Designing a mixed model assembly line with utility workers to satisfy uncertain demands

In a mixed model assembly line, when demands for different products vary, the workload of stations will change and sometimes work overload may occur. Hiring utility workers to help ordinary workers in case of work overload is a common practice in just-in-time (JIT) production systems, and will affect the constraints and objective of assembly line balancing problem, but no study has ever discussed it. This paper aims to design a mixed model assembly line with utility workers to satisfy uncertain demands in all possible scenarios. The decision maker needs to determine the number of utility workers and ordinary workers, and their tasks allocation in order to minimize the total labor cost. This problem is formulated as a mixed integer programming and is proved NP-complete. A method to estimate the lower bound on labor cost is presented, based on which a heuristic and a branch, bound and remember algorithm are proposed. The numerical experiments on 500 instances show that the proposed algorithms are effective and efficient.