Mathematical modelling for multiproduct EPQ problem featuring delayed differentiation, expedited rate, and scrap

The client requirements of present-day markets emphasize product quality, variety, and rapid response. To gain competitive advantages in marketplaces and meet customer needs, manufacturers today seek the most economical and fastest fabrication schemes and strategies to produce their various goods, especially when commonality exists within these multiple end products. Inspired by the above viewpoints, this study uses a mathematical modelling approach for solving a multiproduct economic production quantity (EPQ) problem featuring scrap, delayed differentiation, and expedited rate on the fabrication of the common part. We build a two-stage multiproduct fabrication scheme. Stage one uses an accelerated rate to produce all necessary common parts for multi-item to shorten its uptime, while stage two fabricates finished products sequentially using a rotation cycle rule. Inevitable random scraps produced in both stages are identified and removed to achieve the anticipated quality. We determined the optimal cost-minimization operating cycle length and used a numerical example to show our model’s capability and to explore collective and individual impacts of scrap, expedited-rate, and postponement strategies on various performances of the studied problem (such as uptime of common part, utilization, rotation cycle time, total system cost, and individual cost contributor, etc.) Our model can offer an optimization solution and in-depth managerial insights for fabrication and operations planning in a wide variety of present-day industries, such as household goods, clothing, etc.