The reduction due to soiling of the optical efficiency of the heliostats in the solar field is a significant detrimental factor in concentrating solar power (CSP) plants. Artificial cleaning is required to maintain acceptable values of optical efficiency, especially in those areas where CSP tends to be economically viable, i.e. where the yearly available DNI is high and rain is scarce. The optimization of the cleaning activities is then a fundamental step to properly balance the operation and maintenance (O&M) costs of the plant with the revenue losses due to soiled heliostats. In this work the best cleaning schedule for a given solar field is computed through a mixed integer linear programming (MILP) model and compared with the results of a heuristic approach. The optical efficiency reduction is assessed for each sector of the solar field through a physical model. The MILP model accounts for the soiling impact and finds the most economical solution in terms of cleaning trucks number and number of cleanings. The optimal cleaning schedule for each sector of the solar field is obtained by minimizing the total cleaning cost (TCC), which is the sum of direct cleaning costs and monetized losses due to soiling. A few test cases are evaluated to demonstrate the strength and the applicability of the developed algorithm. The TCC improvements span between 0.7% and 19.6%, depending on the different scenarios and cost structures considered. For the case studies considered, the savings due to the MILP optimized cleaning strategy were between 927 kAU$/yr and 4744 kAU$/yr (575 k(sic)/yr and 2941 k(sic)/yr).