STOCK STOCK –– TIME DIAGRAMTIME DIAGRAM• LT-2 = LT-1 + 2Cycle Time [ LT-2 > LT-1, LT-2>Cycle Time]STOCKSTOCK

TIMETIMELT-1

LT-2 LT-2

LT-2LT-1

Maximum LevelMaximum Level

Reordering LevelReordering Level

Minimum LevelMinimum Level

Danger LevelDanger Level

00

Safety StockSafety Stock

Reserve StockReserve Stock

Buffer StockBuffer Stock

Cycle Time

◙◙ TYPE OF INVENTORYTYPE OF INVENTORYA)A) MATERIAL BASED (MATERIAL BASED (based onbased on nature of Materialnature of Material) :) :1) Production InventoryProduction Inventory : Raw materials and

Components / Parts required processing and assembly work, for the purpose of production.

2) MRO InventoryMRO Inventory (Maintenance, Repair & Operating supplies) : Maintenance Spare parts and Consumables (Lubricating oil, grease, cotton waste, Electrodes, Cleaning & Protecting chemicals, etc).

3) WIP InventoryWIP Inventory ( Work-in-process or Work-in-progress) : Sub-assemblies and components already produced (waiting for final assembly) or all semi-finished work in the production-process line.

4) Finished Goods InventoryFinished Goods Inventory (final Products) : Completed or finished or assembled final products, (after final quality-inspection and labeling) ready for delivery (shipment).

B)B) PURPOSE BASEDPURPOSE BASED ::1)1) Cycle InventoryCycle Inventory : Material procurement in cycle, repeated

manner and in batches / lots with Min. Inventory Level at Zero(nil) and Max. Inventory Level at Order Quantity (Q). Here, there is every chance of Stock-out condition.

2) Safety Stock InventorySafety Stock Inventory : Material procurement in cycle and in batches with Min. Inventory Level at Safety Stock but not at Zero (nil) to avoid chances of Stock-out condition.

3) Anticipation InventoryAnticipation Inventory : Bulk quantity (more than the normal quantity) of stock is maintained purposefully for

a) Anticipated price rise of materials of the stockb) Anticipated Scarcity of Raw Materials, Components, etcc) Anticipated Seasonal rise of demand of final productd) Anticipated sudden rise of demand of final product

4)4) PipePipe-- line Inventoryline Inventory : For WIP or sub-assemblies, between operations/processes, and for raw material or components between supplier and plant inventory (supplier Warehouse), and for final products, products under movementunder movement between between plantplant’’s s finished-product- WareWare--househouse and distributors or and distributors or customers warehousescustomers warehouses..

C) C) Based on the Based on the InventoryInventory--Replenishment TypeReplenishment Type

1)1) SingleSingle--Period InventoryPeriod Inventory : Purchasing through only one ordering opportunity . (A very special occasion or situation when the procurement will not repeat any more). It is applicable to products having a very short Life Cycle.

Example :(1) Inventory of a Retailer to sell to the public the tt--shirtsshirts like the

jersey of Indian teamjersey of Indian team in the World Cup CricketWorld Cup Cricket to be held in India, mainly during the tournament.

(2) The inventory for a marriage ceremonymarriage ceremony in a family and arranged by the family.

(3) CalendarsCalendars or GreetingGreeting--cardscards for specific occasionspecific occasion (or with specific purposespecific purpose), having year and date printedyear and date printed on them.

(4) Order for Electronic Voting Machines, in India to BharatElectronics Ltd. and Electronic Corporation of India Ltd.

# Seeks efficient estimation of accurate quantity of stockestimation of accurate quantity of stock in inventory to avoid

(i) OverOver--stockstock to reduce loss due to waste in disposing surplus, to reduce loss due to waste in disposing surplus, and also

(ii) UnderUnder--stockstock ((stockstock--outout) to reduce chances of foregoing profit ) to reduce chances of foregoing profit through sales.through sales.

2)2) MultiMulti--Period InventoryPeriod Inventory : Material procurement is repeated in batches / lots, having Inventory-Control system maintaining different InventoryInventory Levels.Example : All manufacturing units, Retail outlets, Distributors, etc.

