Production and Operations Management: Inventory Management

Comprehensive practice questions covering inventory types, cost categories, demand classification, single-period and multi-period models, and specific calculation formulas for EOQ and safety stock.

How is inventory defined in an organization?

The stock of any item or resource used in an organization, including raw materials, finished products, component parts, supplies, and work-in-process.

What are the four main types of manufacturing inventory?

1. Items that contribute to or become part of a firm's product. 2. Replacement parts, tools, and supplies. 3. Goods-in-transit to warehouses or customers. 4. Work-in-process.

What are the five main purposes of inventory?

1. To maintain independence of operations. 2. To meet variation in product demand. 3. To allow flexibility in production scheduling. 4. To provide a safeguard for variation in raw material delivery time. 5. To take advantage of economic purchase order size.

What are the four categories of inventory costs?

1. Holding (or carrying) costs. 2. Setup costs. 3. Ordering costs. 4. Shortage costs.

According to the lecture, what is the estimated overall carrying cost as a percent of inventory value?

$$26\%$$

What are the three types of inventory models mentioned in the notes?

1. Single-period model. 2. Fixed-order quantity model. 3. Fixed-time period model.

What is the difference between independent demand and dependent demand?

Independent demand occurs when the demands for various items are unrelated to each other, while dependent demand occurs when the need for an item is a direct result of the need for some other (usually higher-level) item.

How are Multi-period inventory models categorized based on their triggers?

Fixed-order quantity models are event-triggered (e.g., running out of stock), while fixed-time period models are time-triggered (e.g., a monthly sales call).

In a single-period inventory model, what is the formula for the Service Level ($P$)?

$P \leq \frac{C_u}{C_o + C_u}$ where $C_o$ is the cost per unit of demand overstocking and $C_u$ is the cost per unit of demand understocking.

What is another name for the fixed-order quantity model?

Economic Order Quantity ($EOQ$) or Q-model.

What are the alternative names for the fixed-time period model?

Periodic system, periodic review system, fixed-order interval system, and P-model.

Compared to the fixed-time period model, what are two characteristics of the average inventory and item value in a fixed-order quantity model?

It has a smaller average inventory and favors more expensive items.

List the assumptions of the Fixed-Order Quantity (EOQ) model.

Demand is constant and uniform; Lead time is constant; Price per unit is constant; Holding cost is based on average inventory; Ordering/setup costs are constant; All demands will be satisfied.

What is the definition of safety stock?

The amount of inventory carried in addition to expected demand.

In the fixed-order quantity model with safety stock, how is the reorder point ($R$) calculated?

$R = \text{EDDLT} + SS$ where EDDLT is Expected Demand During Lead Time and SS is Safety Stock.

In a fixed-order quantity model with constant lead time ($L$), what is the formula for the standard deviation of demand during lead time ($\sigma_L$)?

$\sigma_L = \sqrt{L} \times \sigma_d$ where $\sigma_d$ is the daily demand standard deviation.

How is the safety stock ($SS$) explicitly calculated using the z-value?

$$SS = z \times \sigma_L$$

In a fixed-time period model, what is the formula for the quantity to be ordered ($q$)?

$q = \overline{d}(T + L) + z \sigma_{T+L} - I$ where $\overline{d}$ is forecast average daily demand, $T$ is days between reviews, $L$ is lead time, $z$ is the number of standard deviations, $\sigma_{T+L}$ is the standard deviation of demand over the review and lead time, and $I$ is current inventory level.

In a fixed-time period model, how is $\sigma_{T+L}$ calculated?

$$\sigma_{T+L} = \sqrt{T + L} \times \sigma_d$$