A graph theory based formulation of multi-period distribution planning problems

In this paper a multi-period planning problem, with arbitrarily defined planning objectives, is formulated in terms of graph theory. The proposed formulation represents a multi-period planning problem as a weighted graph problem and thus decomposes an original problem into a number of sequences (spanning paths) of static planning problems without loss of accuracy. This formulation guaranties that global optimal solution of multi-period planning problems will be found efficiently, assuming that global optimality of static problems is guarantied. Presented numerical results show that proposed approach could improve noticeably the quality of multi-period solutions.