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Chris Jarvis 1MG2066 MG2066
Managing Independent
Inventory
Chris Jarvis 2MG2066 MG2066
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
Chris Jarvis 3MG2066 MG2066
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
Chris Jarvis 4MG2066 MG2066
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?
Chris Jarvis 5MG2066 MG2066
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.)
Chris Jarvis 6MG2066 MG2066
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
Chris Jarvis 7MG2066 MG2066
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
Chris Jarvis 8MG2066 MG2066
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
Chris Jarvis 9MG2066 MG2066
Material-Flows ProcessF
rom
Su
pp
lier
sT
o C
usto
mer
Production Processes
Inventory in transit
Stores warehouse
Finishedgoods
WIP
WIP
Work inprocess
Chris Jarvis 10MG2066 MG2066
Stock : Input (Flow in), Storage (Holding) and Flow out (Usage)
Supply Rate
Inventory Level
Rate of Demand (Usage)
Stock Level
Chris Jarvis 11MG2066 MG2066
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
Chris Jarvis 12MG2066 MG2066
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
Chris Jarvis 13MG2066 MG2066
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
Chris Jarvis 14MG2066 MG2066
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?
Chris Jarvis 15MG2066 MG2066
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.
Chris Jarvis 16MG2066 MG2066
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
Chris Jarvis 17MG2066 MG2066
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.
Chris Jarvis 18MG2066 MG2066
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.
Chris Jarvis 19MG2066 MG2066
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
Chris Jarvis 20MG2066 MG2066
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
Chris Jarvis 21MG2066 MG2066
Minimum point of Total Inventory Costs
EOQ =
minimum TVc point
Total variable costs
Total Hc
Total Oc
EOQ* Order Size (Q)
£ C
ost
s
Chris Jarvis 22MG2066 MG2066
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%
Chris Jarvis 23MG2066 MG2066
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
Chris Jarvis 24MG2066 MG2066
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
Chris Jarvis 25MG2066 MG2066
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)
Chris Jarvis 26MG2066 MG2066
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
Chris Jarvis 27MG2066 MG2066
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
Chris Jarvis 28MG2066 MG2066
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
Chris Jarvis 29MG2066 MG2066
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
Chris Jarvis 30MG2066 MG2066
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.
Chris Jarvis 31MG2066 MG2066
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
Chris Jarvis 32MG2066 MG2066
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?)
Chris Jarvis 33MG2066 MG2066
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.
Chris Jarvis 34MG2066 MG2066
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
Chris Jarvis 35MG2066 MG2066
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)
Chris Jarvis 36MG2066 MG2066
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
Chris Jarvis 37MG2066 MG2066
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
Chris Jarvis 38MG2066 MG2066
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
Chris Jarvis 39MG2066 MG2066
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%.
Chris Jarvis 40MG2066 MG2066
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%
Chris Jarvis 41MG2066 MG2066
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
Chris Jarvis 42MG2066 MG2066
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