Independent – Demand Inventory

Subject: Operation ManagementLecturer: Ms Ta Thi Bich Thuy

Group 2: To Van Phong Vu xxxx xxxx xxxx

Chapter Outline

Definition Purpose of Inventory Inventory Cost Structures Independent versus Dependent Demand Economic Order Quantity Continuous Review System Periodic Review System Using P and Q system in Practice Service level and inventory level ABC inventory Management Reference Q & A

Definition in operation’s view: inventory is a stock of materials used to facilitate production or to satisfy customer demands. It’s include raw materials, work in process and finish goods.

Others: Inventory as an idle resource of any kind that has potential economic value. This definition consider idle equipment or workers as inventory.

Inventory management is among the most important operation management responsibilities Inventory management has an impact on all business functions: operation, marketing, accounting and finance Inventory stock are located at various points in the production process. Inventory act as a buffer between the

difference demand and supply rates.

Definition

Product process

Raw materials

Work in process

Work in process

Work in process

Finish goods

Customer

Figure 1.1 A materials-flow process

Inventory level

Figure 1.2 A water tank analogy for inventory

Purpose of Inventory

1. Protect again uncertainties:

• Safety stock are maintain in inventory in order to protect against uncertainties in supply, demand and lead time.

• Safety stock can often be reduced by better coordination of suppliers and customers in supply chain.

2. Allow economic production and purchase

• Economic production: base on produce material in lots thus offer 2 benefits Able to spread the set up cost of production machine over a larger number of item Permit the use of the same production equipment for different products

• Economic purchase: order in big lots cant take advantages of quantity discounts, ordering cost and transportation cost

3. Cover anticipated changes in demand or supply: to face with expected and foresee changes in demand or supply such as: raw material price increase, plan market promotion or high sales seasons

4. Provide for transit: (or pipeline inventory) consist of materials that is on their way from one point to another as from vendor to factory, from factory to dealers, retailers, from this store to other warehouse….

Inventory cost structure included the following 4 types of cost:1. Item cost: is the cost of buying or producing the individual inventory items

Ordering or set up cost: Ordering cost: is associated with ordering a batch or lot of items such as cost of typing order,

expediting the order, transportation cost, receiving cost, …. Set up cost :include paperwork costs plus cost required to set up the running of production equipments.

This cost often considered as fix cost and can be reduce by changing the way designed and managed operations

2. Carrying ( or holding) cost: The carrying or holding cost is relevant to cost of keeping items in inventory for a certain period of time

Ex: 20% annual holding cost3. Carrying cost usually consist of 3 components

a) Cost of capital: assigned to inventory as opportunity costb) Cost of storage: include variable space cost, insurance and taxes. Exclude inventory storage costc) Cost of obsolescence, deterioration and loss:

Obsolescence cost: assigned to items have high risk of becoming obsolete: ex fashion clothes, shoes, bag, mobile...

Deterioration cost: apply to products that perishable easily over time for example: food, milk, fruit, blood

Loss cost: include pilferage and breakage cost when holding items in warehouse4. Stock out cost: is the cost reflect the economic consequences (lost of sale’s profit and future business) of

running out of stock

Inventory Cost Structure

Set up cost = paperwork cost + production equipment running cost

Holding cost = percentage of dollar value x time unit

Item cost = cost per unit x produced quantity

Item cost = cost per unit x bought quantity

Independent Vs Dependent Demand

Independent demand: is demand that is influenced by market need and conditions, out side of operation controlling.

Ex: finish goods and spare parts inventory for replacement Dependent demand: is related to demand of other item and not determine by market

Ex: products built up from spare parts and assemblies Different types of demand create different approaches to inventory management

Independent demand: apply replenishment philosophy Dependent demand: use requirements philosophy

Independent demand

Finish goods, spare parts

Dependent demand

Work-in-process, raw materials

Time Time

Figure 1.3 Demand patterns

De

ma

nd

Usa

ge

Economic Order Quantity

Economic order quantity ( EOQ) developed by F.W Harris in 1915 and expand widely by Mr Wilson, an consultant

EOQ model base on those consumption:

1) The demand rate is constant, recurring and know

2) The lead time is constant and know

3) No stockouts are allowed

4) Material is ordered or produce in slot or batch and the lot is placed into inventory all at one time

5) Cost structure is used as follows: The unit item cost is constant, and no discounts are given for a large order or purchase The carrying cost depends linearly on the average inventory level.

