Sustainability Economic Production Quantity with Warm-Up Function for a Defective Production System

Inventory management seeks to improve manufacturing by contracting inventory costs in a similar fashion to raise efficiency and profit. One approach is to develop inventory management models according to actual production systems. Furthermore, governmental policies in many countries impose many regulations on firms to fulfill the growing demand for a reduction in carbon emissions. Warm-up is a familiar concept in industrial applications. It allows the manufacturing system to work at a higher level of productivity and efficiency, as well as decreasing the number of defective items and maintenance costs. Along with fewer poor-quality items, the system has less waste as scrap items entering the environment and also requires less energy and workload to focus on reworking. The economic production quantity (EPQ) problems with a warm-up as an input parameter have been studied in a few works recently. This paper proposes a production-inventory model which considers the warm-up period as a decision variable and investigates its impact on the total cost. Furthermore, the defective rate is a decreasing linear function related to the warm-up period's length. The production-inventory model takes into account the carbon emission tax policy. The main aim of this research is to jointly optimize both the length of the warm-up period and the production cycle in order to minimize the total cost of the production-inventory system and, therefore, reduce emitted carbon emissions. The comparison of tax prices and the effect of the proper warm-up period on the amount of carbon emissions are discussed in the sensitivity analysis.