Inventory Control

UNIT- 3

INVENTORY CONTROLINVENTORY CONTROL

Delivered By: Sarita Saxena

Copyright 2006 John Wiley & Sons, Inc. 12-2

• Stock of items kept to meet future demand

• Purpose of inventory control

What & how much of various items to be kept in stock.

Time & quantity of various items to be produced.

What Is Inventory ?


Raw materials

Purchased parts and supplies

Work-in-process (partially completed)

products (WIP)

Items being transported

Tools and equipment

Types of Inventory

Reducing amounts of raw materials and purchased

parts and subassemblies by having suppliers deliver

them directly.

Reducing the amount of works-in process by using

just-in-time production.

Reducing the amount of finished goods by shipping

to markets as soon as possible.

Zero Inventory ?

RawMaterials

WorksinProcess Finished

Goods Finished Goodsin Field

Inventory Positions in the Supply Chain

Improve customer service. Economies of purchasing. Economies of production. Transportation savings. Protection of material from spoilage & deterioration . Unplanned shocks (labor strikes, natural disasters,

surges in demand, etc.). To maintain independence of supply chain.

Benefits of Inventory Control

• Lead Time-It is the time that lapses b/w raising of indent by the stores & receipt of materials.

Administrative Lead TimeDelivery Lead Time

• Safety Stock- Difference b/w amount stocked & average expected demand.

Terms used in inventory


Types of Demand

DependentDependent

Demand for items used to produce final products Demand for items used to produce final products

Ex. : Tires stored at a Goodyear plant..

IndependentIndependent

Demand for items used by external customersDemand for items used by external customers

Ex. : Cars, appliances, computers, and houses.


Carrying costCarrying cost Cost of holding an item in inventory e.g cost related to storage.Cost of holding an item in inventory e.g cost related to storage.

Ordering costOrdering cost Cost of replenishing inventory , e.g travelling expenses.Cost of replenishing inventory , e.g travelling expenses.

Shortage costShortage cost Temporary or permanent loss of sales when demand cannot be met.Temporary or permanent loss of sales when demand cannot be met.

Inventory Costs


• EOQ Optimal order quantity that will minimize total

inventory (Ordering + Carrying costs)

EOQ = (2nco / ch)0.5

Economic Order Quantity


Demand is known with certainty and is constant over time.Demand is known with certainty and is constant over time.

No shortages are allowed.No shortages are allowed.

Lead time for the receipt of orders is constant.Lead time for the receipt of orders is constant.

Order quantity is received all at once.Order quantity is received all at once.

Assumptions of Basic EOQ Model


• Class A5 – 15 % of units70 – 80 % of value

• Class B30 % of units15 % of value

• Class C50 – 60 % of units 5 – 10 % of value

ABC Analysis


11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060

1010 2020 120120

PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGE

ABC Classification: Example


Demand Demand raterate

TimeTimeLead Lead timetime

Lead Lead timetime

Order Order placedplaced

Order Order placedplaced

Order Order receiptreceipt

Order Order receiptreceipt

Inve

nto

ry L

evel

Inve

nto

ry L

evel

Reorder point, Reorder point, RR

Order quantity, Order quantity, QQ

00

Inventory Order Cycle


CCoo - cost of placing order - cost of placing order DD - annual demand - annual demand

CCcc - annual per-unit carrying cost - annual per-unit carrying cost QQ - order quantity - order quantity

Annual ordering cost =Annual ordering cost =CCooDD

QQ

Annual carrying cost =Annual carrying cost =CCccQQ

22

Total cost = +Total cost = +CCooDD

QQ

CCccQQ

22

EOQ Cost Model


EOQ Cost Model

TC = +CoD

Q

CcQ

2

= +CoD

Q2

Cc

2

TC

Q

0 = +C0D

Q2

Cc

2

Qopt =2CoD

Cc

Deriving Qopt Proving equality of costs at optimal point

=CoD

Q

CcQ

2

Q2 =2CoD

Cc

Qopt =2CoD

Cc


EOQ Cost Model (cont.)

