Lecture 5 & 6 - Inventory Management Flashcards
Define inventory
stock of any item or resource used in an organisation
(e.g. raw materials, components WIP, finished goods)
Define an inventory system
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
Key characteristics in inventory modelling
- demand
- lead time
*replenishment
โ> uniform or in batches
- review
โ> continuous or periodical (know inventory all the time or at discrete points)
*excess demand
*changing inventory
- single vs multiple items being sold
two different types of lead time
- external order
- time between placement of an order until arrival of goods
*internal production
- amount of time required to produce a batch of items
two different types of demand in inventory management
*constant (deterministic)
- random (stochastic)
REVISION QUESTION: Different types of costs in inventory modelling
- handling
- storage
- transportation
- obselence
- insurance
- opportunity cost
- production
- fixed cost
- variable cost
- penalty costs
(cost associated with stockouts)
flashcard below
Two types of service level in inventory modelling
*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
Relationship between penalty costs and service level
*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)
examples of penalty costs
- loss of sales
- loss of goodwill (value of brand)
- backordering costs if canโt fulfil orders
Define order cycle
time between two replenishments
Type 1 and Type 2 service example calculation
*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
โ> depends on firm
Two basic questions in inventory policies
Provide 2 typical answers
Q1 : When should we order from supplier / produce our own supplies?
- when inventory drops to R (re-order point) aka โsโ
- 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)
Two types of inventory review and what the another name for these models (in letters)
- Continuous review
(R, Q) and (s, S) - Periodic Review
(T, Q) and (T, S)
MAIN FOCUS: Explain the (R, Q) model
- 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
difference between inventory position and stock on hand
inventory position = stock on hand + ordered stock in transit - back orders
whereas, stock on hand = inventory at warehouse
Explain the s, S model
*continuous review
- when inventory position reaches s order an amount that brings inventory to target level, S
Explain the (T, Q) model
- periodic review
- beginning of review period T, order Q units
- Q units arrive in stock after lead time
Explain the (T, S) model
- periodic review
- beginning of review period, T, order an amount to bring inventory position to target level, S
symbol for lead time
๐
Define ABC analysis
classification method used in inventory management to categorise items based on their revenue contribution
- can distinguish between important and less important items
โ> may implement more control and sophisticated models for the more important inventory
What is akaโฆ and why
- 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
Describe ABC analysis
- 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
What are the two deterministic models for order quantity
- Economic Order Quantity (EOQ model)
- Production Order Quantity (POQ model)
Assumptions of the EOQ
- demand is high, constant and known
*zero lead time
*assume no shortages
Notation in EOQ model
๐ณ๐ถ๐ ๐ฒ๐ฑ ๐ฐ๐ผ๐๐ per order = K
๐๐ฎ๐ฟ๐ถ๐ฎ๐ฏ๐น๐ฒ ๐ฐ๐ผ๐๐ per unit ordered: c
๐ต๐ผ๐น๐ฑ๐ถ๐ป๐ด ๐ฐ๐ผ๐๐ per unit held per unit of time: h
๐๐ฎ๐น๐๐ฒ ๐ผ๐ณ ๐ถ๐๐ฒ๐บ: c
๐ฑ๐ฒ๐บ๐ฎ๐ป๐ฑ per unit per unit of time: ฮป
What does the EOQ model show
Deterministic inventory control method that determines:
- the ๐ผ๐ฝ๐๐ถ๐บ๐ฎ๐น ๐ผ๐ฟ๐ฑ๐ฒ๐ฟ ๐พ๐๐ฎ๐ป๐๐ถ๐๐ that minimises total inventory holding and ordering costs
Cost function notation
G (x)
for re-order quantity level: G(Q)
When including order lead time,๐, what is the reorder point calculation
Reorder point = ฮป x ๐
is the same as the demand during the lead time
What is POQ
*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
Assumptions of POQ
- finite and constant production rate: (P units / time)
*demand rate is high, constant and known (ฮป units / time)
- production of machine (P) is > demand (ฮป)
- assume no shortages
Notation in EOQ model
๐ฝ๐ฟ๐ผ๐ฑ๐๐ฐ๐๐ถ๐ผ๐ป ๐ฟ๐ฎ๐๐ฒ = P
๐ณ๐ถ๐ ๐ฒ๐ฑ ๐ฐ๐ผ๐๐ per order = K
๐๐ฎ๐ฟ๐ถ๐ฎ๐ฏ๐น๐ฒ ๐ฐ๐ผ๐๐ per unit ordered: c
๐ต๐ผ๐น๐ฑ๐ถ๐ป๐ด ๐ฐ๐ผ๐๐ per unit held per unit of time: h
๐๐ฎ๐น๐๐ฒ ๐ผ๐ณ ๐ถ๐๐ฒ๐บ: c
๐ฑ๐ฒ๐บ๐ฎ๐ป๐ฑ per unit per unit of time: ฮป
Time is split into two sections, in the POQ model
T1 = uptime (machine is producing)
T2 = downtime (machine isnโt producing)
What is the stochastic inventory control model called
(R, Q) model
Explain the (R, Q) model
*works best with fast moving items (lot of demand transactions during the lead time)
Two parameters
*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
How does the (R, Q) model address the limitations of deterministic models (like EOQ and POQ)
incorporating a reorder point (R) and an order quantity (Q) to manage inventory levels in the face of uncertain demand.
Assumptions in the (R, Q) model
- continuous review of inventory
*demand is stochastic but also stationary โ> 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
How to calculate R and Q model
- Find order quantity
- use the EOQ formula - Find re-order point, R
R = expected demand during lead time (ฮป x ๐) + safety stock (SS)
Define safety stock
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
What impacts the amount of safety stock a company should hold?
- 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
โ> type 1: - probability of not stocking-out during the lead time of an order cycle
type 2 : proportion of demand met immediately with stock
โ> if high, will need more safety stock to prevent stockout
โ> higher type 1 requires higher safety stock
- reliability of supplier
*substitutability of product
โ> may be comfortable with low stock
How to calculate safety stock, for type 1 service level
SS = zฯ
F(z) = ฯ
- find z from cumulative distribution
What does z mean, in type 1 service level
z = safety stock factor
(higher z results in higher SS and so higher service)
How to calculate safety stock, for type 2 service level
SS = zฯ
n (R) = expected no. of units short per order cycle
n (R) = (1 - ฮฒ) x Q
n (R) = ฯ x L(z)
therefore
n(R)
โโ- = L(z)
ฯ
find z from partial expectation
Therefore,
re order level = (ฮป x ๐) + SS
reorder level =
(ฮป x ๐) + SS
important formulas to remember for calculating SS for type 2 service level
n (R) = (1 - ฮฒ) x Q
find n(R) and sub into:
n(R)
โโ- = L(z)
ฯ
