### Module 10.02 Key Concepts: Order Quantities – How Much to Order?

Inventory is generally classified in two ways – Independent Demand Items and Dependent Demand Items.

- Independent demand – the demand for item is independent of the demand for any other item in inventory
- Dependent demand – the demand for item is dependent upon the demand for some other item in the inventory

In general, Independent Demand is forecast and Dependent Demand is calculated (with Material Requirements Planning).

As mentioned earlier, “Inventory is Money (tied up) and there is a significant cost of carrying it in stock. In addition, there are costs affiliated with Ordering (purchased products) and Set-Up (manufactured products). These costs are typically balanced vs. Inventory Holding Costs when considering different options for quantity to order and timing of ordering.

- Holding costs – the costs of holding or “carrying” inventory over time. Typical components of Holding Cost are shown in the table below. Holding costs vary considerably depending on the business, location, and interest rates. Generally greater than 15%, some high tech and fashion items have holding costs greater than 40%.
- Ordering costs – the costs of placing an order and receiving goods
- Setup costs – cost to prepare a machine or process for manufacturing an order. This may be highly correlated with setup time.

Supply Chain Management functions must have processes in place to determine when to order and how much to order. The text authors focus on three approaches: Economic Order Quantity , Production Order Quantity and Quantity Discount Model for establishing “how much to order”. These will be described shortly.

There are other ways to express Lot Sizing choices that will become relevant when we get to the Module on Material Requirements Planning.

- Lot for Lot;
- Fixed Order Quantity;
- Economic Order Quantity (EOQ); and
- Period Order Quantity.

With **Lot-for-Lot **order quantity, only the required amount is ordered to support Net Requirements. Therefore order quantities change as requirements change. No unused lot-size inventory is created, so that inventory-carrying costs are minimized. Lot-for-Lot is applicable for both dependent and independent demand items. It is especially used for expensive components, perishable items and in a lean or Just-in-Time (JIT) environment.

With **Fixed-order** quantity, a specific amount is ordered each time an order

is placed. Fixed-order quantity is quick and simple, and Is often made on the basis of what seems reasonable. For example, certain suppliers may have specific requirements for packaging or may offer quantity discounts for certain lot sizes. Batch production systems may limit quantities to a specific lot size due to equipment restrictions. Fixed-order quantity typically leads to inventory buildup and may not always produce the best results.

Sometimes it is beneficial to order a certain number of Periods of supply (for example, 2 weeks, 4 weeks, etc.). In this case, the order quantity is set as the required amount to satisfy demand for the specified number of periods. If demand is predictable, no unused lot-size inventory is created. This technique is typically used for both dependent and independent demand items – especially inexpensive, slow-moving components. **Periodic Order Quantity** (POQ) is a special adaptation that uses the Economic Order Quantity (EOQ) formula to compute time between orders.

**Economic Order Quantity** (EOQ) is a simple, widely used technique that has applicability to lot-size determination. The intent is to minimize the combined cost of acquiring and carrying inventory. For Economic Order Quantity to be calculated and provide a meaningful value, demand should be constant and uniform. It may require adjustment when demand is lumpy. In addition, the ordering cost (per order) and inventory carrying cost must be available for use in the formula. While Economic Order Quantity can be determined empirically, it is easily calculated using the equation shown in the text. To summarize some other assumptions:

- Demand is known, constant, and independent
- Lead time is known and constant
- Receipt of inventory is instantaneous and complete
- Quantity discounts are not possible
- Only variable costs are setup (or ordering) and holding
- Stockouts can be completely avoided

The Economic Order Quantity approach provides information on how much to order – not when to order. So, the order quantity will be constant but the ordering period will vary based on demand and inventory levels. We will explore ordering frequency in a following section.

This equation for calculating Economic Order Quantity is derived from the relationship between ordering cost and inventory carrying cost shown in the following slide. The Economic Order Quantity is the point where “Total Cost of Ordering” equals the “Total Cost of Carrying Inventory”.

So, by minimizing the sum of setup (or ordering) and holding costs, total costs are minimized. Optimal order size Q* will minimize total cost. A reduction in either cost reduces the total cost. As noted above, the optimal order quantity occurs when holding cost and setup cost are equal.

By combining these equations (setting the equation for Ordering Cost = the equation for Holding Cost and combining variables we can derive the final equation for Economic Order Quantity (EOQ).

Examples of the use of the EOQ approach are shown below for calculating different aspects. Each component is determined by mathematical manipulation of the core equation.

The text brings in two more involved processes that we are not going to review here: The Production Quantity Method and the Quantity Discount Method. Feel free to explore the text reading and examples for these if you like.