Materials Management
Operations Management
Session 3
1
Objectives
• By the end of this session, student will be
able to:
– Appreciate the need to make key inventory
decisions
– Understand and calculate the costs associated
with inventory
– Use the Economic Order Quantity System to
determine order volumes and frequencies
– Understand the relationship between inventory
control and customer service.
2
Topics
•
•
•
•
How inventory comes about
Decisions and Costs
Economic Order Quantity (EOQ)
Pareto principle of stock control
3
Definitions
• 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
4
Stock
Supply Rate
Inventory Level
Stock Level
Rate of Demand
5
Independent vs. Dependent Demand
Independent Demand (not related to
other items or final end-product)
e.g. Office Stationary
Dependent Demand
(derived from component
parts, sub-assemblies,
raw materials, etc.)
6
Why Does Inventory Arise?
•
•
•
•
Raw-materials bought at advantageous price
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
7
Inventory Types
• Buffer Inventory
compensates for unexpected fluctuations in supply or
demand
• Cycle Inventory
because a stage in the process cannot supply all
items simultaneously
• De-coupling Inventory
in a process layout WIP joins a queue
• Anticipation Inventory
when demand fluctuations are large but predictable
• Pipeline Inventory
when stock is allocated until it is available eg. In
delivery
8
Single & Multi-Stage Inventory Systems
Single-Stage Inventory System
Stock
Sales
Operation
Suppliers
Small Retail Shop
Multi-Stage Inventory System
Input
Stocks
Suppliers
Stage 1
Finished Goods
Stock
WIP
Stage 2
Stage 3
Television Manufacturer
9
Inventory Decisions
•
•
•
•
•
•
How much to order
When to order
How much it will cost
What the re-order level is
How much safety stock needed
How to control a large inventory system
10
The Volume Decision
• Simple Illustration – Food Shopping
– Do we hold little stock in the cupboards
and the refrigerator and shop frequently or
– Do we have a large refrigerator and larder
and buy in bulk
• What issues do we think about when
making the decision?
• Translate these into a business context.
11
Inventory Costs
• Ordering Costs
– Administrative costs of ordering
• Production Inefficiency Cost
– Inventory obscures operational problems
• Holding Costs
–
–
–
–
Working capital cost
Storage costs
Insurance
Deterioration and obsolescence
• Stock Out Costs
– Cost to the business of running out of stock
• Discounts for Bulk Purchase
12
Order Quantities & Re-order Points
No. of units on hand
Average Stock q/2
q
q
Safety or
buffer level
R
L
Time
R = Re-order point
L = Lead time
By having a lower buffer level and re-ordering more often inventory may be reduced
13
EOQ Aim = Cost Minimisation
Holding + ordering costs = total cost curve
Find QEOQ inventory order point to minimise total costs
Cost
Total Cost
Holding
Costs
Ordering Costs
Qeoq
Order Quantity (Q)
14
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
15
Safety Stock and Re-order Levels
• Reserve
–
–
–
–
Buffer
Cushion against uncertain demand (usage) & lead time
"2-bin" system
Use of JIT
• 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
16
Bin Systems
Two-Bin
Bin 1
Items being
used
Bin 2
Re-order
Level
Order when
Bin 1 empty
One-Bin
Periodic Check
Order enough to
refill bin?
17
Order Cost & Holding Cost
Q = number of pieces per order
QEOQ = Optimum number of pieces per order
D = annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual Demand
Annual Order Cost =
X Order Cost per Order
Number of units in each order
D
=
Q S
Annual Holding Cost =
Order Quantity
X Holding cost per unit per year
2
Q
=
2 H
18
Calculate EOQ
Economic (optimal) order quantity is found when annual setup cost equals
annual holding cost
Q
D
S = 2 H
Q
Q2 = 2DS
H
QEOQ =
2DS
H
19
EOQ & ROP
QEOQ=
2DS
=
H
2(Annual Demand)(Order or set-up cost)
Annual Holding Cost
When to place an order – finding Re-order Point (ROP)
ROP = DL
D = Avg daily demand (constant)
L = Lead time (constant)
Exercise – find EOQ and ROP:
•Annual demand = 1,000 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
20
Solution
QEOQ =
2DS
=
H
2(1,000 )(10)
2.50
= 89.443 units
or 90 units
1,000 units p.a.
D=
= 2.74 units/day
365 days p.a.
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.
21
EOQ and ROQ - Example 2
Annual Demand = 10,000 units
Days per year considered in average daily demand = 365
Cost to place an order = £10
Holding cost per unit per year = 10% of cost per unit
Lead time = 10 days
Cost per unit = £15
2DS
Q
=
eoq
H
2(10,000)(10)
=
1.50
D=
= 365.148 (366 units)
10,000 units/year
365 days
= 27.397 units/day
If lead time = 10 days, ROL= 273.97 = 274 units
Place order for 366 units. When 274 left, place next order for 366.
22
Exercise 1
• Each month a particular retailer sells
100 TV sets. The inventory holding cost
is £50 per TV per month. The ordering
cost is £100 and each TV set costs the
retailer £80.
– What is the EOQ?
– How many orders will be placed each
month?
– If the inventory cost is increased by £5 per
TV per month, what will be the change in
the EOQ?
23
Exercise 2
• A fishmonger with a market stall sells 5000kg
of fish each month. It costs £10 to have fresh
fish delivered, and each kg of fish ordered
costs the fishmonger £2. The cost of keeping
the fish is £1 per kg per month, which is
largely due to the cost of refrigeration. All fish
must be sold within a week of delivery or else
be discarded.
• What is the EOQ?
• How many orders will be placed each month?
24
Pareto –
20/80 Principle:• Class A Items
20% of high usage
value items account for
80% of total usage
value
• Class B Items
next 30% accounts for
around 10% of total
usage value
• Class C Items
about 50% of total items
stocked only account
for 10% of usage value
Cumulative % of Inventory Value
ABC System of Inventory Control
100
90
80
C
B
A
20
100
50
% of total number of items
25
Interpretation of ABC System
• Often interpreted as indicating that
managers should concentrate on
A Class Items since these produce most
revenue
• However, could also be interpreted as
indicating that managers should look
closely at C Class items since these tie
up most working capital
26
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
27