Economic lot-size problem for a cleaner manufacturing system with warm-up period

Abstract

There are instances that production machines require a warm-up period to reach their anticipated productivity. This study extends an economic manufacturing quantity (EMQ) problem by considering warm-up issue in the model. Warming up the machine decreases production loss, emission, and machine depreciation. Therefore, this study helps industry to enhance the profitability and also to reduce the environmental impact by decreasing waste generation and improving machine efficiency. In this study, we divide our system into three subsystems based on the relationships between production and consumption. Then we provide a mathematical model for each subsystem (three in total). The first two models are single-item EMQ inventory problems and the third one is a multi-item single-machine EMQ problem. In the third model, a machine/facility manufactures some items under a limited manufacturing volume. The purpose of these proposed models is to find the optimum cycle length to minimize the total system cost that consists of manufacturing, inventory and setup costs. Finally, we propose exact solution procedures after proving the convexity of these mathematical models.