Order Allocation Model for the Production of Asphalt Concrete Mixtures

Abstract

The necessity of solving the problem of order distribution for asphalt-concrete mixtures under varying intensities is substantiated to improve the selected performance criteria for the construction of extended facilities. We propose to use the construct of continuous Markov processes and describe an approach to determining the probabilities of transition from state to state using the Fokker-Planck-Kolmogorov equation. The resulting stationary transition probabilities of a continuous Markov process are the initial values for determining the optimal option of consumer order distribution over the ACP (asphalt-concrete plants), that is, for determining the optimal control variables. A piecewise continuous approximation of the initial function of change in the total intensity of incoming orders was carried out and it was proposed to use stationary values of the intensities of incoming orders at each time interval. The probability of failure to serve an order due to congestion at the ACP has been determined. Simulation results show that the probability of failures in order service reduces with an increase in the total number of ACPs and a decrease in their average load.