Lecture 5 & 6 - Inventory Management

Question 1

Define inventory

Answer 1

stock of any item or resource used in an organisation

(e.g. raw materials, components WIP, finished goods)

Question 2

Define an inventory system

Answer 2

set of policies and controls that:
- monitors levels of inventory
- determines when stock needs to be replenished, the size of orders, and what level stock should be maintained at

Question 3

Key characteristics in inventory modelling

Answer 3

• demand
• lead time

*replenishment
–> uniform or in batches

• review
  –> continuous or periodical (know inventory all the time or at discrete points)

*excess demand

*changing inventory

• single vs multiple items being sold

Question 4

two different types of lead time

Answer 4

• external order
• time between placement of an order until arrival of goods

*internal production
- amount of time required to produce a batch of items

Question 5

two different types of demand in inventory management

Answer 5

*constant (deterministic)

• random (stochastic)

Question 6

REVISION QUESTION: Different types of costs in inventory modelling

Answer 6

• handling
• storage
• transportation
• obselence
• insurance
• opportunity cost
• production
• fixed cost
• variable cost
• penalty costs
  (cost associated with stockouts)
  flashcard below

Question 7

Two types of service level in inventory modelling

Answer 7

*Type 1 service
- probability of not stocking-out during the lead time of an order cycle
- represented by alpha

*Type 2 service (fill rate)
- proportion of demand that can be immediately met from stock
- represented by beta

Question 8

Relationship between penalty costs and service level

Answer 8

*Service level is a target for inventory (desired probability of fulfilling customer demand without stock-outs)

• Failing to meet target service level incurs penalty costs (tangible and intangible consequences)

Question 9

examples of penalty costs

Answer 9

• loss of sales
• loss of goodwill (value of brand)
• backordering costs if can’t fulfil orders

Question 10

Define order cycle

Answer 10

time between two replenishments

Question 11

Type 1 and Type 2 service example calculation

Answer 11

*Fraction of order cycles with no stock-out = 8/10 = 80%
Type 1 service = 80%

*Total demand - stock outs
= 1450 - 55 = 1395
1395/1450 = 96%

*Higher Type 1 service level is stronger service than a higher Type 2 though
–> depends on firm

Question 12

Two basic questions in inventory policies

Provide 2 typical answers

Answer 12

Q1 : When should we order from supplier / produce our own supplies?
- when inventory drops to R (re-order point) aka ‘s’
- or every time T units (e.g. weekly)

Q2 : How much?
- order fixed amount (Q)
- order so that inventory position is at target level (S)

Question 13

Two types of inventory review and what the another name for these models (in letters)

Answer 13

• Continuous review
  (R, Q) and (s, S)
• Periodic Review
  (T, Q) and (T, S)

Question 14

MAIN FOCUS: Explain the (R, Q) model

Answer 14

• continuous review

order Q units when inventory level reaches R

Order Q units arrive in stock after lead time

black line = stock on hand
green dotted line = inventory position

Question 15

difference between inventory position and stock on hand

Answer 15

inventory position = stock on hand + ordered stock in transit - back orders

whereas, stock on hand = inventory at warehouse

Question 16

Explain the s, S model

Answer 16

*continuous review

• when inventory position reaches s order an amount that brings inventory to target level, S

Question 17

Explain the (T, Q) model

Answer 17

• periodic review
• beginning of review period T, order Q units
• Q units arrive in stock after lead time

Question 18

Explain the (T, S) model

Answer 18

• periodic review
• beginning of review period, T, order an amount to bring inventory position to target level, S

Question 19

symbol for lead time

Answer 19

𝜏

Question 20

Define ABC analysis

Answer 20

classification method used in inventory management to categorise items based on their revenue contribution

• can distinguish between important and less important items
  –> may implement more control and sophisticated models for the more important inventory

Question 21

What is aka… and why

Answer 21

• Pareto analysis

because, the Pareto effect is the idea that a large portion of wealth in the 19th century was owned by a small segment of population

Question 22

Describe ABC analysis

Answer 22

• Groups inventory items into three categories: A, B, and C
• A items
• high-value items that represent a small % of total items but contribute to a significant % of total revenue.
• e.g. 20% of items, 80% of revenue
• B items
• a larger portion of total items but contribute to less % of sales revenue
• e.g. 30% of items, 15% of revenue
• C items
• majority of total items but small % of sales revenue
• e.g. 50% of items, 5% of revenue

Question 23

What are the two deterministic models for order quantity

Answer 23

• Economic Order Quantity (EOQ model)
• Production Order Quantity (POQ model)

Question 24

Assumptions of the EOQ

Answer 24

• demand is high, constant and known

*zero lead time

*assume no shortages

Question 25

Notation in EOQ model

Answer 25

𝗳𝗶𝘅𝗲𝗱 𝗰𝗼𝘀𝘁 per order = K

𝘃𝗮𝗿𝗶𝗮𝗯𝗹𝗲 𝗰𝗼𝘀𝘁 per unit ordered: c

𝗵𝗼𝗹𝗱𝗶𝗻𝗴 𝗰𝗼𝘀𝘁 per unit held per unit of time: h

𝘃𝗮𝗹𝘂𝗲 𝗼𝗳 𝗶𝘁𝗲𝗺: c

𝗱𝗲𝗺𝗮𝗻𝗱 per unit per unit of time: λ

Question 26

What does the EOQ model show

Answer 26

Deterministic inventory control method that determines:

