EOQ Formula Explained: How to Calculate Economic Order Quantity

The quantity discount model extends EOQ to account for price breaks offered by suppliers for larger orders. The model balances lower unit prices against increased holding costs from larger order quantities. The decision process involves calculating EOQ for each price level, checking if EOQ falls within the quantity range, and selecting the quantity with lowest total cost. This model encourages bulk purchasing while ensuring cost minimization.

When suppliers offer quantity discounts (lower prices for larger orders), the basic EOQ model must be modified. The total cost function now includes purchase cost DP, which depends on order quantity. The procedure: (1) Calculate EOQ for each price level, (2) Check if EOQ is feasible (within the quantity range for that price), (3) Calculate total cost for feasible EOQs and for quantity breakpoints, (4) Select the option with minimum total cost. The optimal order quantity may be a breakpoint rather than an EOQ.

The quantity discount model addresses situations where suppliers offer reduced prices for larger order quantities. The model extends the basic EOQ framework by incorporating price breaks at different order quantity thresholds. The total cost formula becomes TC = (D/Q) × S + (Q/2) × I × P + P × D, where I is holding cost as a percentage of item price. Since holding cost varies with price, the EOQ formula adjusts to Q* = √(2DS/(IP)). The strategy involves starting with the lowest price level and checking feasibility, moving upward until a feasible solution is found where the computed EOQ falls within the applicable discount range.

The Quantity Discount Model addresses situations where suppliers offer price reductions for larger order quantities. The model involves comparing total costs (ordering + holding + purchase) at different price break points. The process: (1) Calculate EOQ for each price level; (2) Check if EOQ is valid (meets minimum quantity requirement); (3) If valid, calculate total cost; (4) If invalid, use the minimum quantity for that price level; (5) Select the option with the lowest total cost. This model helps determine whether the savings from bulk purchasing outweigh the increased holding costs.

When suppliers offer price breaks for larger order quantities, the EOQ model must be adjusted to account for purchase cost variations. The approach involves calculating EOQ at each price break level and comparing total costs (purchase + ordering + holding) across all feasible ranges. Even though discounted prices reduce per-unit costs, the optimal order quantity may exceed basic EOQ because the discount savings can offset increased holding costs. For example, ordering 1,000 units might yield greater total savings than ordering at the basic EOQ of 184 units due to significant discount benefits.

The Economic Production Quantity (EPQ) model determines the optimal production lot size when items are manufactured incrementally rather than received in single batches, replacing ordering costs with setup costs; unlike the EOQ model, EPQ accounts for continuous production where the production rate P exceeds the demand rate D, resulting in a higher optimal lot size that approaches EOQ when P is much larger than D and approaches continuous flow when P only slightly exceeds D.

The Economic Production Quantity (EPQ) model determines the optimal production batch size that minimizes total inventory costs when production occurs continuously rather than receiving items all at once. The formula for EPQ is: Q* = √[(2 × D × C_not) / (CH × (1 - D/P))], where D is annual demand, C_not is ordering cost per order, CH is holding cost per unit per year, and P is production rate per year. This model accounts for the fact that inventory builds up gradually during production and depletes during consumption. The denominator includes (1 - D/P) to reflect the decreasing inventory level during production. For example, with D=10,000 units/year, C_not=₹10/order, CH=₹20/unit/year, and P=100,000 units/year, the optimal lot size would be approximately 949 units.

The Economic Production Quantity (EPQ), also known as the Production Order Quantity (POQ), is an inventory management model used in manufacturing environments where items are produced internally rather than ordered all at once from a supplier. Unlike the Economic Order Quantity (EOQ) model which assumes complete delivery of ordered items, EPQ accounts for simultaneous production and demand during a production run. The key assumptions include: only one item is involved, annual demand is known and constant, usage rate is constant, production rate is constant, lead time is known and constant, and no quantity discounts are available. The EPQ formula extends the EOQ formula by incorporating the ratio of daily production rate to daily demand rate, with the equation Q* = √[(2DS/H)] × √[p/(p-d)], where D is annual demand, S is setup cost, H is holding cost, p is daily production rate, and d is daily demand rate. The maximum inventory level (IMAX) is calculated as Q × (1 - d/p), and total annual cost is calculated as (D/Q) × S + (IMAX/2) × H.