Order Quantity, Order Quantity, QQ

Annual Annual cost ($)cost ($) Total CostTotal Cost

Carrying Cost =Carrying Cost =CCccQQ

22

Slope = 0Slope = 0

Minimum Minimum total costtotal cost

Optimal orderOptimal order QQoptopt

Ordering Cost =Ordering Cost =CCooDD

QQ


EOQ Example

CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards

QQoptopt = =22CCooDD

CCcc

QQoptopt = =2(150)(10,000)2(150)(10,000)

(0.75)(0.75)

QQoptopt = 2,000 yards = 2,000 yards

TCTCminmin = + = +CCooDD

QQ

CCccQQ

22

TCTCminmin = + = +(150)(10,000)(150)(10,000)

2,0002,000(0.75)(2,000)(0.75)(2,000)

22

TCTCminmin = $750 + $750 = $1,500 = $750 + $750 = $1,500

Orders per year =Orders per year = DD//QQoptopt

== 10,000/2,00010,000/2,000

== 5 orders/year5 orders/year

Order cycle time =Order cycle time = 311 days/(311 days/(DD//QQoptopt))

== 311/5311/5

== 62.2 store days62.2 store days


Production QuantityModel

• An inventory system in which an order is received gradually, as inventory is simultaneously being depleted

• AKA non-instantaneous receipt model– assumption that Q is received all at once is relaxed

• p - daily rate at which an order is received over time, a.k.a. production rate

• d - daily rate at which inventory is demanded


Production Quantity Model (cont.)

QQ(1-(1-d/pd/p))

InventoryInventorylevellevel

(1-(1-d/pd/p))QQ22

TimeTime00

OrderOrderreceipt periodreceipt period

BeginBeginorderorder

receiptreceipt

EndEndorderorder

receiptreceipt

MaximumMaximuminventory inventory levellevel

AverageAverageinventory inventory levellevel


Production Quantity Model (cont.)

pp = production rate = production rate dd = demand rate = demand rate

Maximum inventory level =Maximum inventory level = QQ - - dd

== QQ 1 - 1 -

QQpp

ddpp

Average inventory level = Average inventory level = 1 - 1 -QQ22

ddpp

TCTC = + 1 - = + 1 -ddpp

CCooDD

QQ

CCccQQ

22

QQoptopt = =22CCooDD

CCcc 1 - 1 - ddpp


Production Quantity Model: Example

CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards

dd = 10,000/311 = 32.2 yards per day = 10,000/311 = 32.2 yards per day pp = 150 yards per day = 150 yards per day

QQoptopt = = = 2,256.8 yards = = = 2,256.8 yards

22CCooDD

CCcc 1 - 1 - ddpp

2(150)(10,000)2(150)(10,000)

0.75 1 - 0.75 1 - 32.232.2150150

TCTC = + 1 - = $1,329 = + 1 - = $1,329ddpp

CCooDD

QQ

CCccQQ

22

Production run = = = 15.05 days per orderProduction run = = = 15.05 days per orderQQpp

2,256.82,256.8150150


Production Quantity Model: Example (cont.)

Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 yards

dp

32.2150


Quantity Discounts

Price per unit decreases as order Price per unit decreases as order quantity increasesquantity increases

TCTC = + + = + + PDPDCCooDD

QQ

CCccQQ

22

wherewhere

PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand


Quantity Discount Model (cont.)

QQoptopt

Carrying cost Carrying cost

Ordering cost Ordering cost

Inve

ntor

y co

st (

$)In

vent

ory

cost

($)

QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200

TC TC ((dd2 2 = $6 ) = $6 )

TCTC ( (dd1 1 = $8 )= $8 )

TC TC = ($10 )= ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)200+ 6 (d2)


