Ops5

Chris Jarvis 1MG2066 MG2066

Managing Independent

Inventory


Overview

What is an inventory system and why hold stock?

Textbook prescriptions versus reality and variety?

Independent versus Dependent Demand

Inventory types, flows, costs

Re-order quantities, EOQ & calculations

Safety stocks & service levels

Review systems

Discounts and staged deliveries

JIT

ABC Analysis

Stock taking

Make or buy


What is an Inventory System?

Inventory

the stock of any item or resource used in an organization: raw materials, finished products, component parts, supplies and work-in-process.

An inventory system

policies and controls for monitoring levels of inventory Information system that records transactions and enables

analysis of stock requirements and levels/quantities, costs etc


Organisations, Roles, Methods and Systems?

What type of organisations use systematic inventory management methods? How are the methods manifested? How is inventory management linked to aggregrate planning, buying for MRP, JIT, retail buying, sales

systems, accounting practice? Who does it? buyers, store keepers, production planners, accountants? What manual & IT-based systems are involved? Stock cards, orders, delivery notes, GRNs, return advice notes,

inventory module in integrated accounting packages, stock checks and auditing. Are textbook methods really used? How, where? What is the clerical burden of inventory analysis and control?


E(1)

Independent vs. Dependent Demand

Independent Demand (not related to other items or final end-product)

Dependent Demand(derived from component parts, sub-assemblies, raw materials, etc.)


Independent versus Dependent Demand

Dependent demandWork in progressComponents and raw materials

Time

Dem

and/

usag

e

Independent demand- finished goods- spare parts

Time

Dem

and/

usag

e


Why hold stock?

Provide flexibility

minimum delay in supplying customers

a good range

Protect against uncertainties

Enable economic purchasing

Anticipate changes in demand or supply

Buffers to feed processes and enable efficient scheduling

Strategic stock holdings


Inventory Types

Raw-materials, components and sub-assemblies

Work-in-progress or in-transit

Finished-goods In the warehouse, awaiting shipment, in delivery vehicles,

in tanks, on shelves, in the stores

Strategic inventory

Scrap & re-work


Material-Flows ProcessF

rom

Su

pp

lier

sT

o C

usto

mer

Production Processes

Inventory in transit

Stores warehouse

Finishedgoods

WIP

WIP

Work inprocess


Stock : Input (Flow in), Storage (Holding) and Flow out (Usage)

Supply Rate

Inventory Level

Rate of Demand (Usage)

Stock Level


Costs of Inventory

Ordering costs purchase order & office, shipping and/or set up

Holding Costs tied up capital (item value), staff & equipment,

obsolescence, perishability, shrinkage, insurance & security, m2 - m3 (rent/lease), audit.

Cost of being out of stock, cancelling an order

Scrap and re-working

annual costs= holding cost factor %

average value of stockholding

e.g. 25% or 2p in £ per month of stock


Order Quantities & Reorder Points

R = Reorder pointL = Lead time

LL

q

R

Time

No. of unitson hand

safety orbuffer level

Average stock q/2Average stock q/2

q


Simple inventory system

Raise order for ROQ

<=ROL?

OutstandingOrder?

OrdersMRPCheck stock level

Yes

No

Receive/inspect. Accept into stockSend back?Part-delivery

Duenow?

No

NextCheck point

Yes

No

Yes


Bin systems

Two-Bin - quantity stock in bin 2 = re-order level

Full Empty Order one bin

One-Bin (periodic check)Order enough torefill bin?

ROQ Options

•Keep order costs to a minimum?

•Order one year's supply in one go? OR

•Hand-to-mouth, once per week?

ROQ Options

•Keep order costs to a minimum?

•Order one year's supply in one go? OR

•Hand-to-mouth, once per week?


EOQ Aim = Cost Minimisation

Cost

Ordering Costs

HoldingCosts

Qeoq Order Quantity (Q)

Total Cost

Holding + ordering costs = total cost curve.

Find Qeoq inventory order point to minimise total costs.


Calculate EOQ

Qeoq = 2DS

H =

2(Annual Demand)(Order or set-up cost) Annual Holding Cost

Reorder point R=DL D = Avg daily demand (constant) L = Lead time (constant)

when to place an order.

