Extension of the Minimum Cost Flow Problem (Mcfp or Cnf) by Consideration of Time and Quantity of Loads With Maximum Time

Abstract

This paper extends the general problem of minimizing the total cost of transport on the road network (CNF) by considering the total time, maximum time and total amount of cargo with the longest time. In the literature available to us, models with timing and amount of cargo in the case of a standard transport task were exposed. Optimization is possible by combining 5 criteria, 2 linear and 3 nonlinear ones over the same set of linear constraints. Multicriteria optimization determines Pareto-optimal solutions. Interactive analyst-software algorithms for solving the selected models were defined. The solution of hypothetical problems was illustrated. Closed model with 5 two-way asymmetric communications using software for CNF and it is possible to use software for LP. Four one-criteria problems were solved: total costs, overall transport performance from a time standpoint, transport time (problem of the second type by time) total transport time (problem of the third type by time) and one bi-criteria problem related to the simultaneous minimization of the maximum duration of transport and total costs.