# Inventory Management: Cost and Optimization

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## 30 Questions

### What is the relationship between the Safety Stock and the Probability of a Stockout?

As Safety Stock increases, the Probability of a Stockout decreases

1.96

ROP = μ + ZσdLT

550 units

40 units

95 percent

66 units

616 units

### What is the purpose of calculating the safety stock?

To minimize the probability of stockout

40 units

### What is the primary purpose of calculating the statistical reorder point?

To determine the lowest inventory level at which a new order should be placed.

That the lead time is constant.

x - μ = ZσdLT

### What does the probability (1 - α) represent?

The probability that inventory is sufficient to cover demand.

### What is the purpose of the reorder point?

To avoid stockouts by ensuring that a new order is placed at the right time.

### What is the role of the service level in inventory management?

It determines the desired probability of having sufficient inventory to meet demand.

### What is the relationship between the standard deviation of demand during lead time and safety stock?

The standard deviation affects the calculation of safety stock.

ROP = μ + ZσdLT

### What are the two primary models for calculating the statistical reorder point?

Model 1: ROP with probabilistic demand and constant lead time, and Model 2: ROP with constant demand and probabilistic lead time.

Z-value

stockout

Z-value

550

616

5

99

reorder

## Study Notes

### Inventory Management: Cost and Optimization

• Inventory Turnover Ratio: measures the number of times inventory is sold and replaced within a period
• Average Inventory at Cost: calculates the average cost of inventory held during a period

### Inventory Costs

• Ordering Costs:
• Refers to transaction costs associated with replenishing inventories
• Includes order preparation, transmission, and receiving costs
• Holding (Carrying) Costs:
• Incurred for holding inventory in storage
• Includes opportunity costs, storage and warehouse management, taxes, insurance, obsolescence, spoilage, and shrinkage
• Stockout Costs:
• Refers to the costs incurred when a company does not have inventory available to meet demand
• Includes lost sales, opportunity costs, and potential loss of future sales and profits

### Total Annual Inventory Cost (TAIC)

• TAIC Formula: TAIC = Annual Purchase Cost + Annual Holding Cost + Annual Order Cost
• Annual Purchase Cost: calculates the total cost of purchasing inventory
• Annual Holding Cost: calculates the total cost of holding inventory
• Annual Order Cost: calculates the total cost of ordering inventory

### Economic Order Quantity (EOQ)

• EOQ Formula: EOQ = √(2 * R * S) / (k * C)
• EOQ Cost Trade-Offs: balances the trade-off between annual holding costs and annual order costs
• EOQ Exercise: calculates the optimal order quantity for a company with a steady demand rate, instantaneous replenishment, and known lead time

### Quantity Discount Model

• Quantity Discount Model: considers the trade-off between larger quantities and price discounts vs. higher inventory holding costs
• Price Break Model: computes the total annual inventory cost for each price level to find the optimal order quantity
• Two-Step Procedure: computes the EOQ for each price level and finds the feasible EOQ or price break point

### Reorder Point (ROP) and Probabilistic Demand

• ROP Formula: ROP = μ + ZσdLT
• Z-Value: determines the safety stock and statistical reorder point for a desired service level
• Statistical Reorder Point (ROP): calculates the reorder point based on the average demand during lead time and desired safety stock

### Concept of Inventory Management

• Inventory can be one of the most expensive assets of an organization
• Inventory management policy affects how efficiently a firm deploys its assets in producing goods and services
• The right amount of inventory supports manufacturing, logistics, and other functions
• Excessive inventory is a sign of poor inventory management that creates an unnecessary waste of scarce resources
• Primary functions of inventory are:
• To service the market (downstream players)
• To buffer from uncertainty in the marketplace

### Types of Inventory

• Four broad categories of inventories:
• Raw materials: items that are bought from suppliers to use in the production of a product
• Work-in-process (WIP) inventory: partially processed materials not yet ready for sales
• Finished goods inventory: completed products ready for shipment
• Maintenance, repair & operating (MRO): materials & supplies used in producing products

### Concepts of Inventory Management

• Inventory turnover or turnover ratio: measures how many times inventory “turns” in an accounting period
• Calculated by dividing the cost of revenue (cost of goods sold) by average inventory
• Managerial implication: purchase cost does not affect the order decision if there is no quantity discount

### Economic Order Quantity (EOQ)

• The optimum Q (the EOQ) – method 2: making Annual Holding Cost (AHC) = Annual Order Cost (AOC)
• AHC = average inventory hold across the year * annual holding cost per unit = (Q/2)(kC)
• AOC = (R/Q)*S
• KC = 2R*S
• Q = √(2RS/KC)

### Economic Order Quantity Exercise

• LV Corporation: R = 7,200 units, S = $100 per order, k = 20%, C =$20 per unit, LT = 6 days
• Q = √(2RS/KC) = √(27,200100/0.20*20) = 600 units
• Annual purchase cost = RC = 7,200units$20 =$144,000
• Annual holding cost = Q/2kC = 600/20.20$20 =$1,200
• Annual order cost = R/QS = 7,200/600$100 =$1,200

### Reorder Point (ROP)

• The Statistical Reorder Point (ROP): the lowest inventory level at which a new order must be placed to avoid a stockout
• ROP = Average demand during the order’s delivery lead time + Safety stock
• Two models:
• Model 1: ROP with probabilistic (unknown) demand and constant lead time
• Model 2: ROP with constant demand and probabilistic (unknown) lead time

### Economic Order Quantity (EOQ) Model

• The EOQ model determines the optimal order size that minimizes total annual inventory costs, which is the sum of annual order costs and annual inventory holding costs.
• The model is based on a trade-off between annual inventory holding costs and annual order costs.
• Assumptions of the EOQ model:
• Demand must be known and constant
• Lead time is known and constant
• Replenishment is instantaneous
• Price is constant
• Holding cost is known and constant
• Ordering cost is known and constant
• Stock-outs are not allowed

### Total Annual Inventory Cost (TAIC)

• TAIC = Annual Purchase Cost + Annual Holding Cost + Annual Order Cost
• Annual Purchase Cost (APC) = annual demand * purchase cost per unit
• Annual Holding Cost (AHC) = average inventory hold across the year * annual holding cost per unit
• Annual Order Cost (AOC) = (R/Q) * S

### Economic Order Quantity (EOQ) Formula

• TAIC = (RC) + [(Q/2)(k*C)] + [(R/Q)*S]
• The optimum Q (EOQ) is calculated by taking the first derivative of TAIC with respect to Q and setting it equal to zero.

### Reorder Point (ROP)

• The Statistical Reorder Point (ROP) is the lowest inventory level at which a new order must be placed to avoid a stockout.
• ROP = Average demand during the order's delivery lead time + Safety stock
• In-stock probability is commonly referred to as the service level.

### ROP Model 1 - Probabilistic Demand and Constant Lead Time

• This model assumes that lead time is constant and demand during delivery lead time is unknown (but normally distributed).
• The average demand during the lead time is represented by μ, and the standard deviation formula is σdLT.
• Safety stock is (x − μ) = ZσdLT, and ROP is represented by x = μ + ZσdLT.
• The probability of stockout is represented by α, and the probability that inventory is sufficient to cover demand is (1 − α).

Explore inventory management concepts such as inventory turnover ratio, average inventory at cost, ordering costs, and holding costs. Learn how to optimize inventory management for business success.

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