Inventory Inventory ManagementManagement

Independent vs. Independent vs. dependent dependent demanddemand

Independent demand:Independent demand: Influenced only by market conditionsInfluenced only by market conditions Independent from operationsIndependent from operations Example: finished goodsExample: finished goods

Dependent demand:Dependent demand: RelRelaated to the demand for another item ted to the demand for another item

with independent demandwith independent demand Example: product components, raw Example: product components, raw

materialmaterials, labours, labour

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.

InventoryInventory management management

A subsystem of logisticsA subsystem of logistics Inventory: Inventory:

a stock of materials or other goods ta stock of materials or other goods too facilitate production or to satisfy customer facilitate production or to satisfy customer demanddemand

a stock or store of goodsa stock or store of goods Main decisions:Main decisions:

Which items should be carried in stock?Which items should be carried in stock? How much should be ordered?How much should be ordered? When should an order be placed?When should an order be placed?

The need to hold stocks The need to hold stocks 11

BufferBuffer between Supply and Demand between Supply and Demand To To keep down production costskeep down production costs: :

TTo achieve low unit costs, production have to run as long as o achieve low unit costs, production have to run as long as possible (setting up machines is tend to be costly)possible (setting up machines is tend to be costly)

To To decoupledecouple operations operations To take account of variable supply To take account of variable supply (lead) (lead) times: times: safety safety

stockstock to cover delivery delays from suppliers to cover delivery delays from suppliers To minimize To minimize buying costsbuying costs associated with raising an associated with raising an

orderorder To accommodate To accommodate variations (on the short run) in variations (on the short run) in

demanddemand (to avoid stock-outs) (to avoid stock-outs) To account for To account for seasonal fluctuationsseasonal fluctuations::

There are products popular only in peak timesThere are products popular only in peak times There are goods produced only at a certain time of the yearThere are goods produced only at a certain time of the year

Adaptation Adaptation tto the o the fluctuation of demand with fluctuation of demand with

building up stocksbuilding up stocksDEMAND

CAPACITY

Inventory accumulation

Inventory reduction

The need to hold stocks The need to hold stocks 22

To take advantage of To take advantage of quantity discountsquantity discounts (buying in (buying in bulk)bulk): the price is lower because the of the quantity: the price is lower because the of the quantity

To allow for price fluctuations/To allow for price fluctuations/speculationspeculation: to buy : to buy large quantities large quantities whenwhen a good is cheaper a good is cheaper

To help production and distribution operations run To help production and distribution operations run smoothly: to increase the smoothly: to increase the independence ofindependence of these these activitiesactivities. . Work-in-progress: facilitating production process by Work-in-progress: facilitating production process by

providing semi-finished stocks between different providing semi-finished stocks between different processesprocesses

To provide To provide immediate service for customersimmediate service for customers To To minimize production delaysminimize production delays caused by lack of caused by lack of

spare parts (for maintenance, breakdowns)spare parts (for maintenance, breakdowns)

Types of Types of Stock-holding/InventoryStock-holding/Inventory

raw material, component and packaging stockraw material, component and packaging stock in-process stocks (work-in-progress; WIP)in-process stocks (work-in-progress; WIP) finished products (finished goods inventory; finished products (finished goods inventory;

FGI)FGI) pipeline stocks: held in the distribution chainpipeline stocks: held in the distribution chain general stores: contains a mixture of products general stores: contains a mixture of products

to support to support spare partsspare parts for production for production: :

Consumables (nuts, bolts, etc.)Consumables (nuts, bolts, etc.) Rotables and repairablesRotables and repairables

An alternative An alternative typology typology of stocksof stocks

working stockworking stock: reflects the : reflects the normal normal demanddemand

cycle stockcycle stock: follows the production (or : follows the production (or demand) cyclesdemand) cycles seasonal stockseasonal stock: goods stockpiled before : goods stockpiled before

peakspeaks safety stocksafety stock: to cover unexpected : to cover unexpected

fluctuations in demandfluctuations in demand speculative stockspeculative stock: built up on : built up on

expectationsexpectations

Inventory costInventory cost Item costItem cost: the cost of buying or producing : the cost of buying or producing

inventory itemsinventory items Ordering costOrdering cost: does not depend on the : does not depend on the

number of items ordered. Form typing the number of items ordered. Form typing the order to transportation and receiving costs.order to transportation and receiving costs.

