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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

What is the Z-value corresponding to a 97.5 percent service level?

1.96

What is the formula to calculate the statistical reorder point?

ROP = μ + ZσdLT

What is the average demand during lead time (μ) for the part at L Inc.?

550 units

What is the standard deviation of demand during lead time (σdLT) at L Inc.?

40 units

What is the service level desired by the supply chain manager at L Inc.?

95 percent

What is the required safety stock to achieve a 95 percent service level?

66 units

What is the statistical reorder point (ROP) for the part at L Inc.?

616 units

What is the purpose of calculating the safety stock?

To minimize the probability of stockout

What is the additional safety stock required to attain a 99 percent service level?

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.

What assumption is made about the lead time in ROP Model 1?

That the lead time is constant.

What is the formula for calculating safety stock in ROP Model 1?

x - μ = ZσdLT

What does the probability (1 - α) represent?

The probability that inventory is sufficient to cover demand.

What is the primary difference between ROP Model 1 and ROP Model 2?

The assumptions about demand and lead time.

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.

What is the formula for calculating the statistical reorder point (ROP)?

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.

A 97.5 percent service level corresponds to the _______________ of 1.96.

Z-value

The required safety stock is 0 and the probability of _______________ would be 50%.

stockout

The statistical reorder point (x) can be calculated as the average demand during the order's delivery _______________ time plus the desired safety stock.

lead

The standard deviation of demand during _______________ time (σdLT) is 40 units.

lead

A 95 percent service level corresponds to a _______________ of 1.65 standard deviations above the Average.

Z-value

The ROP for Q1 is _______________ + 66 units = 616 units.

550

The manager must reorder the part from their supplier when their current stock level reaches _______________ units.

616

The supply chain manager wants to determine the safety stock and statistical reorder point that result in _______________ percent stockouts.

5

The manager wants to know the additional safety stock required to attain a _______________ percent service level.

99

L Inc. stocks a crucial part that has a normally distributed demand during the _______________ period.

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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