Determining the optimal cycle length for a multiproduct EMQ problem considering rework and overtime options

Abstract To satisfy the increasing trend of diverse customer product needs and to cope with internal capacity constraints, the management of current manufacturing firms must plan multiproduct batch fabrication and be able to reduce its completion time and/or smooth overall production schedules. Furthermore, because of various unforeseen problems in real fabrication processes, defective items may be randomly produced. These items need to be identified and separated from perfect stocks to maintain the required quality level. Inspired by these facts, we explore a multiproduct economic manufacturing quantity (EMQ) problem considering rework and overtime options. An exact model is built to study the characteristics of the problem that have not yet been explicitly examined in the literature. This newly developed model employs a mathematical technique together with differential calculus to not only obtain the total cost function of the system, but also to prove its convexity and determine the optimal cycle time that minimizes the total system cost. A numerical illustration is provided to demonstrate its applicability. Subsequently, the impact of overtime and rework on the optimal solution, relevant cost variables, and the completion time of batch fabrication, machine utilization, can be obtained. This information on the cost-effectiveness of problem characteristics is valuable in facilitating managerial decisions.

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