God, grant me the serenity to accept the things I cannot change, The courage to change the things I can, And the wisdom to know the difference. (Serenity Prayer, Reinhold Niebuhr)

Inventory Management

Inventory management is primarily about specifying the size and placement of stocked goods (Wikipedia).

There are three basic reasons for keeping inventory (Wikipedia):
  1. Time lags - lead time between each stage in the supply chain
  2. Uncertainty - uncertainty in demand, supply and movement
  3. Economies of scale

There are various types of inventory, which include (Wikipedia):

ABC Analysis

ABC Analysis provides a mechanism for identifying items that will have a significant impact on overall inventory cost and helps to identify different categories of stock that will require different management and controls (Wikipedia).

Related to Pareto analysis (80/20 rule) the A inventory items are the most important or items with the most capital tied up. These items are managed more carefully than the 'less important' or less costly items (B & C).Classification can be based on sales, profit contribution, inventory value, usage rate and item category (Bowersox, 2010).

Classification Procedure

  1. For each stock keeping unit (SKU) record its annual volume and unit cost
  2. Calculate the dollar volume for each SKU as volume * unit cost
  3. Sort the items in descending order of dollar volume
  4. Add up the total dollar volume for all items
  5. Calculate the percentage of each SKU toward the total dollar volume as: SKU dollar volume / total dollar volume
  6. Assign SKUs to the A category until the percentage of the total dollar volume assigned represents 80% of the total (usually 80%).
  7. Assign the next set of SKUs to the B category until the total dollar volume assigned represents 15% of the total (usually 15%).
  8. The remaining items represent the lowest 5% of the dollar volume, which are the C category items.

Inventory management of the category A items should utilize the latest in inventory management techniques and technologies since this represents the most important inventory. The category B items should also be well managed, but do not require the investment that the A items warrent. The C category items are slower moving and represent a small investment and can be managed using less onerous methods.

Cycle Counting

cycle count is an inventory auditing procedure where a small subset of inventory, in a specific location, is counted on a specified day (Wikipedia). For example, if the policy is to manually count the A cateogry items once per month (20 working days), the B items once per quarts (60 working days) and the C items once every six months (120 working days) you can calculate how many SKUs of each type should be counted each day as:

  1. Count the number of SKUs for category A, B and C
  2. Divide the number of SKUs for each category by the number of working days in the cycle count period for that category (see above). That gives you the number of SKUs of each category that should be counted each day.
  3. Assign that number of SKUs of each type to a manual count schedule. This smoothes out the manual counting across all working days.

Perpetual (Continuous Review, EOQ) Inventory Systems

A perpetual inventory or continuous inventory describes systems of inventory where information on inventory quantity and availability is updated on a continuous basis as a function of doing business. Generally this is accomplished by connecting the inventory system with order entry and in retail the point of sale system (Wikipedia). For continuous review systems, the economic order quantity is the most common method.

The economic order quantity is the order quantity that minimizes total inventory holding costs and ordering costs (Wikipedia).

Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs. It is one of the oldest classical production scheduling models (Wikipedia 2011).

The EOQ model is a continuous replenishment system, which means that inventory is checked upon every withdrawal to see if that withdrawal will cause the inventory level to fall below the restocking level. If so, an order is immediately place for the EOQ number of units. This is also known as a fixed order quantity model because the quantity ordered (EOQ) does not change unless the parameters of the model change.

Basic EOQ Model

Total Inventory Cost Formula

Total annual cost = annual purchase cost + annual ordering cost + annual holding cost

TC = DC + (D/Q)*S + (Q/2)*H, where:

Basic EOQ and Reorder Point Formula

Quantity to Order = EOQ = Square Root of ((2*D*S)/H)
Reorder Point = R = d * L

where,

EOQ Model with Demand Uncertainty

When demand varies and is not constant, which is the usual case in business, you must protect against stockouts by holding additional inventory. This additional inventory held to protect against variation is called safety stock. To protect against variation given demand uncertainty, the Reorder Point is increased for safety stock with the following formula:

Reorder Point = R = (d * L) + (z * σL), where

Using Microsoft Excel, the z-score of a given desired service level, p and the standard deviation of demand during the lead time (σL) is:

Reorder Point = R = (d * L) + (NORMSINV(p) * [SqRoot(L * σd^2)])

Quantity to Order = EOQ = Square Root of ((2*D*S)/H)

EOQ Model with Demand & Delivery Uncertainty

If you have both demand and delivery (lead time) uncertainty, you must use a convolution formula (Bowersox 2010) to calculate the safety stock level.