◙◙ The basic Costs of InventoryThe basic Costs of InventoryBasic Costs of Inventory for a certain period (say,

annually) include :1) 1) Cost of the materialCost of the material : :

Procured Quantity of Material during the period x Procured Quantity of Material during the period x Price (ie Unit Cost of materialPrice (ie Unit Cost of material)

= (D x P)(D x P)2)2) Total Cost of OrderingTotal Cost of Ordering and Procurementand Procurement ::

No. of Ordering for procurement of Material during the No. of Ordering for procurement of Material during the period x Ordering Cost /Order period x Ordering Cost /Order

= (N x Co)(N x Co) = (D/Q) x Co(D/Q) x Co3)3) Total Inventory Carrying CostTotal Inventory Carrying Cost ( ( Inventory maintenance Inventory maintenance

CostCost or or Inventory Holding CostInventory Holding Cost)) ::Average Value of the Stock during the period x Rate Average Value of the Stock during the period x Rate

of Inventory Carryingof Inventory Carrying--Cost (%)Cost (%)= ½½ x x ValueValue of Ordering Quantity x Ccof Ordering Quantity x Cc= ½½ x (Q x P) x Ccx (Q x P) x Cc

Cost ComponentsCost Components of of Inventory CarryingInventory Carrying CostCost or or Holding CostHolding Cost

1.1. INTERESTINTEREST on the on the INVESTMENTINVESTMENT on Stock of Material in Inventory

2.2. Cost of Cost of INSURANCEINSURANCE of the Stocked Material3.3. Cost of Cost of INVENTORY SPACEINVENTORY SPACE and Warehouse/ shed/ room4.4. Cost of Cost of MAINTENANCEMAINTENANCE of Inventoryof Inventory including :

(i) Stock keeping Arrangement (Rack or Trays or Binsor Tanks or Silo, etc

(ii) In-plant Material Handling, (iii) Protecting Stock from damage, spoilage, pilferage(iv) Infrastructures in Stores (light, water, fan, AC, etc)

(v) Accounting and Records Keeping for Stock. 5.5. Cost of Cost of MANPOWERMANPOWER ( for receiving, keeping, issuing,

maintaining of materials and Cleaning & Maintenance of stores room, ),

6.6. Cost of (Loss due to) Cost of (Loss due to) SPILLAGESPILLAGE and and SPOILAGESPOILAGE (Damage)(Damage) of material

7. 7. Cost of Cost of OBSOLESCENCEOBSOLESCENCE, if any.

ECONOMIC ORDERING QUANTITY ECONOMIC ORDERING QUANTITY (EOQ)(EOQ)

Let, Let, DD = = Annual DemandAnnual Demand (or requirement or consumption or(or requirement or consumption orprocurement) of materialprocurement) of material

QQ = = Ordering QuantityOrdering Quantity or size (Quantity per order)or size (Quantity per order)PP = = Unit cost of materialUnit cost of material (effective price)(effective price)CoCo = = Ordering CostOrdering Cost per Orderper OrderCcCc = = Carrying CostCarrying Cost of Inventories of Inventories in %in % on the on the value ofvalue of

Average StockAverage Stock,, ororCCHH = = HoldingHolding / / Carrying CostCarrying Cost of Inventories in of Inventories in RsRs per unitper unit

QuantityQuantity (per piece or MT or Cu M) (per piece or MT or Cu M) of Average Stockof Average Stock[[ieie CCHH = Cc x P= Cc x P]]

[[Average stock = Q/2,Average stock = Q/2, iin case of n case of Cycle InventoryCycle Inventory , where , where Min. Level is 0Min. Level is 0]]

Total Annual Cost of InventoryTotal Annual Cost of Inventory,,CCtt = = Annual Cost of the materialAnnual Cost of the material + +

(Annual Cost of Ordering + Annual Carrying Cost)(Annual Cost of Ordering + Annual Carrying Cost)

EOQ (contd.)

CCt = (D x P) + (D/Q) x Co + = (D x P) + (D/Q) x Co + ½½ (Q x P) x Cc(Q x P) x CcTo find out the most economic ordering quantity, CTo find out the most economic ordering quantity, Ctt willwill be minimumbe minimum, and thus , and thus

at the minimum conditionat the minimum condition

the first differentiation, the first differentiation, CCtt’’ = = d(Cd(Ctt) = 0) = 0dQdQ

d(D X P)d(D X P) + + d[(D/Q) x Co]d[(D/Q) x Co] + + d[(Qd[(Q x P x Cc) / 2 ]x P x Cc) / 2 ] = 0= 0dQ dQ dQdQ dQ dQ

