Pigou's problem has many applications in real life scenarios like traffic networks, graph theory, data transfer internet etc. The two player classical network an unique Nash equilibrium with the Price of Stability and Anarchy agreeing each other. situation changes for $k-$person $n$ being total number people. If we fix behaviour $(n-2)$ people assume that $k-$persons take path $P_2$ where $k<(n...

assembly lines are special kinds of production systems which are of great importance in the industrial production of high quantity commodities. in many practical manufacturing systems, configuration of assembly lines is fixed and designing a new line may be incurred huge amount of costs and thereby it is not desirable for practitioners. when some changes related to market demand occur, it is wo...

due to shortage of precipitation and the spatial and periodical disparity of rainfalls, iran iscounted among the arid and semi-arid countries of the world, and therefore the water utilities have put thecontrol of consumption and efficient use of water high on their priorities. water consumption management isconsidered as a field of energy management, and the impacts of effective measure related...