• the 𝗼𝗽𝘁𝗶𝗺𝗮𝗹 𝗼𝗿𝗱𝗲𝗿 𝗾𝘂𝗮𝗻𝘁𝗶𝘁𝘆 that minimises total inventory holding and ordering costs

Question 27

Cost function notation

Answer 27

G (x)

for re-order quantity level: G(Q)

Question 28

When including order lead time,𝜏, what is the reorder point calculation

Answer 28

Reorder point = λ x 𝜏

is the same as the demand during the lead time

Question 29

What is POQ

Answer 29

*Production Order Quantity

• an extension of the EOQ model that considers the production environment, where items are produced on a machine with finite production rate P
• determines the optimal production quantity that minimises inventory holding and production setup costs per unit time

Question 30

Assumptions of POQ

Answer 30

• finite and constant production rate: (P units / time)

*demand rate is high, constant and known (λ units / time)

• production of machine (P) is > demand (λ)
• assume no shortages

Question 31

Notation in EOQ model

Answer 31

𝗽𝗿𝗼𝗱𝘂𝗰𝘁𝗶𝗼𝗻 𝗿𝗮𝘁𝗲 = P

𝗳𝗶𝘅𝗲𝗱 𝗰𝗼𝘀𝘁 per order = K

𝘃𝗮𝗿𝗶𝗮𝗯𝗹𝗲 𝗰𝗼𝘀𝘁 per unit ordered: c

𝗵𝗼𝗹𝗱𝗶𝗻𝗴 𝗰𝗼𝘀𝘁 per unit held per unit of time: h

𝘃𝗮𝗹𝘂𝗲 𝗼𝗳 𝗶𝘁𝗲𝗺: c

𝗱𝗲𝗺𝗮𝗻𝗱 per unit per unit of time: λ

Question 32

Time is split into two sections, in the POQ model

Answer 32

T1 = uptime (machine is producing)

T2 = downtime (machine isn’t producing)

Question 33

What is the stochastic inventory control model called

Answer 33

(R, Q) model

Question 34

Explain the (R, Q) model

Answer 34

*works best with fast moving items (lot of demand transactions during the lead time)

Question 35

Two parameters

Answer 35

*re-order point (R)
- inventory falls below R, an order for Q units is placed
- acts as a buffer to prevent stockouts

• order quantity (Q)
• fixed quantity of inventory ordered each time re-order point is reached
• considers trade-off between ordering costs and holding costs

Question 35

How does the (R, Q) model address the limitations of deterministic models (like EOQ and POQ)

Answer 35

incorporating a reorder point (R) and an order quantity (Q) to manage inventory levels in the face of uncertain demand.

Question 36

Assumptions in the (R, Q) model

Answer 36

• continuous review of inventory

*demand is stochastic but also stationary –> can forecast expected demand rate

*constant lead time

• demand during lead time is normally distributed

*stock-outs can only occur during replen lead time (use probability distribution for the demand to find likelihood of stockouts

Question 37

How to calculate R and Q model

Answer 37

1. Find order quantity
   - use the EOQ formula
2. Find re-order point, R
   R = expected demand during lead time (λ x 𝜏) + safety stock (SS)

Question 38

Define safety stock

Answer 38

refers to extra quantity of inventory intentionally held, in addition to the expected demand during a lead time, that:

• acts as a buffer against uncertainties in supply and demand
• reduces risk of stock-outs

Question 39

What impacts the amount of safety stock a company should hold?

Answer 39

• variability in demand (seasonal or sudden spikes)

*lead time
- longer lead time = more chance of demand fluctuations or delays during lead time
- variability of lead time

*holding cost

*type and desired level of service
–> type 1: - probability of not stocking-out during the lead time of an order cycle
type 2 : proportion of demand met immediately with stock
–> if high, will need more safety stock to prevent stockout
–> higher type 1 requires higher safety stock

• reliability of supplier

*substitutability of product
–> may be comfortable with low stock

Question 40

How to calculate safety stock, for type 1 service level

Answer 40

SS = zσ

F(z) = σ

• find z from cumulative distribution

Question 41

What does z mean, in type 1 service level

Answer 41

z = safety stock factor

(higher z results in higher SS and so higher service)

Question 42

How to calculate safety stock, for type 2 service level

Answer 42

SS = zσ

n (R) = expected no. of units short per order cycle

n (R) = (1 - β) x Q

n (R) = σ x L(z)

therefore
n(R)
——- = L(z)
σ

find z from partial expectation

Therefore,

re order level = (λ x 𝜏) + SS

Question 43

reorder level =

Answer 43

(λ x 𝜏) + SS

Question 44

important formulas to remember for calculating SS for type 2 service level

Answer 44

n (R) = (1 - β) x Q

find n(R) and sub into:

n(R)
——- = L(z)
σ