Inventory Models

Primary purpose of inventory models

To minimize the costs associated with inventory while maintaining a certain level of inventories needed to sustain smooth operations.

Two main components of inventory costs

Ordering costs and carrying costs.

Behavior of carrying costs as order size increases

Carrying costs increase with order size or quantity of inventory on hand.

Examples of carrying costs

Storage costs, insurance on inventory, normal spoilage, and record keeping cost.

Behavior of ordering costs as order size increases

Ordering costs decrease with order size or quantity of inventory on hand.

Examples of ordering costs

Delivery costs, administrative costs inspection, purchasing and receiving, quantity discount lost, and handling costs.

Economic Order Quantity (EOQ)

The number of units that should be placed every order to economize on the sum of ordering costs and carrying costs.

Economic Order Quantity (EOQ) formula

EOQ = square root of ((2 * C * N) / K)

Variable C in the EOQ formula

Cost per order.

Variable N in the EOQ formula

Annual demand in units.

Variable K in the EOQ formula

Carrying cost per unit.

Total Costs formula at EOQ

Total Costs = (EOQ * K / 2) + (N * C / EOQ)

Average inventory formula when there is no safety stock

EOQ / 2

Average inventory formula when there is safety stock

(EOQ / 2) + safety stock

Average inventory formula if EOQ is not available

(Beginning inventory + Ending inventory) / 2

Step 1 in using the EOQ formula

Calculate demand by determining the annual demand for the product (units per year).

Step 2 in using the EOQ formula

Estimate ordering cost by finding out the cost of placing and receiving an order.

Step 3 in using the EOQ formula

Estimate holding cost by estimating the cost of holding one unit of inventory for a year.

Step 4 in using the EOQ formula

Apply the EOQ formula by plugging the values into the formula to find the optimal order quantity.

Order (Reorder) Point

The inventory level (in units) that automatically calls for placing a new order.

Objective of determining when to reorder

To order at a point in time so as not to run out of stock before receiving inventory, but not so early that unnecessary safety stock is kept.

Two situations where a stock-out can occur when an order point is computed

1. Demand is greater than expected during lead time, or 2. The order time exceeds the anticipated lead time.

Lead Time

The period from the time an order is placed until such time the order is received.

Normal (Average) Lead Time

The usual delay in the receipt of ordered goods.

Maximum Lead Time

The normal lead time plus a reasonable allowance for further delay.

Normal Lead Time Usage formula

Normal lead time * average usage

Safety Stock formula

(Maximum lead time - Normal lead time) * average usage

Reorder Point formula without safety stock

Normal lead time usage

Reorder Point formula with safety stock

Normal lead time usage + safety stock (or maximum lead time * average usage)

Economic Lot Size (ELS)

The term used for the EOQ formula when it is applied to production operations.

Economic Lot Size (ELS) formula

ELS = square root of ((2 * C * N) / K)

Variable C in the ELS formula

Set-up cost.

Variable N in the ELS formula

Annual production requirement.

Variable K in the ELS formula

Carrying cost per unit.

Trade-off behavior of ordering costs as order quantity increases

The number of orders placed in a year decreases, reducing total ordering costs.

Trade-off behavior of holding costs as order quantity increases

The average inventory on hand increases, raising total holding costs.

EOQ cost minimization point

The specific point where the sum of ordering and holding costs is minimized.

Total Inventory Cost (TIC) algebraic equation

TIC = (D * S / Q) + (Q * H / 2)

Optimal value represented by Q in the TIC equation

The Economic Order Quantity (EOQ).

Constant demand:

Demand is steady and known, and no fluctuations in customer demand are considered.

Fixed ordering cost:

The cost to place an order is constant, regardless of the number of items ordered.

Constant holding cost:

The cost of holding inventory does not change with time or quantity.

Instantaneous replenishment:

As soon as an order is placed, the items arrive immediately with no lead time.

No stockouts:

It assumes that there will be no stockouts or shortages; inventory is replenished before running out.

Single product:

The EOQ model is typically used for one product at a time.

Demand Variability:

The EOQ formula assumes constant demand, which may not always be the case in the real world where demand fluctuates.

No Lead Time Consideration:

EOQ assumes instantaneous replenishment, which isn't realistic when there is lead time in the supply chain.

Single Product Focus:

The formula typically applies to one product at a time and doesn't address multi-product inventory systems.

Fixed Costs Assumption:

It assumes that ordering and holding costs are constant, but in practice, they can vary over time.