4.1 Inventory Models and Economic Order Quantity

Inventory models and Economic Order Quantity (EOQ) are crucial tools in managing inventory efficiently. They help businesses balance costs and customer demand, ensuring optimal stock levels and minimizing expenses.

These models are key to effective inventory management and control. By understanding EOQ, companies can make smarter decisions about when to order, how much to order, and how to keep costs down while meeting customer needs.

Inventory Management in Industrial Engineering

Importance and Key Concepts

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• Inventory management controls and oversees ordering, storage, and use of components for product production
• Balances minimizing inventory costs with ensuring sufficient stock to meet customer demand
• Key performance indicators include inventory turnover ratio, days of inventory on hand, and stock-out rate
• Impacts production scheduling, supply chain efficiency, and customer satisfaction
• Requires specific management approaches for different inventory types (raw materials, work-in-progress, finished goods)
• Incorporates technology like Enterprise Resource Planning (ERP) systems and Radio-Frequency Identification (RFID) for real-time tracking and analysis

Strategies and Techniques

• Implement just-in-time (JIT) inventory systems to reduce holding costs and improve efficiency
• Utilize ABC analysis to categorize inventory items based on their importance and value (A items most valuable, C items least valuable)
• Apply safety stock calculations to determine appropriate buffer levels for demand fluctuations
• Implement cycle counting techniques for ongoing inventory accuracy (periodic physical counts of a subset of inventory)
• Use forecasting methods to predict future demand and adjust inventory levels accordingly (moving average, exponential smoothing)
• Develop vendor-managed inventory (VMI) programs to shift inventory management responsibilities to suppliers

Economic Order Quantity Model

EOQ Formula and Applications

• Fundamental inventory management technique determining optimal order quantity to minimize total inventory costs
• EOQ formula derived from total cost function $EOQ = \sqrt{\frac{2DS}{H}}$
  • D represents annual demand
  • S represents ordering cost per order
  • H represents annual holding cost per unit
• Assumes constant and known demand, instantaneous replenishment, no stockouts, and constant ordering and holding costs
• Can be modified for quantity discounts, backorders, and multiple items
• Serves as basis for more complex inventory models (Economic Production Quantity, EPQ)
• Integrates with other production planning tools (Material Requirements Planning, MRP)

Sensitivity Analysis and Model Limitations

• Perform sensitivity analysis to understand impact of parameter changes on optimal order quantity
• Analyze effects of demand variability on EOQ model accuracy
• Consider limitations in real-world scenarios (non-constant demand, variable lead times)
• Evaluate impact of product characteristics (perishability, obsolescence risk) on model applicability
• Assess influence of supplier constraints and minimum order quantities on EOQ calculations
• Explore extensions of EOQ model for specific industry applications (retail, manufacturing, healthcare)

Ordering vs Holding Costs

Cost Components and Trade-offs

• Ordering costs include fixed expenses for placing an order (administrative, transportation, setup costs)
• Holding costs encompass variable expenses for storing inventory (warehouse space, insurance, taxes, opportunity costs)
• Trade-off fundamental to inventory management ordering less frequently increases holding costs but decreases ordering costs
• Optimal inventory policy minimizes sum of ordering and holding costs
• Marginal ordering cost equals marginal holding cost at optimal point
• Factors influencing trade-off include demand variability, lead time, and product nature
• Advanced models like Economic Production Quantity (EPQ) incorporate additional factors (production rate)

Practical Applications and Considerations

• Analyze impact of bulk purchasing discounts on ordering and holding cost trade-off
• Evaluate effect of seasonal demand patterns on optimal inventory policies
• Consider impact of storage space limitations on holding cost calculations
• Assess influence of product shelf life on holding cost and optimal order frequency
• Explore strategies for reducing ordering costs through supplier partnerships and electronic ordering systems
• Analyze impact of inventory financing options (consignment inventory, supplier credit terms) on holding costs

Total Inventory Cost

Cost Calculation and Components

• Total cost of inventory sums ordering costs, holding costs, and item costs $TC = \frac{D}{Q}S + \frac{Q}{2}H + DC$
  • D represents annual demand
  • Q represents order quantity
  • S represents ordering cost per order
  • H represents annual holding cost per unit
  • C represents unit cost
• Annual ordering cost calculated by multiplying number of orders per year (D/Q) by cost per order (S)
• Annual holding cost determined by multiplying average inventory level (Q/2) by annual holding cost per unit (H)
• Purchase cost of inventory product of annual demand (D) and unit cost (C)
• At EOQ, ordering cost equals holding cost (quick check for optimal order quantity calculations)
• Total cost function convex, unique minimum point corresponds to optimal order quantity

Analysis and Optimization Techniques

• Perform sensitivity analysis to understand impact of cost component changes on total inventory cost
• Utilize graphical methods to visualize relationship between order quantity and total cost
• Explore impact of quantity discounts on total cost function and optimal order quantity
• Analyze effect of inflation and time value of money on long-term inventory cost calculations
• Consider impact of stockout costs and service level requirements on total inventory cost
• Develop strategies for reducing total inventory cost through supplier negotiations and process improvements