# Inventory Analytics

# Inventory

Inventory is the raw material, component parks, or finished goods that are held at some location in the supply chain.

## Types of Inventory

- Raw materials (wood, steel, oil, ect)
- Component parts (bought from somewhere else)
- Finished goods (what you made)

## Inventory Management

- Balance and matching of supply and demand in supply chain.
- It’s important because inventories are a big company asset (big investment)

## Reason to Keep Inventory

- Protect against spikes in demand
- Protects against supply disruptions (can’t get stuff)
- Discount on high quantity order
- Good for uncertain conditions

## Reason to Not Have Inventory

- Inventory can become obsolete
- Things can spoil
- Opportunity costs (money not liquid)
- Holding costs
- insurance, security, spacing, warehouse costs

## Important Decisions

- HOW MUCH should we order?
- WHEN should we order more?

### How much should I order

Simple models start by assuming:

*D*: Demand is known and constant*S*: The ordering cost is known and fixed.- Instant replenishment
- No limit on order quality
*H*: Annual holding cost per unit*Q*: The limit to which we build back up*P*: Price per unit

This would mean *Q* units would be bought. They would be depleted linearly till 0, then a price *S* would be paid to order more back up to *Q* level. Hence the average inventory would be *Q/2*

EOQ - Economic Order Quantity - The Size

$TotalCost=OrderingCost+InventoryCost$

$OrderingCost=NumberOrdersPerYear \cdot CostPerOrder$

In this case, $OrderingCost=\frac{D}{Q}\cdot S$

$InventoryCost=AverageInventory \cdot HoldingCostPerYear$

In this case $HoldingCost=\frac{Q}{2}\cdot H$

To find the minimum and optimal total cost, it is when holding cost equals ordering costs. Could also set the derivative to 0.

This leads to:

$Q^{*} \sqrt{\frac{2SD}{H}}=EOQ$

Expected orders: $N=\frac{D}{Q^*}$

Expected time between orders: $T=\frac{NumberOfDaysPerYear}{N}$

## How Can We Account for a Quantity Discount?

$Expand Equation for Total Cost (ETC) = \frac{D}{Q}\cdot S + \frac{Q}{2}\cdot H + P\cdot D$

This will allow for discount in price/unit on large quantity orders. Discounts encourage to hold more inventory.

## At What Point do you reorder?

In real life, a instant replenishment time is unrealstic and impossible. Hence, there are lead times.

*L*: Lead time in days*d*: average daily demand

ROP = Reorder Point.

$ROP = d\cdot L$

But what if demand is not constant? How does ROP change?

Well we can model it with a probability distribution. Will add a buffer of extra inventory and call it our safety pile. This size will depend on demand uncertainty, the penalty of running out, lead time.

Use a normal curve for the probability of having enough stock.

The safety stock can be lead to be represented as

$Safety Stock = Safety Factor \cdot STD(Lead Time Demand)$

The safety factor is just the Z from the % you don’t want to be out of stock.

Instead of standard deviation of the lead time, is set to be

$STD(LeadTime) = Z\cdot \sigma_D \cdot \sqrt{LT}$

Hence we end up with $ROP = d\cdot L + SS$