Nonlinear programming approach for spatial scheduling problem

To solve the spatial scheduling problem of blocks on multi nonempty working-plates in block assembly workshop, an integer nonlinear programming model was formulated which included the due date and precedence constraints of blocks simultaneously. The average spatiotemporal utilization ratio was defined and established as the benchmark in the model which evaluated time and space utilization simultaneously. Then, this model was extended to formulate some special spatial scheduling problems. Finally, application data were obtained from a shipyard to validate the model, and the result showed that the model performed well in the mentioned spatial scheduling problems.