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Materials Management

Operations ManagementSession 3

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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.

3

Topics

• How inventory comes about

• Decisions and Costs

• Economic Order Quantity (EOQ)

• Pareto principle of stock control

4

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

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Stock

Supply Rate Inventory Level

Rate of Demand

Stock Level

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Independent vs. Dependent Demand

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

e.g. Office StationaryDependent Demand

(derived from component parts, sub-assemblies,

raw materials, etc.)

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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

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Inventory Types

• Buffer Inventorycompensates for unexpected fluctuations in supply or demand

• Cycle Inventorybecause a stage in the process cannot supply all items simultaneously

• De-coupling Inventoryin a process layout WIP joins a queue

• Anticipation Inventorywhen demand fluctuations are large but predictable

• Pipeline Inventorywhen stock is allocated until it is available eg. In delivery

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Single & Multi-Stage Inventory Systems

Small Retail Shop

Television Manufacturer

Multi-Stage Inventory System

Single-Stage Inventory System

Stock

SalesOperation

Suppliers

Suppliers

InputStocks

Stage 1 Stage 2 Stage 3

Finished GoodsStockWIP

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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

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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.

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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

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Order Quantities & Re-order Points

R = Re-order pointL = Lead time

L

q

R

Time

No.

of

units

on

hand

Safety orbuffer level

Average Stock q/2Average Stock q/2

q

By having a lower buffer level and re-ordering more often inventory may be reduced

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EOQ Aim = Cost Minimisation C

ost

Ordering Costs

HoldingCosts

Qeoq Order Quantity (Q)

Total Cost

Holding + ordering costs = total cost curve

Find QEOQ inventory order point to minimise total costs

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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

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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

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Bin Systems

Two-Bin

Order when Bin 1 empty

One-Bin

Periodic CheckOrder enough torefill bin?

Bin 1Items being

used

Bin 2Re-order

Level

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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 Holding Cost =Order Quantity

2X Holding cost per unit per year

Q2 H=

X Order Cost per OrderAnnual Demand

Number of units in each orderDQ S=

Annual Order Cost =

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Calculate EOQ

Economic (optimal) order quantity is found when annual setup cost equals annual holding cost

DQ S

Q2 H=

Q2 = 2DSH

2DSHQEOQ =

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EOQ & ROP

QEOQ = 2DS

H =

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

ROP = DL D = Avg daily demand (constant) L = Lead time (constant)

When to place an order – finding Re-order Point (ROP)

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

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

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Solution

QEOQ = 2DS

H =

2(1,000 )(10)

2.50 = 89.443 units

or 90 units

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.

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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.

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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?

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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?

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ABC System of Inventory Control

% of total number of items

9080

100

Cu

mu

lati

ve %

of

Inve

nto

ry V

alu

eA

BC

20 50 100

Pareto – 20/80 Principle:-

• Class A Items20% of high usage value items account for 80% of total usage value

• Class B Itemsnext 30% accounts for around 10% of total usage value

• Class C Itemsabout 50% of total items stocked only account for 10% of usage value

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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

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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