adeyl khan, faculty, bba, nsu. pencils, papers, clips, advertisements-flyer, visiting cards, nuts,...

Adeyl Khan, Faculty, BBA, NSU


C 11Inventory ManagementPencils, papers, clips, advertisements-flyer, visiting cards, nuts, bolts, trucks,

needles, airplanesRaw materials, semi-finished goods,

finished goods

What is the worth?Let top management see the money

withheld


Inventory- a stock or store of goods

12-3

Independent Demand

B(4)

E(1)D(2)

C(2)

F(2)D(3)

A Dependent Demand

Independent demand is uncertain. Dependent demand is certain.


Inventory Models

Independent demand – finished goods, items that are ready to be sold

• E.g. a computer

Dependent demand – components of finished products

• E.g. parts that make up the computer

12-4


Types of Inventories

Raw materials & purchased partsPartially completed goods called

work in progressFinished-goods inventories

manufacturing firms retail stores (merchandise )

Replacement parts, tools, & suppliesGoods-in-transit to warehouses or customers

12-5


Functions of Inventory

To meet anticipated demand Anticipation stock

To smooth production requirements Seasonal demand (e.g. Potato case!)

To decouple operations Buffer for continuous operation

To protect against stock-outs Delayed delivery, abrupt demand Safety stocks

12-6


Functions of Inventory …

To take advantage of order cycles Purchasing, Producing in Batches (Lots) Cycle stock for periodic

To help hedge against price increases Oil price

To permit operations Intermediate Stocks (WIP)

Pipeline inventory

To take advantage of quantity discounts

12-7


Objective of Inventory Control

To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service Costs of ordering and carrying inventory

Inventory turnover Ratio of average cost of goods sold to average inventory investment.

Days of inventory on hand

12-8


Effective Inventory Management

A system to keep track of inventory (and S.O.)A reliable forecast of demandKnowledge of lead times (and variability)Reasonable estimates of

Holding costs Ordering costs Shortage costs

A classification system

12-9


Inventory Counting Systems

Periodic System Physical count of items made at periodic intervals Small Retailers- checks and orders replenishment

Perpetual Inventory System Keeps track of removals from inventory continuously, thus monitoring current levels of each item Reorder point Q Also requires periodic counting

Errors, pilferage, spoliage

12-10

Cost?


Inventory Counting Systems …

Two-Bin System - Two containers of inventory; reorder when the first is empty 2nd cart has enough inventory for the lead

time Order card

Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached

12-11


Key Inventory Terms

Lead time: time interval between ordering and receiving the orderHolding (carrying) costs: cost to carry an item in inventory for a length of time, usually a yearOrdering costs: costs of ordering and receiving inventoryShortage costs: costs when demand exceeds supply

12-12


The Inventory Cycle- Figure 12.2Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time


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

12-14

Annual $ value of items

A

B

C

High

Low

Low HighPercentage of Items

Example 1- P 549


Cycle Counting

A physical count of items in inventoryCycle counting management

How much accuracy is needed? When should cycle counting be performed? Who should do it?

12-15


Economic Order Quantity Models

Economic order quantity (EOQ) model The order size that minimizes total annual cost

Economic production modelQuantity discount model

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Adeyl Khan, Faculty, BBA, NSU12-17

Total Cost*

Annualcarryingcost

Annualorderingcost

Total cost* = +

TC = Q2H D

QS+


Cost Minimization Goal- Figure 12.4C

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQ

HD

QS

2

Minimum Total Cost


• Only one product is involved• Annual demand requirements

known• Demand is even throughout the

year• Lead time does not vary• Each order is received in a

single delivery• There are no quantity discounts

Assumptions of EOQ Model

12-19


Deriving the EOQ

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal.

12-20

Q2H D

QS=

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

H

2DS = QOPT


Economic Production Quantity (EPQ)

Production done in batches or lotsCapacity to produce a part exceeds the

part’s usage or demand rate

Similar to EOQ Orders are received

incrementally during production

12-21

Assumptions

• Only one item is involved

• Annual demand is known

• Usage rate is constant• Usage occurs

continually• Production rate is

constant• Lead time does not

vary• No quantity discounts


Economic Run Size

QDS

H

p

p u0

2

We do not buy the product. We produce it. Total demand / year is DDemand / day or consumption rate is uProduction rate is p / day


Instantaneous Replenishment

Incremental Replenishment


u

p

p-u

u × ( number of working days ) = D = Total demand per year

EPQ: Incremental Replenishment(Production and Consumption)

Demand / day or consumption rate is uProduction rate is p / day


State Imax in terms of Q!

SQ

DH

I

2maxTC

EPQ: Ordering Cost and Carrying Cost


How much do we produce each time? QHow long does it take to produce Q? d1

What is our production rate per day? p1pdQ

)( 21 dduQ

EPQ : Production & Consumption; rate & time

1max )( dupI

2max udI

p-u u

I max

d1d2

How long does it take to consume Q? d1 +d2 What is our consumption rate per day ? u


Example- What is the optimal production size?A toy manufacturer

Uses 48000 parts for one of its products. Consumption rate is uniform throughout the

year. Working days are 240 / year. The firm can produce at a rate of 800 parts /

day Carrying cost is $1 / part / year Setup cost for production run is $45 / setup


What is Run Time, What is Cycle Time

1pdQ )(2002400 21 dd

18002400 d31 d

)( 21 dduQ

12)( 21 dd

Q0 using formula = 2400u = 48000 /240 = 200 units/day

QDS

H

p

p u0

2

p-u u

I max

d1d2


What is the Optimal Total Cost

1max )( dupI

2MaxI

HQ

DSTC

1800900900 TC

1800max I

3)200800(max I

2

18001

2400

4800045 TC


EPQ : Optimal Q

)(

2

upH

SDpEPQ

up

p

H

SDEPQ

2


Reorder Point- ROP Reorder Point

When the quantity on hand of an item drops to this amount, the item is reordered

If setup time takes 2 days, at which level of inventory we should start setup? 2(200) = 400 200 ?


