Economic Order Quantity Models
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1. EOQ models determine the optimal order quantity to minimize total inventory costs by balancing ordering and holding costs. The basic EOQ formula considers constant demand, lead time, and costs. 2. Extensions of EOQ include EPQ, which accounts for continuous production, and quantity discount models, which optimize order size to receive lower per-unit prices. 3. Planned shortage models factor backorders, where unfulfilled customer demand is recorded and met by subsequent deliveries to minimize lost sales from stockouts. Formulas balance ordering, holding, and shortage costs.
Economic Order Quantity Models
- 1. EOQ MODELS Presentation By: Shashank Shekhar
- 2. Economic Ordering Quantity EOQ is the amount of inventory to be ordered at one time for purposes of minimizing annual inventory cost. Formula for Economic Ordering Quantity : ◦ Ordering Cost: Cost of placing single order. ◦ Holding Cost: Cost to hold one unit inventory for a year
- 3. EOQ ASSUMPTIONS Known & constant demand Known & constant lead time Instantaneous receipt of material No quantity discounts Only order (setup) cost & holding cost No stockouts
- 4. Various EOQ Models Economic Production Quantity (EPQ) Quantity Discount Model Planned Shortage With Backorders
- 5. 1.Economic Production Quantity EPQ determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. Assumptions : ◦ Demand for items from inventory is continuous and at a constant rate. ◦ The production of items is continuous and at a constant rate. ◦ Ordering cost is fixed (independent of quantity produced). ◦ The purchase price of the item is constant i.e. no discount is available. ◦ The replenishment is made incrementally.
- 6. Derivation of EPQ Formula Holding Cost Per Year = Q/2*(F(1-x)) Q/2 is average inventory & F(1-x) is the average holding cost. F(1-x) is the average holding cost. Ordering Cost per Year =D/Q*(K) ◦ K = ordering/setup cost ◦ D = demand rate ◦ F = holding cost ◦ Q = order quantity ◦ P=Production Rate ◦ x=D/P
- 7. How TO Get EPQ Formula ? Holding Cost = Ordering Cost So, We get:
- 8. 2. Quantity Discount Model Quantity discounts are price reductions designed to induce large orders. The buyer's goal in this case is to select the order quantity that will minimize total costs, where total cost is the sum of carrying cost, ordering cost, and purchase cost. Two approach are there: ◦ With the Incremental Approach, we would pay $65 for the first 100 units and $60 for rest of the 150 units. ◦ But, with the All Units Approach, we would pay $60 a piece for all the 250 units.
- 9. Understanding Quantity Discont QUANTITY PRICE Co = Rs.2,500 1 - 49 Rs.1,400 Ch = Rs.190 per unit 50 - 89 1,100 D = 200 90+ 900 2CoD 2(2500)(200) Qopt = = = 72.5 PCs Ch 190 For Q = 72.5 Co D ChQopt TC = + 2 + PD = Rs.233,784 Qopt For Q = 90 CoD ChQ TC = + 2 + PD = Rs.194,105 Q
- 11. Continued.. Shortage: when customer demand cannot be met. Shortage may result into: ◦ Lost of goodwill. ◦ Reduction in future orders. ◦ Unfavorable Changes in the market share. ◦ Loss of customers. In some situation customer may not withdraw order and wait till next shipment arrives.