EOQ and EPQ Production-Inventory Models with Variable Holding Cost: State-of-the-Art Review

In production-inventory control, economic order quantity (EOQ) and economic production quantity (EPQ) models are used to determine the optimal order quantities for purchasing and manufacturing. Most EOQ and EPQ models are constructed assuming constant costs. Recently, however, EOQ/EPQ models assuming varying costs (i.e., holding, ordering, and purchasing costs) have been receiving considerable attention. The objective of this paper is to review and classify EOQ and EPQ inventory models formulated under the assumption of variable holding costs. The relevant papers are reviewed and classified into three main types: time-dependent holding cost, stock-dependent holding cost, and multiple dependence or other holding cost variability. Additional classification is proposed for the reviewed models according to their objectives, solution methods, and applications. The paper identifies research trends and includes several suggestions for future research directions.