The models for uncoordinated service and coordination with a common headway are formulated as
nonlinear programming problems (NLP). Since constraints in the proposed models are not convex
functions, standard heuristic algorithms for solving these NLPs can guarantee convergence only to a local
minimum. The model of integer-ratio coordination including both integer and linear variables (i.e. integer
ratio multipliers) with nonlinear cargo time values is known as a mixed-integer nonlinear program
(MINLP). The optimization of such models is typically difficult due to their combinatorial nature and
potential existence of multiple local minima.