0 + ( 0 + ( -- D/ Q D/ Q 22 ) x Co + (P x Cc) / 2 = 0 ) x Co + (P x Cc) / 2 = 0

Q* = Q* = √√ [ (2 x D x Co) / (P x Cc)][ (2 x D x Co) / (P x Cc)]= = √√ [ (2 x D x Co) / C[ (2 x D x Co) / CHH)])]

-- W I L S O NW I L S O N’’ S F O R M U L AS F O R M U L ANow, the second differentiation of Csecond differentiation of Ctt ,

CCtt”” = (2D/Q3) x C0 + 0 > 0 ie PositivePositive,

This indicates that “First differentiation, Ct’ = 0” is for the minimum CCtt and thus

Q* is the Order quantity for minimum Total Inventory CostQ* is the Order quantity for minimum Total Inventory Cost .

EOQ (contd.)

◙◙ COST TRADE-OFF of inventory

From Cost Trade-off of inventory, it is noted that at Q*, Total Inventory Carrying Cost = Total Ordering CostTotal Inventory Carrying Cost = Total Ordering Cost

Total Annual Cost

Order Qty (Q)

Ordering Cost

Inv. CarryingCost

Total Cost = Inv Carrying Cost +Ordering Cost

Q*

½½ (Q x P) x Cc = (Q x P) x Cc = ½½ (Q x C(Q x CHH) )

2(D/Q) x Co = (Q x P) x Cc (D/Q) x Co(D/Q) x Co

ProbProb--1)1) Omega Manufacturing Co. procures 40,000 pcs of bushes quarterly. Procurement Cost per order is Rs 800/-, Inventory Carrying Cost is 10% half yearly on the value of average stock maintained, Unitprice of the bush is Rs 20/-, Lead Times of various suppliers are 3, 4,and 5 days. Determine, (1) EOQ, (2) No. of Orders per year, (3) Spacing betweenTwo consecutive orders, if the Co. operates 360 days in a year,(4) Total Cost tied up with the present inventory, (5) Saving Inventory-Cost with proposed EOQ.

SolnSoln ::

D = 40,000 per quarter = 160,000 pcs per year, P = Rs 20, Cc = 10% half yearly = 20% yearly = 0.2, Co = Rs 800, No. of working days in a year, d = 360 Av. Lead Time = (3+4+5) / 3 = 4 days

Q* = √√ [ (2 x D x Co) / (P x Cc)][ (2 x D x Co) / (P x Cc)] = √ [ (2 x 160,000 x 800) / (20 x 0.2)] = 80008000

No. of Orders per year = D/ Q* = 160,000 / 8000 = 2020

Problem-1 (contd.)

Space between consecutive orders = 360 / 20 = 18 days18 days

Present Total Inventory Cost

= (D x P) + (D/Q) x Co + ½ (Q x P) x Cc

= 160,000 x 20 +(160,000/40,000)x800 +(40,000 x 20 x 0.2) /2

= 3,200,000 + 3,200 + 80,000 = Rs 3,283,200/Rs 3,283,200/--

Total Inventory Cost with EOQ

= (D x P) + (D/Q) x Co + ½ (Q x P) x Cc

= 160,000 x 20 + (160,000/8000) x 800 + (8000 x 20 x 0.2) /2

= 3200,000 + 16,000 + 16,000 = Rs 3,232,000/Rs 3,232,000/--

Cost saving with EOQ = 3,283,200 - 3,232,000

= Rs 51,200/Rs 51,200/--

Economic Production Economic Production QuantityQuantity (EPQEPQ)

Usage Usage

Pro

duct

ion

& U

sage

Pro

duct

ion

& U

sage

Quantity

Time

Max Inv Level (Qmax )

Production / Order Quantity. (Q)

pd

Demand/Consumption

Production

Production (Supply) rate = pp

Demand (Consumption) rate = dd

Production (Supply) time, tt11 = Q/p

Qmax = (p – d) x t1 = (p – d) x Q/p

Total Holding CostTotal Holding Cost = (Qmax / 2) x CH

= (p (p –– d) x (Q/ 2p) x Cd) x (Q/ 2p) x CHH

tt11 t2Total Inventory Cost, Tc = Holding Cost + Ordering Cost

Tc = (p – d) x (Q/ 2p) x CH + (D/Q) x Co

For minimizing the Total Inventory Cost, Tc d (Tc) = 0dQ

(p – d) CH / 2p – (D/Q2) x Co = 0 _____________________

Q2 = 2p . => Q Q = = (2D.C(2D.Coo)) x (x ( p .p .))D. Co (p – d) . CH √√ CCH H p p -- dd

