Generalization of Johnson's and Talwar's scheduling rules in two-machine stochastic flow shops

The paper deals with the classical problem of minimizing the makespan in a two-machine flow shop. When the job processing times are deterministic, the optimal job sequence can be determined by applying Johnson's rule. When they are independent and exponential random variables, Talwar's rule yields a job sequence that minimizes the makespan stochastically. Assuming that the random job processing times are independent and Gompertz distributed, we propose a new scheduling rule that is a generalization of both Johnson's and Talwar's rules. We prove that our rule yields a job sequence that minimizes the makespan stochastically. Extensions to m-machine proportionate stochastic flow shops, two-machine stochastic job shops, and stochastic assembly systems are indicated.