The EOQ model extended to permit stockouts and backorders introduces a second control variable—the backorder level—creating a more complex cost minimization problem that balances inventory holding costs against backorder costs. The classical model with no shortages is a special case where backorder cost is prohibitively high; allowing backorders reduces total cost by permitting deliberate temporary shortages when holding inventory is expensive relative to customer wait time, with formulas for optimal order quantity and backorder level derived from the same marginal cost principle. Table of Contents: - Backordering vs. no-shortage models: relaxation of stock-zero assumption - Two control variables in backorder model: order quantity Q and backorder level S - Economic Order Quantity with backordering: Q = √(2DC_n / C_c) · √((C_c + C_s) / C_s) - Backorder level formula: S = Q · C_c / (C_c + C_s) - Cost components in extended model: ordering cost, inventory holding cost, backorder cost - Total cost decomposition: TC = (D/Q)C_n + (Q-S)²/(2Q)·C_c + S²/(2Q)·C_s - Relationship between holding cost and backorder cost: determines optimal shortage proportion - Cost unit consistency: C_c and C_s expressed in same units (rupees/unit/period) - Model reduction: basic EOQ emerges when backorder cost approaches infinity - Stock movement pattern: cyclical rise to Q, consumption to S (backorder), reorder
The EOQ model extended to permit stockouts and backorders introduces a second control variable—the backorder level—creating a more complex cost minimization problem that balances inventory holding co…