Study objective was to maximize income over feed cost (IOFC) by mixed-integer programing (MIP), an optimization engine with objective function: max(IOFC) = Σ(g_1i × MY_i × P) − Σ(g_1i × DMI_i × P_ath(g_1i × NEC_i) × C₁) − Σ(g_1i × DMI_i × P_bth(g_1i × CPC_i) × C₂) + Σ(g_2i × MY_i × P) − Σ(g_2i × DMI_i × P_ath(g_2i × NEC_i) × C₁) − Σ(g_2i × DMI_i × P_bth(g_2i × CPC_i) × C₂), s.t. g_ji∈(0,1), g_1i + g_2i = 1, where j is group, i is cow. Milk yield of cow i (MY_i) is constant. NEC_i, CPC_i and DMI_i are cow i’s NE requirement (Mcal/kg DM), CP requirement (%) and daily dry matter intake (kg/cow), respectively calculated according to NRC. P_ath()is the value ranking as a*0.01*(vector length) and “a” is between 0 and 100. P, C1 and C2 are milk (0.35 $/kg), NE (0.07 $/Mcal) and CP (0.4 $/kg) prices, respectively. BW was calculated with Korver function as described by van Arendonk. We compared MIP with cluster (by NE) strategy in even and uneven grouping using same IOFC function, groups sizes and percentiles of NE and CP. The daily data of 471 cows from the University of Wisconsin-Madison Dairy Science herd (BW = 604.6 ± 28.9kg, DIM = 152 ± 103days, Milk yield = 43.1 ± 10.4kg/day) were used. MIP had greater average IOFC than cluster strategy in both even grouping (10.175 vs. 9.996 $/cow per d) and uneven grouping (10.383 vs. 10.193 $/cow per d). Compared with cluster strategy, MIP had 202 (42.89%) and 150 (31.85%) cows grouped differently in even and uneven grouping. FCM, feed efficiency (FCM/DMI) and IOFC were compared (Table 1). MIP approach seems to have better performance than cluster nutritional grouping, but animal experiments are needed. Table 1. Summary of MIP and cluster grouping strategy

Scenarios	Group	MIP (low)	Cluster (low)	t	P-value	MIP (high)	Cluster (high)	t	P-value
Even grouping (79th NE, 75th CP)	FCM(kg/d/cow)	44.5±9.1	40.1±7.8	−5.6	<0.001	43.5±10.7	47.9±10.3	4.5	<0.001
	FCM/DMI	1.7±0.3	1.5±0.2	−8.9	<0.001	1.7±0.3	1.9±0.3	7.3	<0.001
	IOFC($/cow per d)	10.3±2.8	9.0±2.3	−5.3	<0.001	10.1±3.2	11.0±2.7	3.3	0.001
Uneven grouping (79th NE, 57th CP)	FCM(kg/d/cow)	44.0±9.4	43.8±9.5	−0.2	0.9	44.1±12.1	44.5±11.7	0.3	0.8
	FCM/DMI	1.7±0.31	1.6±0.2	−4.4	<0.001	1.8±0.2	2.2±0.2	10.4	<0.001
	IOFC($/cow per d)	10.3±3.0	10.2±2.9	−0.4	0.7	10.7±3.4	10.0±3.2	−1.3	0.2