The Economic Production Quantity (EPQ) model is an inventory management tool used to determine the optimal production lot size when production occurs in batches rather than receiving items all at once. Unlike the basic EOQ model, the EPQ model accounts for the fact that inventory builds up gradually during production at a rate equal to the difference between the production rate and the usage rate. The optimal production quantity is calculated using the formula QP = √(2DS/H) × √(P/(P-U)), where D is annual demand, S is setup cost per run, H is carrying cost per unit per year, P is production rate, and U is usage rate. This model helps minimize total annual costs by balancing setup costs and carrying costs.

The Economic Production Quantity (EPQ) model determines the optimal production quantity that minimizes total costs (carrying cost + setup cost) when a company produces items internally rather than purchasing them externally. The optimal production quantity formula is Q* = √[(2DS)/(H × (1 - D/P))], where D is demand rate, S is setup cost, H is holding cost per unit per year, and P is production rate. The model accounts for the gradual buildup of inventory during production, unlike the EOQ model which assumes instantaneous replenishment. Key components include maximum inventory (I_max = Q × (1 - D/P)), average inventory (I_avg = I_max/2), cycle time (Q/D), run time (Q/P), and idle time (cycle time - run time).

EOQ is based on several key assumptions that also become its limitations: (1) Uniform consumption throughout the year - demand is constant and predictable, (2) Uniform supply availability - materials are available continuously throughout the year, (3) No price increases - purchase prices remain constant, (4) No quantity discounts - unit cost does not change with order size, (5) Instantaneous replenishment - orders arrive immediately, (6) No stockouts - demand is always met. If these assumptions are violated, EOQ may not provide optimal results. For example, if prices are expected to increase, ordering more than EOQ may be beneficial despite higher carrying costs.

The EOQ model has limitations: it underestimates holding costs (missing opportunity costs, spoilage, obsolescence) and overestimates ordering costs (due to modern technology). This creates an imbalance where actual holding costs are higher than modeled. The implication is that companies should reduce order quantities and increase order frequency, aligning with Just-in-Time (JIT) principles. JIT originated from Japanese manufacturing practices in the 1980s, demonstrating superior efficiency through minimal inventory and production-to-demand systems.

Economic Order Quantity (EOQ) determines optimal order quantity minimizing total inventory costs: EOQ = √(2 × R × S / (P × L)), where R is demand, S is ordering cost, P is unit price, and L is holding cost. EOQ balances ordering costs (administrative, delivery) against holding costs (storage, insurance, capital). For example, with 1,200 units demand, Rp15M ordering cost, and 40% holding cost, EOQ is 300 units. Just-In-Time (JIT) is a production system minimizing waste by receiving materials only as needed, improving efficiency and reducing holding costs. JIT requires reliable suppliers and accurate demand forecasting.

The basic EOQ model assumes: constant demand, constant lead time, fixed ordering costs, holding costs proportional to average inventory, no quantity discounts, instantaneous replenishment, and no stockouts. The instructor explains that violations of these assumptions require modified models. For example, when production rate is limited (P < D), the EPQ model applies with average inventory = Q × (1 - D/P) / 2. When items are outsourced (P = ∞), the basic EOQ applies.

EOQ determines optimal order quantity: √(2AP/S), where A=annual demand, P=order cost, S=carrying cost per unit. For A=100, P=$2, S=$4, EOQ=10 units. High carrying costs favor smaller, more frequent orders; high order costs favor larger, less frequent orders. Just-in-Time (JIT) minimizes inventory through frequent small orders (low order costs) and negligible inventory (high carrying costs). JIT requires reliable suppliers and strong relationships. JIT uses backflush costing where manufacturing costs go directly to COGS since there is little or no inventory. At period end, any actual inventory is allocated from COGS to inventory accounts using standard costs.