Holding (carrying) costHolding (carrying) cost:: Capital cost: the opportunity cost of tying up Capital cost: the opportunity cost of tying up

capitalcapital Storage cost: space, insurance, taxStorage cost: space, insurance, tax Cost of obsolescence, deterioration and lossCost of obsolescence, deterioration and loss

StockStock--out costout cost: economic consequences of : economic consequences of running out of stock (lost profit and/or running out of stock (lost profit and/or goodwill)goodwill)

Evaluating stocks: Evaluating stocks:

the ABC analysisthe ABC analysis

Data CaptureData Capture Techniques and error rates Techniques and error rates (Rushton et al. 2006)(Rushton et al. 2006)

Written entry – 25,000 in 3,000,000Written entry – 25,000 in 3,000,000 Keyboard entry – 10,000 in 3,000,000Keyboard entry – 10,000 in 3,000,000 Optical character recognition (OCR) – 100 in 3,000,000Optical character recognition (OCR) – 100 in 3,000,000

labels that are both machine- and human-readablelabels that are both machine- and human-readable for example: license platesfor example: license plates

Bar code (code 39) – 1 in 3,000,000Bar code (code 39) – 1 in 3,000,000 fast, accurate and fairly robust fast, accurate and fairly robust reliable and cheap techniquereliable and cheap technique

Transponders (radio frequency tags) – 1 in 30,000,000Transponders (radio frequency tags) – 1 in 30,000,000 a tag (microchip + antenna) affixed to the goods or containera tag (microchip + antenna) affixed to the goods or container receiver antennareceiver antenna readerreader host station that relays the data to the serverhost station that relays the data to the server can be passive or activecan be passive or active

Inventory modelsInventory models

Economic Order Quantity Economic Order Quantity (EOQ)(EOQ)

Assumptions of the model:Assumptions of the model: Demand rate is constant, recurring and knownDemand rate is constant, recurring and known The lead time (from ordThe lead time (from ordeer placement and r placement and

order delivery) is constant and knownorder delivery) is constant and known No stockouts are allowedNo stockouts are allowed Goods are ordered and produced in lots, and Goods are ordered and produced in lots, and

the lot is placed into inventory all at one timethe lot is placed into inventory all at one time Unit item cost is constant, carrying cost is Unit item cost is constant, carrying cost is

linear function of average inventory levellinear function of average inventory level Ordering cost is independent of the number of Ordering cost is independent of the number of

items in a lotitems in a lot The item is a single product (no interaction The item is a single product (no interaction

with other products)with other products)

The ‘SAW-TOOTH’The ‘SAW-TOOTH’Inventory level

Time

Orderquantity(Q)

Order inteval

Average inventory level = Q/2

Total cost of inventory Total cost of inventory (trade(trade--off between ordering frequency and off between ordering frequency and

inventory level)inventory level)

Minimumcost

Total cost

Ordering cost

(S ∙ ∙ D/Q)

Holding cost

(H ∙∙ Q/2)

EOQ

cost

lot size

Calculating the total costCalculating the total cost of of inventoryinventory

Let… Let… SS be the ordering cost (setup cost) per oder be the ordering cost (setup cost) per oder DD be demanded items per planning period be demanded items per planning period HH be the stock holding cost per unit be the stock holding cost per unit

HH==ii∙∙CC, where, where C C is the unit cost of an item,is the unit cost of an item, andand i i is the is the carrying ratecarrying rate

P P be the market price of the item demandedbe the market price of the item demanded QQ be the ordered quantity per order (= lot) be the ordered quantity per order (= lot)

TCTC = = SS ∙ ( ∙ (DD//QQ) + ) + HH ∙ ( ∙ (QQ/2)/2) + + PP ∙ ∙ DD ((DD//QQ) is the number of orders per period) is the number of orders per period ((QQ/2) is the average inventory level in this model/2) is the average inventory level in this model

The minimum The minimum costcost (EOQ) (EOQ)

TCTC = = SS ∙ ( ∙ (DD//QQ) + ) + HH ∙ ( ∙ (QQ/2) + /2) + PP ∙ ∙ DD ббTCTC//ббQQ = 0 = 0 0 = – 0 = – SS ∙ ( ∙ (DD//Q Q 22) + ) + HH/2/2 HH/2 = /2 = SS ∙ ( ∙ (DD//Q Q 22)) Q Q 2 2 = (2 ∙ = (2 ∙ SS ∙ ∙ DD)/)/HH EOQEOQ = √ (2 ∙ = √ (2 ∙ SS ∙ ∙ DD)/)/HH

ExampleExampleDD = 1000 units per year = 1000 units per year

SS = 100 euro per order = 100 euro per order

HH = 20 euro per unit = 20 euro per unit per per yearyear

Find the economic order quantity! (we assume a saw-tooth model)

EOQEOQ = = √ (2 ∙ 1,000√ (2 ∙ 1,000unitsunits ∙ 100 ∙ 100euroeuro)/20)/20euro/uniteuro/unit

EOQEOQ = = √ 10,000√ 10,000unitsunits2 2 = = 100100unitsunits

Reordering Reordering (or (or replenishment) replenishment) pointpoint

When to start the ordering process?When to start the ordering process? It depends on the…It depends on the…

Stock position: stock on-hand (+ stock on-Stock position: stock on-hand (+ stock on-order)order)

in a simple saw-tooth model it is in a simple saw-tooth model it is Q, Q, in some cases, there can be an initial stockin some cases, there can be an initial stock, , that is that is

different fromdifferent from Q. Q. lead time (lead time (LL): the time interval from setting up ): the time interval from setting up

order to the start of using up the ordered stockorder to the start of using up the ordered stock Average demand per day (Average demand per day (dd))

ROPROP = = dd ∙ ∙ LL

ExamplesExamples QQ = 200 tons = 200 tons dd = 10 tons per day = 10 tons per day LL = 8 days = 8 days ROPROP = ? = ?

