Glossary · approach
EOQ Extensions
The family of relaxations and extensions to the classical Economic Order Quantity model — quantity discounts (all-units / incremental), planned shortages / backordering, finite replenishment rate (EPQ), perishable / shelf-life constraints, multi-item joint ordering, and inflation-adjusted variants.
Quantity Discount EOQEPQEconomic Production QuantityPlanned Shortage EOQInflation-Adjusted EOQ
EOQ extensions denote the family of variants and relaxations to the basic Wilson (1934) model. (1) Quantity-discount EOQ — all-units quantity discount (if order total exceeds a threshold the discount applies to all units) and incremental quantity discount (only units above the threshold are discounted); solved by computing Q* per discount tier, checking feasibility, and table-searching for the global optimum. (2) Planned-shortage / backordering EOQ — stockouts are consciously allowed with a backorder cost b/unit-year; Q* expands by a factor of sqrt((H+b)/b). (3) Economic Production Quantity (EPQ, Taft 1918) — replenishment is not instantaneous but accumulates at a finite production rate P > D, average inventory drops to (Q/2)(1-D/P). (4) Perishable / shelf-life EOQ — adds Q ≤ demand × shelf-life as an upper bound. (5) Multi-item joint replenishment (linked to JRP) — multiple products share a setup cost, requires the Joint Replenishment Problem framework. (6) Inflation-adjusted EOQ (Buzacott 1975; Bierman and Thomas 1977) — opens the time-varying component of H for high-inflation economies, important when the capital-tied rate moves materially within the order cycle. References: Zipkin (2000) and Silver-Pyke-Peterson (1998) survey the full family.
Örnek
A wholesaler buying a packaging material faces a 100-unit-threshold 5% discount and a 500-unit-threshold 10% discount. Under classical EOQ Q* ≈ 350 units; the all-units quantity-discount EOQ comparison finds the global optimum at Q = 500 (the 10% discount tier), saving 7% on total annual cost despite carrying more inventory.