The budgeted minimum cost flow problem (BMCF(K)) with unit upgrading costs extends the classical minimum cost flow problem by allowing to reduce the cost of at most K arcs. In this paper, we consider complexity and algorithms for the special case of an uncapacitated network with just one source. By a reduction from 3-SAT we prove strong NP-completeness and inapproximability, even on directed ac...

optimal pricing of public parking can improve parking management. this leads to traffic flow, thereby reduces the cost of transportation network. in this paper, the transportation network with some origins, destinations, and public parking was considered. in the network, private cars drivers depending on travel time between origin and parking (driving time), travel time between parking and dest...

This article considers the problems of maximum flow and minimum cost flow determining in fuzzy network. Parameters of fuzzy networks are fuzzy arc capacities in the case of maximum flow finding and transmission costs of one flow unit in the case of minimum cost flow finding. These parameters are represented as fuzzy triangular numbers. Conventional rules of operating with fuzzy triangular numbe...

Information on the productivity, costs and applications of the logging system is a key component in the evaluation of management plans for the rehabilitation and utilization of Caspian forests. Skidding and road construction costs are expensive forest operations. Determining the optimum forest road network density is one of the most important factors in sustainable forest management. Logging me...