6) The item is a single product, there ‘s no interaction with other product

Lot size = Q

Order interval

Average inventory level =Q/2

Time

On

ha

nd

Figure 1.4 EOQ inventory levels

Economic Order Quantity Classic Wilson economic order quantity ( EOQ)

Q =

The total annual cost of inventory:

TC = SD/Q + iCQ/2

Total cost per year = ordering cost per year + carrying cost per year

Ordering cost (SD/Q)

Total cost (SD/Q + iCQ/2)

Carrying cost (iCQ/2)

Lot size (Q)

Min

imu

m c

ost

An

nu

al c

ost

T

C (

UD

S/y

ea

r)

Figure 1.5 Total cost of inventory

0

2SDiC

With symbols:

D= demand rate (unit per year)

S= cost per unit order or set up cost (dollars per year)

C= unit cost (dollar per unit)

i = carrying interest rate ( percent of dollars value per year)

Q= lot size (units)

TC= total of ordering cost plus carrying cost ( dollars per year)

Economic Order Quantity

Advantages Disadvantages

The assumptions are reasonably accurate EOQ can be adjust a little to suitable with reality without greatly affecting the costs (total cost of inventory) Giving the basic concepts of total cost minimization and economic lot size

Assumption of constant demand No stock out are allowed Insufficient flexible to use for independent-demand inventory management

Advantages and disadvantages of EOQ model

Stock position (or available stock) = on-hand material + on-order material Definition of continuous review system ( called Q system or fixed-order quantity system)

Continually review stock position ( on-hand plus on-order). When the stock position drops to the reorder point R, a fixed quantity Q is ordered.

In continuous review system, the stock available is monitored continuously, after each transaction. Some criteria of this method:

Random demand Fixed quantity order at a predetermined order or reorder point Order interval will vary depend on the random of demand.

Continuous Review System (Q system)

Where:

Q = and D = average demand

R= determined by stock out probability

QQ

Q

L L L

R

Time

Sto

ck

on

ha

nd

Figure 1.6

A continuous review (Q) system

R = reorder point

Q = order quantity

L = lead time

2 SDiC

Continuous Review System

Service-level probability

Stock out probability

Demand over Lead time

Fre

qu

en

cy

Figure 1.7

Probability distribution

of demand over lead time

m = mean demand

R= reorder point

s = safety stock

sm R

Service level: (3 definitions lead to different reorder points) Is the probability that all orders will be filled from stock during the replenishment lead time of one reorder cycle Is the percentage of demand filled from stock during a given period of time Is the percentage of time the system has stock on hand

Reorder point: Where

R = reorder point

m = average demand over the lead time

s = safety stock

Or

safety stock s = z

z = safety factor

= standard deviation of demand over the lead time

R = m + z

R = m + s

Z Services level (%) Stockout (%)

0 50.0 50.0

0.5 69.1 30.9

1.0 84.1 15.9

1.1 86.4 13.6

1.2 88.5 11.5

1.3 90.3 9.7

1.4 91.9 8.1

1.5 93.3 6.7

1.6 94.5 5.5

1.7 95.5 4.5

1.8 96.4 3.6

1.9 97.1 2.9

2.0 97.7 2.3

2.1 98.2 1.8

2.2 98.6 1.4

2.3 98.9 1.1

2.4 99.2 0.8

2.5 99.4 0.6

2.6 99.5 0.5

2.7 99.6 0.4

2.8 99.7 0.3

2.9 99.8 0.2

3.0 99.9 0.1

Continuous Review System

Table 1.8

Normal Demand

Percentage

Periodic Review System (P system)

A periodic review system provides another way to handle random demand The stock position is reviewed at fixed intervals P and an amount is ordered equal to the target

inventory T minus stock position. The amount ordered at each review period will vary depend on actual demand The value of P is set by use of the EOQ and the value of T is base on the services level desired This method also called: the fixed – order – interval system, period system or P system

L

Q1

Time

L

Sto

ck

on

ha

nd

P P PL

T

Q1Q2

Q2

Q3

Q3

Figure 1.9

A Period review

system

Periodic Review System

Where T = target inventory level

m’ = average demand over P+ L

s’ = safety stock

’ = the standard deviation of demand over P

z = safety factor

The safety stock should be set high enough to assure the desired service level By controlling z, we can control the target inventory and the resulting service level provided The P equation provides an approximately optimal review interval P, when the demand is highly

uncertain, the approximation may be quite poor and not correct. P system always require more safety stock than Q system for the same service level

iCD

SD.2

With s’ = z ’

