A system for dispensing a liquid treatment substance in a laundry washing machine, the system comprising: - one or more multi-dose tanks adapted to contain each an initial volume (V_init) of a liquid treatment substance, - one or more volumetric dosing pumps connected in flow communication to said one or more multi-dose tanks and which can be activated to selectively extract said liquid treatment substance from said one or more multi-dose tanks and dispense it, - an electronic control unit which: - actuates said one or more dosing pumps, - determines for each of said one or more multi-dose tanks a total dispensable quantity (Q_tot_init) value depending on said initial volume (V_init), - counts, during the actuation of said one or more dosing pumps, for each of said one or more multi-dose tanks, a pumping quantity (t_p) of the respective dosing pump, - determines for each of said one or more multi-dose tanks a total dispensed quantity (Q_tot_disp) value depending on the counted pumping quantity (t_p), characterized in that: - said electronic control unit selectively generates, for each of said one or more multi-dose tanks, a warning of liquid treatment substance exhaustion or residual quantity, depending on said total dispensable quantity (Q_tot_init) value and on said total dispensed quantity (Q_tot_disp) value, wherein the pumping quantity (t_p) of the dosing pump is counted as volume expressed in terms of operating time of the volumetric dosing pump or, alternatively, in terms of number of pumping cycles of the volumetric dosing pump, wherein the control unit generates a treatment substance exhaustion warning, depending on a comparison between a predetermined exhaustion threshold value (Q_limit_1) and a difference between said total dispensable quantity value (Q_tot_init) and said total dispensed quantity value (Q_tot_disp), wherein the predetermined exhaustion threshold value (Q_limit_1) corresponds to a residual quantity (Q_res) of treatment substance which is lower than a quantity of treatment substance required for a single washing cycle. - one or more multi-dose tanks adapted to contain each an initial volume (V_init) of a liquid treatment substance, - one or more volumetric dosing pumps connected in flow communication to said one or more multi-dose tanks and which can be activated to selectively extract said liquid treatment substance from said one or more multi-dose tanks and dispense it, - an electronic control unit which: - actuates said one or more dosing pumps, - determines for each of said one or more multi-dose tanks a total dispensable quantity (Q_tot_init) value depending on said initial volume (V_init), - counts, during the actuation of said one or more dosing pumps, for each of said one or more multi-dose tanks, a pumping quantity (t_p) of the respective dosing pump, - determines for each of said one or more multi-dose tanks a total dispensed quantity (Q_tot_disp) value depending on the counted pumping quantity (t_p), - actuates said one or more dosing pumps, - determines for each of said one or more multi-dose tanks a total dispensable quantity (Q_tot_init) value depending on said initial volume (V_init), - counts, during the actuation of said one or more dosing pumps, for each of said one or more multi-dose tanks, a pumping quantity (t_p) of the respective dosing pump, - determines for each of said one or more multi-dose tanks a total dispensed quantity (Q_tot_disp) value depending on the counted pumping quantity (t_p), - said electronic control unit selectively generates, for each of said one or more multi-dose tanks, a warning of liquid treatment substance exhaustion or residual quantity, depending on said total dispensable quantity (Q_tot_init) value and on said total dispensed quantity (Q_tot_disp) value,