Reordering PointReordering Point when both both demand and lead time varydemand and lead time vary

• Example– Average Usage = 12 order forms/day; σd = 3

– Average Lead time = 7 days; σLT = 1

– ROP = (12)(7) + 1.96[(7)(9) + (144)(1)] = 84 + 1.96(14.4) = 84 + 27.7 = 112

– Reorder when 112 order forms are left

222LTd dTLzTLdROP

2)2)(P(P--System)System) FixedFixed--Time Period Model with Safety StockTime Period Model with Safety Stock

1)1) REVIEW PERIODREVIEW PERIOD, , RR = = Annual period / Annual No. of OrderAnnual period / Annual No. of Order

= = Annual period / (Annual demand / EOQ)Annual period / (Annual demand / EOQ) , 2)2) TARGET Inventory LevelTARGET Inventory Level, ,

where σσ R+ LR+ L = = σσd d √√(R+L)(R+L)

3)3) ORDER QUANTITYORDER QUANTITY,, Q = Q = QQTT -- II , Where,

σR+ LR+ L = Standard DeviationStandard Deviation of demandof demand during (Review Period + Lead during (Review Period + Lead Time) Time)

σσdd = Standard Deviation of weekly demand.

QQ = Quantity to be ordered (Ordering Quantity)

dd = Estimated Normal Rate of demand (i.e. Av. Consumption RateAv. Consumption Rate)Z Z = Service Level ConstantService Level Constant = Factor corresponding to specified

“SERVICE LEVELSERVICE LEVEL”

RR = Review Period = Time gap between consecutive reviews / Ordering

LL = Lead timeII =Current inventory level (includes items on order) i.e. Stock-in-hand

QQTT = d x (R + L) = d x (R + L) ++ Z x Z x σσ R+ LR+ L

QQTT = Buffer Stock + Safety stockBuffer Stock + Safety stock

ExampleExample--66 ::The normally distributed weekly demands of an item has the meanThe normally distributed weekly demands of an item has the meanvalue 18 units per week with a standard deviation of weekly demavalue 18 units per week with a standard deviation of weekly demand nd of 5 units. The Lead Time being 5 weeks, EOQ with Qof 5 units. The Lead Time being 5 weeks, EOQ with Q--system 75 unitssystem 75 unitsand Service Level is 90%.and Service Level is 90%.Design PDesign P--system for Inventory Management.system for Inventory Management.

-- Annual demand, Annual demand, DD = Mean Weekly Demand (= Mean Weekly Demand (dd) x Weeks/year) x Weeks/year(where, mean demand, (where, mean demand, d = 18d = 18 ) = ) = 1818 x 52 = x 52 = 936 units936 units

No. of orders per year = Annual Demand / EOQ = 936 No. of orders per year = Annual Demand / EOQ = 936 ÷÷ 75 (as 75 (as EOQ=75EOQ=75))

Review PeriodReview Period, , RR = Total Period / no. of order = 52 weeks = Total Period / no. of order = 52 weeks ÷÷ (936 / 75)(936 / 75)

= (52 x 75) = (52 x 75) ÷÷ 936 weeks = 936 weeks = 4.2 weeks4.2 weeks ≈≈ 4 weeks4 weeks

Standard Deviation of demandStandard Deviation of demand during (Lead Time + Review Periodduring (Lead Time + Review Period),),

σσ R+LR+L = = σσd d ..√√(R+L)(R+L) == 5 5 .. √√(4+5)(4+5) == 5 5 .. √√99 = = 15 units15 units

where, where, σσdd is Standard Deviation of weekly demand, (is Standard Deviation of weekly demand, (σσd d = 5).= 5).

Now,Now, for for 90% of service level90% of service level, ,

ServiceService--Level ConstantLevel Constant, , Z = 1.28Z = 1.28 (from the table)(from the table)

Safety StockSafety Stock = Z x Z x σσ R+LR+L = 1.28 x 15 = 19.2 units =19 units19 units

(say)

Buffer StockBuffer Stock = dd .(R+L).(R+L) [where, mean demand, dd =18 /week ]

= 18 x ( 4+5) = 162 units162 units

Target Inventory LevelTarget Inventory Level = Buffer stock + Safety Stock

= 162 + 19 = 181 units181 units

AnswerAnswer ::

1. At the interval of 4 weeks4 weeks (Review Period),(Review Period), review of the Actual Stock is done and the Actual Stock position is compared with the Target Inventory Level.

