inventory module 4

Overview of Inventory and Materials Management

• Course: MGT1218

• Instructor: Professor Shahin Basiratzadeh

Inventory Models

Deterministic Demand Models

• Economic Order Quantity (EOQ)

• Economic Production Quantity (EPQ)

• Quantity Discount

Probabilistic Demand Models

• Fixed-Quantity Models

• Fixed-Period Inventory Models

Concept of Probabilistic Inventory Models

• Inventory models typically assume constant and certain demand.

• In contrast, probabilistic models are used when:

  • Product demand is uncertain and is described using a probability distribution.

• These models include the concept of safety stock to prevent stockouts.

Safety Stock

• Safety stock (SS) must be maintained to mitigate the risk of stockouts.

  • Important in both Fixed Order Quantity Models and Fixed Time Period Models:

  • Fixed Order Quantity Models

    • Inventory levels are monitored continuously.

    • Stockout protection is necessary only during lead time.

  • Fixed Time Period Models

    • Inventory levels are known at specific intervals.

    • Stockout protection required during the lead time plus the next order cycle.

Safety Stock Calculations

• Reorder Point (ROP): The inventory level at which a new order should be placed to replenish stock.

  • Depends on:

  • Lead time demand

  • Variability in demand

  • Desired service level (probability of not stocking out).

Example Calculation

• ROP formula:
  $ROP = ext{Expected demand during lead time} + ext{Safety Stock}$

• Example Data:

  • Minimum, maximum, and mean demand during lead time are used in calculations.

  • Example:

  • Mean demand: 350 kits

  • Safety stock: 16.5 units

  • Resulting ROP: $ROP = 350 + 16.5 = 366.5$

Practical Example: Hospital Inventory Management

Haliburton Regional Hospital Case

• Product: “Code Blue” resuscitation kit

  • Mean demand during reorder period: 350 kits

  • Standard deviation: 10 kits

  • Desired stockout risk: 5%

• Safety Stock Calculation:

  • Determine Z value for 95% service level; Z = 1.645

  • Safety Stock Formula:
    $ext{Safety Stock} = Z imes ext{Standard Deviation during lead time}$

  • $ext{Safety Stock} = 1.645 imes 10 = 16.45$

• ROP Calculation: $ROP = ext{Demand during lead time} + ext{Safety Stock}$

  • Result: Calculate ROP from mean demand.

Example Calculation: Pens Inventory

• Average daily demand: 60 units

  • Total annual demand: $D = 60 imes 365 = 21,900$

  • Lead time: 6 days

  • Ordering cost: $10

  • Holding cost: $80

  • Required Service Level: 95%

• Economic Order Quantity (EOQ) Calculation:
  $Q^* = ext{Optimal Order Quantity} = ext{Calculated using EOQ formula}$

• ROP Calculation

  • Required ROP for 5% stockout risk to serve 95% customers:
    $R = ext{Mean daily demand during lead time} + Z imes ext{Standard deviation during lead time}$

  • Complete calculation with actual values.

Fixed-Period Demand Model

• Characterizes ordering at fixed intervals:

  • Orders placed based on the time, not on stock levels.

  • Useful in settings with regular vendor visits.

• Example Variables:

  • $S$: Target safety stock

  • $d$: Average daily demand

  • $T$: Review period

  • $L$: Lead time

• Order Quantity (Q) Calculation:
  $Q = S I_1$

• Example Given: Daily demand, standard deviation, review period, and lead time used for order calculations.

Single-Period Inventory Model

• Application: Situations with a single order for high-demand but low-reuse items (e.g., seasonal products).

• Demand is uncertain; characterized using a probability distribution.

  • Considerations include average demand and standard deviation to establish service level.

Example: Chris Ellis's Newsstand

• Daily demand for newspapers: 120 copies

  • Standard deviation: 15 papers

  • Cost per paper: $0.70; selling price: $1.25

  • Unsold paper credit: $0.30

• Objective: Determine optimal daily order quantity.

  • Assess stockout risk associated with order quantity.

Use of Software in Inventory Management

Sample Calculation Scenario: Nathan Manufacturing

• Annual Demand: 1,000 units

• Setup cost per order: $10

• Holding cost per unit per year: $0.50

  • Daily demand calculated and reflected in total costs.

• Analysis includes max inventory levels, average levels, setup frequency, and costs.

In-Class Activities

• Additional examples and calculations to reinforce students' understanding of these concepts.

Conclusion

• Key focus on understanding different inventory models, particularly how to manage uncertainty in demand, determining safety stock, reorder points, and making informed inventory decisions through examples and statistical methods.