Potatoes require water and fertilizer management systems to optimize economic outcomes and fertilizer use, especially in arid areas such as Ningxia, China. In this study, three irrigation quotas (1200 (W1), 1650 (W2), and 2100 (W3) m3/hm2) and three nitrogen application treatments (110 (N1), 190 (N2), and 270 (N3) kg/hm2) were evaluated. Potato growth, final yield, and quality indices were assessed in relation to fertility periods, irrigation utilization efficiency, nitrogen and fertilizer bias productivity, and economic efficiency, using the TOPSIS model. Stem thickness and plant height varied significantly with irrigation and nitrogen treatments; total yield and vitamin C, reducing sugar, and starch contents were the highest under the W3N1, W3N1, W1N2, and W2N3 treatments, increasing by 54.56, 17.00, 69.00, and 45.00%, respectively, compared with those in the control. The regression relationships between water and nitrogen regulation and yield, irrigation water use efficiency, nitrogen fertilizer bias productivity, and economic efficiency agreed with the binary quadratic regression model, and the coefficients of determination (R2) were >0.85. W3N1 was optimal for model yield, nitrogen fertilizer bias productivity, and economic efficiency, and W1N3 was optimal for irrigation water use efficiency. Our findings will help optimize potato management in central Ningxia.