Quantity Discount: ExampleQUANTITYQUANTITY PRICEPRICE

1 - 491 - 49 $1,400$1,400

50 - 8950 - 89 1,1001,100

90+90+ 900900

CCoo = = $2,500 $2,500

CCcc = = $190 per computer $190 per computer

DD = = 200200

QQoptopt = = = 72.5 PCs = = = 72.5 PCs22CCooDD

CCcc

2(2500)(200)2(2500)(200)190190

TCTC = + + = + + PD PD = $233,784 = $233,784 CCooDD

QQoptopt

CCccQQoptopt

22

For For QQ = 72.5 = 72.5

TCTC = + + = + + PD PD = $194,105= $194,105CCooDD

QQ

CCccQQ

22

For For QQ = 90 = 90


Reorder Point

Level of inventory at which a new order is placed Level of inventory at which a new order is placed

RR = = dLdL

wherewhere

dd = demand rate per period = demand rate per periodLL = lead time = lead time


Reorder Point: Example

Demand = 10,000 yards/yearDemand = 10,000 yards/yearStore open 311 days/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 Daily demand = 10,000 / 311 = 32.154 yards/dayyards/dayLead time = L = 10 daysLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 yardsR = dL = (32.154)(10) = 321.54 yards


Safety Stocks

Safety stockSafety stockbuffer added to on hand inventory during lead buffer added to on hand inventory during lead

timetime

Stockout Stockout an inventory shortagean inventory shortage

Service level Service level probability that the inventory available during lead probability that the inventory available during lead

time will meet demandtime will meet demand


Variable Demand with a Reorder Point

ReorderReorderpoint, point, RR

QQ

LTLT

TimeTimeLTLT

Inve

nto

ry le

vel

Inve

nto

ry le

vel

00


Reorder Point with a Safety Stock

ReorderReorderpoint, point, RR

QQ

LTLT

TimeTimeLTLT

Inve

nto

ry le

vel

Inve

nto

ry le

vel

00

Safety Stock


Reorder Point With Variable Demand

RR = = dLdL + + zzdd L L

wherewhere

dd == average daily demandaverage daily demandLL == lead timelead time

dd == the standard deviation of daily demand the standard deviation of daily demand

zz == number of standard deviationsnumber of standard deviationscorresponding to the service levelcorresponding to the service levelprobabilityprobability

zzdd L L == safety stocksafety stock


Reorder Point for a Service Level

Probability of Probability of meeting demand during meeting demand during lead time = service levellead time = service level

Probability of Probability of a stockouta stockout

RR

Safety stock

ddLLDemandDemand

zd L


Reorder Point for Variable Demand

The carpet store wants a reorder point with a 95% The carpet store wants a reorder point with a 95% service level and a 5% stockout probabilityservice level and a 5% stockout probability

dd = 30 yards per day= 30 yards per dayLL = 10 days= 10 days

dd = 5 yards per day= 5 yards per day

For a 95% service level, For a 95% service level, zz = 1.65 = 1.65

RR = = dLdL + + zz dd L L

= 30(10) + (1.65)(5)( 10)= 30(10) + (1.65)(5)( 10)

= 326.1 yards= 326.1 yards

Safety stockSafety stock = = zz dd L L

= (1.65)(5)( 10)= (1.65)(5)( 10)

= 26.1 yards= 26.1 yards


Order Quantity for a Periodic Inventory System

QQ = = dd((ttbb + + LL) + ) + zzdd ttbb + + LL - - II

wherewhere

dd = average demand rate= average demand ratettbb = the fixed time between orders= the fixed time between orders

LL = lead time= lead timedd = standard deviation of demand= standard deviation of demand

zzdd ttbb + + LL = safety stock= safety stock

II = inventory level= inventory level


Fixed-Period Model with Variable Demand

dd = 6 bottles per day= 6 bottles per daydd = 1.2 bottles= 1.2 bottles

ttbb = 60 days= 60 days

LL = 5 days= 5 daysII = 8 bottles= 8 bottleszz = 1.65 (for a 95% service level)= 1.65 (for a 95% service level)

QQ = = dd((ttbb + + LL) + ) + zzdd ttbb + + LL - - I I

= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8

= 397.96 bottles= 397.96 bottles

Inventory Control

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