


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Fixed order-quantity models Economic order quantity (EOQ)

Economic production quantity (EPQ)or Production order quantity (POQ)

Quantity discount

Probabilistic models

Fixed order-period models

Help answer theinventory planningquestions!

Inventory Models


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Economic order quantity (EOQ) model

The order size that minimizes total annual cost

Economic production model

Quantity discount model

Economic Order Quantity Models

The Inventory CycleProfile of Inventory Level Over Time

Quantityon hand

Q

Receiveorder

Placeorder

Receiveorder

Placeorder

Receiveorder

Lead time

Reorderpoint

Usagerate

Time


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Deriving the EOQ

Using calculus, we take the derivative of the totalcost function and set the derivative (slope) equal tozero and solve for Q.

Q =2DS

H=

2(Annual Demand )(Order or Setup Cost )

Annual Holding CostOPT

Minimum Total Cost

The total cost curve reaches its minimum wherethe carrying and ordering costs are equal.

QQ22

HHDDQQ

SS==


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EOQ

A local distributor for a national tire companyexpects to sell approx. 9,600 steel-belted radialtires of a certain size and tread design next year.Annual carrying cost is $16 per tire, and orderingcost is $75. The distributor operates 288 days ayear.

a. EOQ?

b. How many Orders?

c. Length of an order cycle?d. Total Annual Cost?

a. 300 tires; b. 32; c. 9 working days; d. $4800


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Production done in batches or lots

Capacity to produce a part exceeds the part susage or demand rate

Assumptions of EPQare similar to EOQ exceptorders are received incrementally duringproduction

Economic Production Quantity (EPQ)

EOQ EPQ Model

When To Order

ReorderReorderPointPoint

(ROP)(ROP)TimeTime

Inventory LevelInventory Level

Lead TimeLead Time

OptimalOptimalOrderOrderQuantityQuantity(Q*)(Q*)


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EPQ Model Inventory Levels

Inventory LeveInventory Levell

TimeTimeSupplyBegins

SupplyEnds

Production portion ofProduction portion ofcyclecycle

Demand portion of cycle with noDemand portion of cycle with nosupplysupply

EPQ Model Inventory Levels

Time

Inventory Level

ProductionPortion of Cycle

Imax Max. InventoryQ(1-u/p)

Q*

SupplyBegins

SupplyEnds

Inventory level with no demand

Demand portion of cycle withno supply


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EconomicRun Size

QDS

H

p

p u0

2

D= Demand per year

S= Setup cost

H= Holding cost

u= Demand per day

p= Production perday

EPQ Model Equations

Optimal Order Quantity

Setup Cost

Holding Cost

= =

-

= *

= *

=

Q

H*u

p

Q

D

Q

S

p*

1

(

0.5 * H * Q -u

p1

)- up1

( )

2*D*S

( )Maximum inventory level

Imax


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EPQ

A toy manufacturer uses 48,000 rubber wheelsper year for its popular dump truck series. Thefirm makes its own wheels, which it can produceat a rate of 800 per day. The toy trucks areassembled uniformly over the entire year. Carryingcost is $1 per wheel a year. Setup cost for aproduction run of wheels is$45. The firm operates240 days per year.

a. EPQor POQor Optimal Run Size?

b. Minimum Total Annual Cost?c. Cycle Time?

d. Run Time?

a. 2400 wheels;b. $1800;c. 12 days;d. 3 days


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Answers how much to order & when to order

Allows quantity discounts

Reduced price when item is purchased in largerquantities

Other EOQassumptions apply

Trade-off is between lower price & increasedholding cost

Buyers Goal: Select the order quantity that will minimize the total cost.

Quantity Discount Model

Total Costs with Purchasing Cost

Annualcarryingcost

PurchasingcostTC = +

QQ22

HHDDQQ

SSTC =TC = ++

+Annualorderingcost

PDPD++


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Total Costs with PD

Cost

EOQ

TCwith PD

TCwithout PD

PD

0 Quantity

Adding Purchasing costdoesnt change EOQ

Case1: Constant Holding Costs

OC

EOQ Quantity

TotalCost

TCa

TCc

TCbDecreasingPrice

HC a,b,c


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Quantity Discount

When D = 816 cases per year, S=$12, andH=$4 per case per year, determine for thefollowingdiscounts:

a. Optimal Order Quantity?

b. Total Cost?

a. 100 cases;b. TC100=$13354

Range Price1 to 49 $2050 to 79 1880 to 99 17100 or more 16

Quantity Discount


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Case2: Holding Cost

as Percentage of Purchase Price

Quantity Discount

When D = 4000 switches per year, S =$30,and H=0.40P per unit per year, determinefor the followingdiscounts:

a. Optimal Order Quantity?

b. Total Cost?

a. 1000 switches;b. TC1000=$3480

Range Price1 to 499 $0.90

500 to 999 0.851000 or more 0.80


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Case2: Holding Cost

as Percentage of Purchase Price


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When to Reorder with EOQOrdering Reorder Point - When the quantity on hand of an

item drops to this amount, the item is reordered

Safety Stock - Stock that is held in excess ofexpected demand due to variable demand rateand/or lead time.

Service Level - Probability that demand will notexceed supply during lead time.

Determinants of the Reorder Point

The rate of demand

The lead time

Demand and/or lead time variability

Stockout risk (safety stock)


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ROPand Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP =ExpectedDemandduring Leadtime + SafetyStock

Quantity

Safety stock

Safety stock reduces risk ofstockout during lead time

ROPROP == dd xx LTLT


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Orders are placed at fixed time intervals

Order quantity for next interval?

Suppliers might encourage fixed intervals

May require only periodic checks of inventorylevels

Risk of stockout

Fill rate the percentage of demand filled by thestock on hand

Fixed-Order-Interval Model

TimeTime

Inventory LevelInventory Level Target maximumTarget maximum

PeriodPeriod PeriodPeriodPeriodPeriod

Fixed Period Model

When to Order?


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Benefits:

Items from same supplier may yield savings in: Ordering

Packing

Shipping costs

May be practical when inventories cannot beclosely monitored

Disadvantages:

Requires a larger safety stockIncreases carrying cost

Costs of periodic reviews

Fixed-Interval Model


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REFERENCES

Operations ManagementWilliam J. Stevenson

Operations ManagementBarry Render & Jay Heizer

unit08 - inventory management

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