Standard Deviation of Combined Probabilities

σc = Square Root of [(L * σd^2) + (d^2 * σl^2)], where

Reorder Point = R = (d * L) + (NORMSINV(p) * σc)

Reorder Point = R = (d * L) + (NORMSINV(p) * Square Root of [(L * σd^2) + (d^2 * σl^2)])

Total Inventory Cost with Safety Stock

When you include safety stock in a model to accomodate variation, the amount of the average inventory on hand (Q/2) is incresaed by the amount of the safety stock. This new total average inventory is multiplied by the annual holding cost to obtain the total cost.

TC = DC + (D/Q)*S + [(Q/2)+SS]*H, where:

Echelon Inventory EOQ Models

If a supply chain is either owned by one firm or the supplier partnerships in the supply chain are such that information is immediately shared and all members of the chain operate as one, you can use an Echelon inventory model.

The echelon inventory at any stage of the system is equal to the inventory on hand at that echelon, plus all downstream inventory (Simechi-Levy 2008).

In the case of an echelon inventory system, the Reorder Point (R) uses the Echelon Lead Time (Le) instead of the standard lead time in its calculation. The Echelon Lead Time (Le) is the lead time between the entity doing its inventory calculation PLUS the lead times between all downstream supply chain partners. For example, for a distributor to a retailer, the echelon lead time (Le) is the lead time between the retailer and distributor PLUS the lead time between the distributor and their supplier. The average demand and standard deviations of demand are those of all the retail customers in this model, even when calculating reorder point for the distributor.

For systems with stable, constant lead times, use the following formula:

Reorder Point = R = (d * Le) + (NORMSINV(p) * [SqRoot(Le * σd^2)])

Periodic Inventory System

Periodic inventory is a system of inventory in which updates are made on a periodic basis (Wikipedia).

A periodic inventory review system is one where inventory is checked and reordered at a set time interval (e.g. weekly). In this case the quantity ordered varies based on the amount of inventory on hand following the review. The danger of this system is that inventory is not being checked until the review system. The benefit is that since inventory levels are only checked periodically, the administrative cost of the system can sometimes be less than with a fixed order quantity (EOQ) model.

The Order Quantity with Demand Uncertainty

The formula for calculating the quantity to order is:

Fixed Order Quantity = Q = d(T+L) + zσT+L – I, where

Single Period Inventory System

A single period inventory model is used to identify the amount of inventory to purchase given a perishable good or single opportunity to purchase.

A single period inventory model is used to identify the amount of inventory to purchase given a perishable good or single opportunity to purchase.

The amount of the single order is based on balancing the cost of over- and under-estimating demand. This is a very common problem in areas such as: When you know: You can calculate the safety stock needed to balance the costs of over- and under-estimating demand, by (assuming sales are normally distributed):

1. Calculate the probability of a unit will not be sold:

P <= Cu / (Co + Cu)

2. Find the point on our demand distribution that corresponds to the cumulative probability of a unit not being sold by finding the Z-score (using a table or by using the NORMSINV function in Excel).

Z-score = NORMSINV(P)

3. Calculate the amount of safety stock as:

Safety stock = ROUND(Z-score * σ)

References

Bowersox, Closs & Cooper, 2010. Supply Chain Logistics Management, 3rd Edition. McGraw-Hill, New YorkSimchi-Levi, Kaminsky, Simchi-Levi, 2008. Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies, 3rd Edition. McGraw-Hill, New York