Quantity Discount Lecture V.14

10.4 Quantity Discounts for the EOQ Model

Introduction to Quantity Discounts

  • The quantity discount model modifies assumption 4 of the EOQ model by varying the cost per unit based on the ordered quantity.

  • Suppliers often provide incentives for larger order quantities by offering lower purchase costs for larger orders.

Discount Schedule Example

  • Example discount schedule:

    • Discount Category 1: 0 to 999 units: Cost: $5.00 (No discount)

    • Discount Category 2: 1000 to 2499 units: Cost: $4.85 (3% discount)

    • Discount Category 3: 2500 units and over: Cost: $4.75 (5% discount)

  • The higher discount for larger quantities leads to increased inventory holding costs, necessitating a thorough cost analysis before deciding on order quantity.

Cost Analysis Scenario

  • Given:

    • Annual holding cost rate: 20%

    • Ordering cost: $49 per order

    • Annual demand: 5000 units

  • Calculate order quantities for each discount category using EOQ formula:

    • EOQ Formula: Q = √(2DC/Ch)

  • Calculated EOQs for each discount category:

    • Q1 for discount category 1: Q1 <= 700

    • Q2 for discount category 2: Q2 <= 711

    • Q3 for discount category 3: Q3 <= 718

Adjusting Order Quantity

  • Since calculated Q may not meet the minimum order quantity for discounts, adjustments are made:

    • For Q1 <= 700: Adjust to 1000 to qualify for discount.

    • For Q2 <= 711: Remains at 1000 to qualify for 3% discount.

    • For Q3 <= 718: Adjust to 2500 to qualify for 5% discount.

Total Cost Calculation in Quantity Discounts

  • The annual purchase cost is relevant and included as it varies with order quantity:

    • Total Cost Equation: TC = C₁ + C + DC (10.28)

  • Steps to find optimal order quantity:

    • Step 1: Calculate EOQ for each discount category.

    • Step 2: Adjust quantities to meet discount thresholds.

    • Step 3: Compute total annual cost using the appropriate unit price and determine the order quantity with minimum cost.

Optimal Order Quantity Findings

  • Summary of total annual costs for various discount categories:

    • For Category 1: Order quantity 700 leads to $25,700 total cost.

    • For Category 2: Order quantity 1000 leads to $24,980 total cost (minimum).

    • For Category 3: Order quantity 2500 leads to $25,036 total cost (not optimal due to high holding cost).

  • Conclusion: To minimize costs, ordering 1000 units at 3% discount is optimal, despite the higher discount available at larger quantities.