The lot size problem and the learning curve : A review of mathematical modeling (1950’s -2020)

Abstract

The economic order/production quantity (EOQ/EPQ) model is the most celebrated and the first scientific treatment of inventory management. It has been a fundamental topic covered in all production and operations management textbooks and the edifice on which complex inventory and logistics models have been built. It has been extended in many ways to make it more representative of real situations and settings. One of these extensions, which is the focus of the paper, is learning in production, where inventory builds in a convex rather than a linear form. Starting from the seminal work of Keachie & Fontana (Management Science, 13(2), B-102, 1966), this paper reviews the mathematics of those papers that stemmed from that work in an attempt to provide almost a comprehensive but rather concise presentation of more than 50 years of mathematical modeling. It also provides numerical examples to illustrate the expected behavior when learning occurs in activities other than production (setups and quality). It concludes with some insights and suggestions for future research directions for those who continue to be interested in the topic.