Two-machine flowshop scheduling to minimize mean flow time under simple linear deterioration

A real industrial production phenomenon, referred to as deteriorating jobs, has drawn increasing attention. However, most research on this issue considers only single-machine problems. Motivated by this limitation, this paper considers a simple linear deterioration model in a two-machine flowshop where the objective is to minimize the mean flow time. Several dominance rules and three lower bounds are proposed to speed up the search for an optimal solution, and several heuristic algorithms are provided to derive near-optimal solutions. In addition, a computational experiment is conducted to evaluate their performances. Results indicate that the algorithms perform well, and a combined heuristic algorithm is recommended for practitioners.