2. If the Actual Stock is Actual Stock is atat or or aboveabove the Target Inventory the Target Inventory LevelLevel, skip Reorderingskip Reordering till next Review Periodtill next Review Period.

3. If the Actual Stock is tual Stock is belowbelow the Target Inventory Levelthe Target Inventory Level, Place OrderPlace Order and order a quantityorder a quantity is equal to is equal to difference between Target Inventory and Actual difference between Target Inventory and Actual StockStock..

INVENTORY CONTROL TECHNIQUESINVENTORY CONTROL TECHNIQUES

ABCABC : : Cumulative CostCumulative Cost basis : basis : AA ––Highest cost, Highest cost, BB ––Medium cost, Medium cost,

CC ––Lowest costLowest cost

HMLHML : : Unit CostUnit Cost basis :basis : H H –– High price, High price, MM –– Medium price, Medium price, LL –– Low priceLow price

======================================================================================================================

VEDVED : : Requirement CriticalityRequirement Criticality basis : basis : VV –– Vital, Vital, E E –– Essential, Essential, DD –– DesirableDesirable

======================================================================================================================

FSNFSN : : Consumption rateConsumption rate basis : basis : FF –– Fast moving, Fast moving, SS –– Slow moving, Slow moving,

NN –– NonNon--moving moving

========================================================================================================================

SDESDE : (Procurement) : (Procurement) AvailabilityAvailability basis : basis : SS ––Scarcely available, Scarcely available, DD ––Difficultly Difficultly

available, available, EE –– Easily available Easily available

or or SAPSAP : : S S –– ScaresScares, A , A –– AvailableAvailable, P , P -- PlentyPlenty

GOLFGOLF : : Procurement SourceProcurement Source basis :basis : GG –– Govt. quota (priority), Govt. quota (priority), OO –– Ordinary, Ordinary,

LL –– Local, Local, F F -- ForeignForeign

ABCABC ((Always Better ControlAlways Better Control oror PARETO AnalysisPARETO Analysis))Cumulative Cost in % of Total Material Cost

Quantity(in % of Total Qty)10%10% 25%25% 100%100%

AA

BBCC

7070

9090100100

20%

10%

70%

A : cost = 70%, qty = 10%A : cost = 70%, qty = 10%

B : cost = 20%, qty = 15%B : cost = 20%, qty = 15%

C : cost = 10%, qty = 75%C : cost = 10%, qty = 75%

ExampleExample--66 :: Show ABC Analysis for the inventory in one unit of M/s Show ABC Analysis for the inventory in one unit of M/s Pop Bazar, if their inventory item details is as given below,Pop Bazar, if their inventory item details is as given below,

ItemItem Unit Price (Rs)Unit Price (Rs) Consumption Qty (Units/year)Consumption Qty (Units/year)AA 100100 100100 10,00010,000BB 200200 300300 60,00060,000CC 5050 700700 35,00035,000DD 300300 400400 120,000120,000EE 500500 10001000 500,000500,000FF 30003000 3030 90,00090,000GG 10001000 100100 100,000100,000HH 70007000 500500 3,500,0003,500,000II 50005000 105105 525,000525,000JJ 6060 10001000 60,00060,000

ItemItem Annual Cost (Rs)Annual Cost (Rs) Annual Cumulative Value (Rs)Annual Cumulative Value (Rs)

HH 3,500,0003,500,000 ^̂ 3,500,0003,500,000 :: :: 70% 70% AA--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

II 525,000525,000 ^̂ 4,025,000 4,025,000

EE 500,000500,000 ^̂ 4,525,0004,525,000 :::: 90%90% BB--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

DD 120,000120,000 ^̂ 4,645,0004,645,000

GG 100,000 ^100,000 ^ 4,745,0004,745,000

FF 90,000 ^90,000 ^ 4,835,0004,835,000

BB 60,00060,000 ^̂ 4,895,0004,895,000

JJ 60,000 ^60,000 ^ 4,955,0004,955,000

CC 35,00035,000 ^̂ 4,990,0004,990,000

AA 10,00010,000 ^ ^ 5,000,0005,000,000 :: :: 100% 100% CC==============================================================================================================

ClassificationClassification ::

Item Item HH is class is class AA, Items , Items I & EI & E are class are class BB, ,

Items Items D,G,F,B,J,C & AD,G,F,B,J,C & A are class are class CC