T = m’ + s’

P = Q/D =

USING P & Q SYSTEM IN PRACTICE

P & Q systems are both in wide use for independent demand inventory management. The choice between P & Q system should be made on the basis of timing of replenishment,

the type of record keeping system in use, and the cost of the item

In some conditions P system is prefer to used to Q system:

1. The P system should be used when the inventory order must be place or delivered at specified intervals with regular scheduled

2. The P system should be used when the multiple items are ordered from the same supplier and delivered in the same shipment ( single order of multiple items)

3. The P system should be used for inexpensive items that are not maintained on perpetual inventory record ( less record keeping)

Note: In practice there’re a mix system of P & Q inventory rules called hybrid systems, that limited inventory level within min and max level

Min = reorder point Max = target inventory

min max

Safety levelOrder level

Compare P & Q system Similars: Both are systems to handle random demand By control z can control service level The value of R ( for Q system) and T (P system) is base on service level desired Economic order quantity Q is set equal to EOQ (Q system) and time between order P also

set base on EOQ (P system) Differences

Q system P system Have reorder point Don’t have a reorder point but target inventory

Have a economic order quantity Q Don’t have economic order quantity Q

Fix order quantities Various order quantities depend on real demand

Fix order quantities Fix order interval ( not order quantity)

• Expensive, single items Inexpensive, multiple items

• Less safety stock High safety stock

• High attention to record accuracy Less record keeping

R base on fix dropping point of stock position R is reviewed at fix interval P of stock position

Require less safety stock for a service level Require more safety stock for the same service level

Inventory order is not regular scheduled (more order) Inventory orders is regular scheduled (less order)

Compare P & Q system

System Advantages Disadvantages

P system

Advantage of scheduled replenishment Less record keeping

Require large safety stock than Q system Require higher cost of storage

Q system Require a smaller stock Require high record keeping and controlling, accuration.

Note:

P system used for inexpensive, multiple items, regular schedule of replenishment, high safety stock, less record keeping

Q system often used for expensive, single items, less safety stock inventory, high attention to record accuracy

Service level and Inventory level

The average inventory formula:

There’s an important trade-off between service level and inventory level, that effect to management decisions of controlling independent-demand inventory

High service levels require higher inventory investment ( for a given order quantity (Q) and standard deviation )

Services level is a costly decision. A little change in service level can dramatically increase required inventory level.

Management should study the service level and investment relationship ( and decide the trade –off) before setting the service levels desired.

The relationship between service level and inventory level helps to determine appropriate inventory turnovers

Management should seek to continuously reduce Q and by that reducing the inventory required for a certain service level

I = Q/2 + z

85

95

100

90

Z=1.0

Z=1.2

Z=1.3

Z=2.1

Z=1.7Z=1.9

Z=2.4

250200 300150

Z=1.5

Average Inventory Level

Se

rvic

e l

ev

el

(%)

Figure 1.10

Service level versus

inventory level

ABC CONCEPT: In 1960 Vilfredo Pareto develop a rule of 80/20 proportion: that a few items ( around 20%) in any

group can contribute the significant proportion (up to 80%) of the entire group. ABC analysis also know as Pareto rule or 80-20 rule, this is base on the significant few and the

insignificant many. In inventory, a few items (20%) usually take most of inventory value (80% of capital investment) The concept should be use to carefully control the significant A items to spend less effort and cost on

the B and C items For A class items, we should use continuous review system, and periodic review system for C

items. Take intermediate level of attention and management level to B items.

100%254,725Total

2,4 %6,0002,003,00010

6,9 %17,5002,507,0009

2,2 % 5,6251,254,5008

1,5 %3,7500,755,0007

32,0 %81,60013,606,0006

1,5 %3,7500,507,5005

4,7 %12,0002,006,0004

41,2%105,00010,5010,0003

4,7 %12,0008,001,5002

2,9 %7,5001,505,0001

Percentage of Total Dollar Usage

Dollar Usage

(USD)

Unit Cost

(USD)

Annual Usage in Unit

Item

A class = 73,2 %

C class = 10,5 %

References

www.apics.org. Finding interested information about inventory control www.effectiveinventory.com/articles.html . Read articles and write a short summary of them www.cissltd.com. Run online demo of Inventory program www.Retailpro.com. Software system for controlling of retail inventories Books

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