Yet Another ExampleA company has a yearly demand of 120,000

boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year.

a) What is the demand rate per dayb) What is the Economic Production Quantity

(EPQ)c) What is the run time d) What is the maximum inventorye) What is the total cost of the system


up

p

H

SDEPQ

2

5002000

2000

10

)120000)(8000(2

EPQ =16000

Yet Another Example …a) What is the demand rate per day

Demand per year is 120,000 there are 240 days per year Demand per day = 120000/240 = 500 u = D/240 = 500

b) What is the Economic Production Quantity (EPQ)


Yet Another Example … c) What is the run time

We produce 16000 units Our production rate is 2000 per day It takes 16000/2000 = 8 days d1 = EPQ/p = 8 days

d) What is the maximum inventory We produce for 8 days. Each day we produce 2000 units

and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That is

Imax = 8(1500) = 12000 Imax = pd1 = 8(1500) = 12000


Yet Another Example …e) What is the total cost of the system

2MaxI

HQ

DSTC

2

1200010

16000

1200008000 TC

1200006000060000 TC


Including the Purchasing Cost12-36

Annualcarryingcost

PurchasingcostTC = +

Q2H D

QSTC = +

+Annualorderingcost

PD +


Total Costs with Vs. Quantity Ordered

12-37

Co

st

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing costdoesn’t change EOQ


Total Cost with Constant Carrying Costs

12-38

OC

EOQ Quantity

Tota

l Co

st

TCa

TCc

TCbDecreasing Price

CC a,b,c

Adeyl Khan, Faculty, BBA, NSUTotal Cost with Variable Carrying Costs 12-39

Do the MathEx 5, 6


ROP with EOQ Ordering Safety Stock

Stock that is held in excess of expected demand due to variable demand rate and/or lead time.

Service Level Probability that demand will not exceed

supply during lead time.

12-40

When to Reorder


Determinants of the Reorder Point

The rate of demandThe lead timeDemand and/or lead time variabilityStockout risk (safety stock)

12-41


Safety Stock- Figure 12.12

12-42

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Safety stock reduces risk ofstockout during lead time


Reorder Point- Figure 12.13

12-43

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

The ROP based on a normalDistribution of lead time demand

ROPs = Exp. Demand + z. σdLT

See also: Fig 11.14


Shortage and Service LevelService level determines ROP

E(n) = E(z) z σdLT

E(n) = Expected number of short/cycle E(z) = Standardized number of units-short

from table 11.3 σdLT = Standard deviation of lead time

Example 10 @ Page 56844


Fixed-Order-Interval Model

Orders are placed at fixed time intervalsOrder quantity for next interval?Suppliers might encourage fixed intervalsMay require only periodic checks of inventory levelsRisk of stockout

Fill rate – the percentage of demand filled by the stock on hand

12-45


Calculations

46

Ex 13


Fixed-Interval tradeoffsBenefits

• Tight control of inventory items

• Items from same supplier may yield savings in:• Ordering• Packing• Shipping costs

• May be practical when inventories cannot be closely monitored

Disadvantages

• Requires a larger safety stock

• Increases carrying cost

• Costs of periodic reviews

12-47


Single Period Model

Model for ordering items with limited useful livesPerishables

Shortage cost is generally the unrealized profits per unit

Excess cost is the difference between purchase cost and salvage value of items left over at the end of a period

Continuous stocking levels• Identifies optimal stocking

levels• Optimal stocking level

balances unit shortage and excess cost

Discrete stocking levels• Service levels are discrete

rather than continuous• Desired service level is

equaled or exceeded

12-48


Optimal Stocking Level

12-49

Service Level

So

Quantity

Ce Cs

Balance point

Service level =Cs

Cs + CeCs = Shortage cost per unitCe = Excess cost per unit


Example 15

Ce = $0.20 per unitCs = $0.60 per unitService level = Cs/(Cs+Ce) = .6/(.6+.2)Service level = .75

12-50

Service Level = 75%

Quantity

Ce Cs

Stockout risk = 1.00 – 0.75 = 0.25


Operations Strategy

Too much inventory Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain

Wise strategy Reduce lot sizes Reduce safety stock

12-51

Adeyl Khan, Faculty, BBA, NSU52


Learning Objectives

Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. Discuss the nature and importance of service inventoriesDiscuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful.

12-53


Learning Objectives

Describe the basic EOQ model and its assumptions and solve typical problems. Describe the economic production quantity model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the single-period model would be appropriate, and solve typical problems.

12-54

adeyl khan, faculty, bba, nsu. pencils, papers, clips, advertisements-flyer, visiting cards, nuts,...

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