This paper considers the problem of scheduling loading and unloading operations of a crane in a railway terminal motivated from rail-road container transshipment operations at Uiwang Inland Container Depot (ICD). Unlike previous studies only considering the total handling time of containers, this paper considers a bi-criteria objective of minimizing the weighted sum of the total handling time and tenant service time. The tenant service time is an important criterion in terms of terminal tenants who are private logistics companies in charge of moving containers from/to the terminal using their trucks. In the rail-road container shipment yard, the tenant service time of a tenant can be defined by a time difference between beginning and finishing loading and unloading operations of a crane. Thus, finding a set of sequences and time of the crane operations becomes a crucial decision issue in the problem. The problem is formulated as a nonlinear program which is improved by linearizing a nonlinear constraint in the model. This paper develops a genetic algorithm to solve the problem and performs a case study on the Uiwang ICD terminal. Computational experiment results show that the genetic algorithm shows better performance than commercial optimization solvers. Operational implications in terms of tenants are drawn through sensitivity analyses.