ROP ROP = 10 ∙ 8 = 80 tons= 10 ∙ 8 = 80 tons

QQ = 400 tons = 400 tons dd = 16 tons per day = 16 tons per day LL =20 days =20 days ROP = ?

ROP ROP = 16 = 16 ∙ 20 = 320 tons

Example on both Example on both EOQEOQ and and RR

D D = 2,000 tons= 2,000 tonsS S = 100 euros per order= 100 euros per orderH H = 25 euros per unit = 25 euros per unit

per yearper yearLL = 12 days = 12 daysNN = 250 days = 250 days

EOQEOQ = √ (2 ∙ 2,000 = √ (2 ∙ 2,000tsts ∙ 100 ∙ 100euroeuro)/25)/25euro/tseuro/ts = 126,49= 126,49tonstons

dd = 2,000 = 2,000tsts/250/250ds ds = 8 = 8 ts/dsts/ds

ROPROP = 8 ∙ 12 = 96 = 8 ∙ 12 = 96 tonstons

Calculate the Calculate the following:following:

EOQEOQ

dd

ROPROP

The SAW-TOOTHThe SAW-TOOTHwith safety stockwith safety stock

Inventory level

Time

Orderquantity

Continuous demand

Safety stock or buffer stock

b

Buffer (safety) stockBuffer (safety) stock

b = zb = z ∙ σ ∙ σ

wherewhere

z = z = safety factor from the (normal) distributionsafety factor from the (normal) distribution

σ σ = = sandard deviation of demand over lead timesandard deviation of demand over lead time

LetLet z z be 1,65 (95%), and the standard be 1,65 (95%), and the standard deviation of demand is 200 units/lead deviation of demand is 200 units/lead

time.time.bb = 1,65 = 1,65 ∙∙ 200 200units units = 330= 330unitsunits

When to order, when there When to order, when there is a buffer stock?is a buffer stock?

ROP = d ROP = d ** L + b L + b

If If Q Q = 60tons, = 60tons, LL = 2 days, = 2 days, bb = 10tons, = 10tons, DD = 300tons, = 300tons, NN = 100 days, then = 100 days, then ROP ROP = ?= ?

ROP = 2 ROP = 2 ** 3 + 10 3 + 10 = 16 tons= 16 tons

ExampleExample Lead time = 10 daysLead time = 10 days Average demand over lead time: 300 tonsAverage demand over lead time: 300 tons Standard deviation over lead time: 20 tonsStandard deviation over lead time: 20 tons Accepted risk level: 5%Accepted risk level: 5% Safety stock = ? Reorder quantity = ?Safety stock = ? Reorder quantity = ?

bb = = zz * * σσ = = 1,65 * 20 = 33 tons 1,65 * 20 = 33 tons ROPROP = 300 + 33 = 333 tons = 300 + 33 = 333 tons

ExamplesExamples QQ00 = 600 tons = 600 tons QQ = 200 tons = 200 tons dd = 10 tons per day = 10 tons per day LL = 8 days = 8 days bb = 33 tons = 33 tons

ROP ROP = 8 * 10 + 33 = 113= 8 * 10 + 33 = 113

QQ00 = = QQ = 400 tons = 400 tons dd = 16 tons per day = 16 tons per day LL =20 days =20 days bb = 66 tons = 66 tons

ROP ROP = 386= 386

Alternative models 1Alternative models 1

Periodic review system:Periodic review system: Stock level is examined at regular Stock level is examined at regular

intervalsintervals Size of the order depends on the quantity Size of the order depends on the quantity

on stock. it should bring the inventory to on stock. it should bring the inventory to a predetermined levela predetermined level

time

Stock on hand

L

Q Q

LLT TT

Q

Alternative models 2Alternative models 2

Fixed-order-quantity system:Fixed-order-quantity system: A predetermined stock level (reorder A predetermined stock level (reorder

point) is given, at which the point) is given, at which the replenishement order will be placedreplenishement order will be placed

The order quantity is constantThe order quantity is constant

R

Stock on hand

L LL

QQ

Some more examplesSome more examples

Calculate Calculate ROPROP, and , and EOQEOQ, if…, if…

1.1. LL = 2 days, = 2 days, bb = 12tons, = 12tons, DD = 300tons, = 300tons, NN = = 100 days, 100 days, SS = 50 euro, = 50 euro, HH = 20 = 20 euro/tons/yeareuro/tons/year

2.2. LL = 12 days, = 12 days, bb = 20tons, = 20tons, DD = 1300tons, = 1300tons, NN = = 80 days, 80 days, SS = 10 euro, = 10 euro, HH = 25 euro/ton/year = 25 euro/ton/year

3.3. DD = 1000 units, = 1000 units, NN = 500 days, = 500 days, SS = 110 = 110 euro, euro, HH = 100 euro/unit/year, = 100 euro/unit/year, L L = 20 days, = 20 days, bb = 50tons = 50tons