Exercise EOQ and reorder point?•Annual demand = 2,000 units•Days/year in average daily demand = 365•Cost to place an order = £10•Holding cost /unit p.a. = £2.50•Lead time = 7 days•Cost per unit = £15

Exercise EOQ and reorder point?•Annual demand = 2,000 units•Days/year in average daily demand = 365•Cost to place an order = £10•Holding cost /unit p.a. = £2.50•Lead time = 7 days•Cost per unit = £15


EOQ Solution

Q = 2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or 90 units eoq

d = 1,000 units p.a.

365 days p.a. = 2.74 units/day

Reorder point D L = 2.74 units/day = 19.18 or 20 for 7 day lead time

EOQ order = 90 units.

When only 20 units left, place next order for 90 units.


EOQ and ROQ example 2

Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = £10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = £15

Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = £10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = £15

365.148 (366 units)=1.50

2(10,000)(10)=H

2DS=Q

eoq

D =10,000 units/year

365 days= 27.397 units/day

If lead time = 10 days, ROL= 273.97 = 274 unitsPlace order for 366 units. When 274 left, place next order for 366.


Total variable cost

Demand2

x unit cost x Hc% + Oc

12002

x £3 x 25% = £450 + £10Once per year

= £460

1200/522

x £3 x 25% = £9 + £510Once per week

= £519 approx

Find point of minimum TVc

Avg.stockAvg.stock


EOQ Table – minimum TVc

Item £ 3 Holding cost % = 25%

No. of Quantity Order Average Holding Total

orders Ordered cost stock cost cost1 1200 10 600 450 4602 600 20 300 225 2453 400 30 200 150 1804 300 40 150 113 1536 200 60 100 75 1358 150 80 75 56 136

10 120 100 60 45 14512 100 120 50 38 158

Avg.stock x item £ x hc % Oc + Hc


Minimum point of Total Inventory Costs

EOQ =

minimum TVc point

Total variable costs

Total Hc

Total Oc

EOQ* Order Size (Q)

£ C

ost

s


EOQ Example

Cheapo Bags wants to calculate the EOQ for tapestry cloth used to produce hand bags.

Last year demand = 10,000 metres (constant rate).

Value per metre of tapestry = £6.40

Oc – each order = £250.

Hc = £1.20 per metre = 18.75%

What is the EOQ?2 x 10,000 x £250

= 2042 metres£6.40 x 18.75%


Economic Order Quantity (EOQ) Assumptions

Single product line

Demand rate: recurring, known, constant

Lead time: constant , known

No quantity discounts - stable unit cost

No stock-outs allowed

Items ordered/produced in a lot or batch

Batch received all at once

Holding cost is linear based on average stock level

Fixed order + set up cost


Order Point with Safety StockU

nit

s

Days

Safety Stock

Actual leadtime is 3 days!

(at day 21)

2200

2000

OrderPoint

400

200

0 18 21

Dip into safety stock


Safety Stock and Re-order Levels

Reserve - buffer - cushion against uncertain demand (usage) & lead time.

A basis for a "2-bin" system

Application to JIT?

EOQ assumes certain demand & lead time. If uncertain, then:

ROL =

Average usage in lead time + safety stock(Avg. lead time x Avg. daily usage)


How Much Safety Stock? Cost vs. safety level

Depends on:Uncertainty: demand & lead time

cost of

being out of stock

carrying inventory

increasingly better service

Service level policy

% confidence of not hitting a stock-out situation


Cost vs service level

£

Service level 70 80 90 100 %

Cost ofbetter and better service

Cost of poor service (out-of-stock)Loss of-part order-future order-customer goodwill-buying from non-regular sources

0


Normal Distribution of Demand over Lead Time

m = mean demandr = reorder points = safety stock

frequency

probability ofstock out

demand over lead time

service level probability

m s r


Service level protection

ROL = Average usage in lead time + Safety stock

(Avg. usage (day/week) x Avg. Lead time)

K x stdev demand x Avg. lead time

Confidence of % non –stock outK = 2 for 97.5 confidenceK = 3 for 99.87


ROL AND Service Level Example

ROL = Average usage in lead time + Safety stock

(Avg. usage … day/week x Avg. lead time)

K x stdev demand x Avg. lead time

ROL = (250 per week x 4 weeks) + ( 2 x 50 x (4) ) = 1000 + 200 =

1200

Stock falls to or below ROL & no order is outstanding? Place a new order for 1200. Service level @ 97.5% stock-out for 1 in 40 reorder situations.


