Heterogeneous project scheduling for optimal Six-Sigma cost reduction using linear programing

This paper presents a linear programming (LP) model for a multi-mode resource-constrained project scheduling problem (MRCPSP) in a manufacturing environment. Heterogeneously skilled employees with varying availability were scheduled for Six-Sigma cost reduction projects. Using typical projects from the local manufacturing division of a major diversified food manufacture (which motivated this research), a labor assignment problem using the work-time-project concept is formulated and solved using integer programming optimization procedures. The setting represents a multiple-project environment where projects are separate and independent, but require the same renewable resource mix for their completion. Projects require assignment of both supervisor and engineering staff with the requisite skills. The projects are scheduled to achieve the greatest cost reduction across all areas. The paper demonstrates how the output of the model can be used to identify bottlenecks (or critical resource skills), and also demonstrates how cross-training the critical individuals can increase throughput. The results established the division could not achieve their cost reduction goals with the assigned resources. Though our algorithm was applied to a manufacturing environment, our optimization algorithm has the potential to be utilized for other heterogeneous staffing scheduling such as health care or services.