Review Systems

Top-up with regular review Stock not to exceed upper limit (perishables, corrosives,

limited capacity) use with – regular review (continuous or periodic)

Continuous review relax “constant demand” assumption Continuous system to monitor “stock-on-hand”

Periodic review Apply EOQ (demand constant + “no stock-out”) orders must be placed at specified intervals. Use when multiple, items ordered from same supplier (joint-

replenishment) inexpensive items


Price discounts and staged deliveries

Quantity Discounts, buying frequency & Oc, Hc more storage space

different payment terms

if demand changes – surplus stock

Staged deliveries & EOQ? Extra delivery & handling cost?

Assumes constant order cost

Requires reliable deliveries & steady demand

JIT – collaborative supplier relationships

Affect on supplier (locate nearer customer?)


Price-Break Model

Holding cost per annum

2(Demand p.a.)(Order or Setup-cost) =

iC

2DS = QOPT

Assumptions similar to as EOQ model

i = % of unit cost as carrying costC = cost per unit

“C” varies for each price-break so apply the formula to each price-break cost value.


Price-Break Example

Brunel University can reduce ordering costs for photocopy paper by placing larger quantity orders. What is the optimal order quantity?

• e-mail order cost = £4• carrying cost % = 2%• Demand p.a. = 10,000 units?

Order Quantity(units) Price/unit(£)

0 to 2,499 £1.20

2,500 to 3,999 1.00

4,000 or more 0.98

Quantity pricebreaksQuantity pricebreaks

iC

2DS


Solution

= 1,826 units0.02(1.20)

= iC

2DS

D = 10,000 unitsOrder cost (S) = £4

Put data into formula for each price-break of “C”.

=2,000=

=2,0204)2(10,000)(

=

Carrying cost % (i) = 2%Cost per unit (C) = £1.20, £1.00, £0.98

Qopt 0 - 2499 Feasible2500-3999 and 4000+ Not feasible

Are Qopt values feasible for the price breaks?

2(10,000)(4)

0.02(1.00)

0.02(0.98)

2(10,000)(4)


U-shaped function

True Qopt values occur at the start of each price-break interval.The total annual cost function is a “u” shaped function

0 1826 2500 4000 Order Quantity

Total annual costs

Price-breaks


Price-Break Solution

iC 2

Q + S

Q

D + DC = TC

Now apply the Qopt values to total annual cost & identify the total cost for each price-break.

TC(0-2499)=(10000x1.20)+(10000/1826)x4+(1826/2)(0.02x1.20) = £12,043.82

TC(2500 -3999) = £10,041TC(4000+) = £9,949.20

Least cost Qopt = 4000


Just-in-Time

Accurate production & inventory information system Highly efficient purchasing Reliable suppliers Efficient inventory-handling system

approach to inventory management & control in which inventories are acquired & inserted in production at exact time when needed.

Requirement


ABC - 20/80 Principle and Inventory Control

Items not of equal importance:–£ invested & profit potential–Sales/usage volume–stock-out penalties

Control expensive items closely.

“A” items – review frequently

Review “B” & “C” items frequently.

0 15 45 100

Cumulative %

70

90

100

Cu

mu

lati

ve P

erce

nta

ge

of

Inve

nto

ry V

alu

eA

BC

Pareto - 20/80 PrincipleIdentify inventory items based on % of total £ value. “A” items top 20 %, “B” next 40 %, "C" the lower 20%.

Pareto - 20/80 PrincipleIdentify inventory items based on % of total £ value. “A” items top 20 %, “B” next 40 %, "C" the lower 20%.


Annual Usage by £ Value

Item Usage p.a.Unit Cost £ Usage

% of Total £ Usage

p3 4800 1.40 6720 1.3%t6 3400 8.00 26500 5.2%h8 950 112.00 106400 21.0%j23 4600 3.40 15640 3.1%f45 9200 0.85 7820 1.5%v33 6400 46.00 294400 58.1%m88 5200 0.90 4680 0.9%s32 6700 1.78 11926 2.4%tt6 7700 3.40 26180 5.2%b88 3250 2.10 6825 1.3%

Total £507,091 100.0%


ABC Chart

3 6 9 2 4 1 10 8 5 7

Item No.

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Per

cen

t U

sag

e

0%

20%

40%

60%

80%

100%

120%

Cu

mu

lati

ve %

Usa

ge

Cumulative %

A B C


Stock Check

Book stock vs physical stock

Stock valuation – wastage & shrinkage

Audit stock security systems

Organising the stock check

Internal & external audit Segmentation of duties

Date post:	20-Jan-2015
Category:	Education
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