Least distance day-matching

[luboxing]

Hi,

I came across this problem with table below.

Here Y, M are year and month, and Y2 and M2 are the next month of (Y, M). In each month here are days (totaling 28/29/30/31 depending on month) designated by DY. For each month, I am going to pick one day as the beginning day of the month (DY) and another day as the ending day (DY1) so that DY is rotated. For example, if 5 is picked as the beginning day, 4 would be the ending day, as days follow 5, 6,..., 31, 1, 2, 3, 4 assuming the month has 31 days, and so on. Once the beginning day has been picked for the month (ending day implied), I move to the next month and do the same. At the end, I need to minimize:

sum((MWB(i) - MWE(i+1))**2), where i = 1... # of months. 

The example below has 3 months so the total space is 31*30*31. The actual problem involves one year and a much larger space of 31*30*31...*31.

I am considering optmodel but still trying to specify the problem with it. Any help is appreciated!

Y	M	M2	Y2	DY	DY1	MWB	MWE
2022	1	2	2022	1	31	3,060.79	2,847.60
2022	1	2	2022	2	1	2,795.53	2,755.11
2022	1	2	2022	3	2	2,711.12	2,723.58
2022	1	2	2022	4	3	2,585.14	2,357.31
2022	1	2	2022	5	4	2,856.69	2,336.30
2022	1	2	2022	6	5	2,585.89	2,314.10
2022	1	2	2022	7	6	2,708.57	2,537.95
2022	1	2	2022	8	7	2,761.23	2,327.29
2022	1	2	2022	9	8	2,550.63	2,352.52
2022	1	2	2022	10	9	2,970.52	2,354.57
2022	1	2	2022	11	10	2,995.84	2,281.79
2022	1	2	2022	12	11	3,453.13	2,612.58
2022	1	2	2022	13	12	3,000.57	2,619.14
2022	1	2	2022	14	13	2,886.60	2,875.82
2022	1	2	2022	15	14	3,054.25	2,646.22
2022	1	2	2022	16	15	2,983.17	2,611.71
2022	1	2	2022	17	16	2,516.30	2,709.25
2022	1	2	2022	18	17	2,670.58	2,623.86
2022	1	2	2022	19	18	2,784.30	2,254.84
2022	1	2	2022	20	19	2,570.44	2,331.93
2022	1	2	2022	21	20	2,451.75	2,354.15
2022	1	2	2022	22	21	2,423.53	2,283.58
2022	1	2	2022	23	22	2,455.70	2,130.18
2022	1	2	2022	24	23	2,512.75	2,028.61
2022	1	2	2022	25	24	2,493.90	2,104.30
2022	1	2	2022	26	25	2,529.80	2,213.52
2022	1	2	2022	27	26	2,574.74	2,228.63
2022	1	2	2022	28	27	3,012.91	2,277.01
2022	1	2	2022	29	28	3,163.53	2,289.61
2022	1	2	2022	30	29	3,372.30	2,690.60
2022	1	2	2022	31	30	3,150.71	2,840.38
2022	2	3	2022	1	30	4,147.38	2,937.49
2022	2	3	2022	2	1	4,774.03	3,289.59
2022	2	3	2022	3	2	4,144.49	4,371.40
2022	2	3	2022	4	3	4,090.07	3,824.04
2022	2	3	2022	5	4	4,085.97	3,807.31
2022	2	3	2022	6	5	3,766.41	3,786.18
2022	2	3	2022	7	6	3,382.19	3,770.40
2022	2	3	2022	8	7	3,331.66	3,463.21
2022	2	3	2022	9	8	2,985.52	3,040.08
2022	2	3	2022	10	9	3,420.95	2,888.73
2022	2	3	2022	11	10	3,336.96	2,751.84
2022	2	3	2022	12	11	2,849.19	3,120.61
2022	2	3	2022	13	12	2,923.18	2,870.00
2022	2	3	2022	14	13	3,466.61	2,598.92
2022	2	3	2022	15	14	3,581.33	2,630.91
2022	2	3	2022	16	15	3,751.99	3,145.85
2022	2	3	2022	17	16	3,793.83	3,315.29
2022	2	3	2022	18	17	3,927.19	3,409.43
2022	2	3	2022	19	18	3,958.74	3,521.23
2022	2	3	2022	20	19	3,767.45	3,619.12
2022	2	3	2022	21	20	3,569.70	3,727.37
2022	2	3	2022	22	21	3,951.63	3,494.98
2022	2	3	2022	23	22	3,893.76	3,311.69
2022	2	3	2022	24	23	3,710.34	3,664.18
2022	2	3	2022	25	24	3,100.67	3,606.88
2022	2	3	2022	26	25	3,164.81	3,345.92
2022	2	3	2022	27	26	2,974.90	2,768.13
2022	2	3	2022	28	27	3,391.46	2,798.68
2022	2	3	2022	29	28	3,377.84	2,738.24
2022	2	3	2022	30	29	3,499.97	3,046.27
2022	3	4	2022	1	31	3,653.04	3,733.46
2022	3	4	2022	2	1	3,992.26	3,705.17
2022	3	4	2022	3	2	4,419.02	3,384.90
2022	3	4	2022	4	3	4,390.42	3,612.65
2022	3	4	2022	5	4	4,330.79	3,914.40
2022	3	4	2022	6	5	3,968.64	3,965.32
2022	3	4	2022	7	6	3,781.22	3,805.89
2022	3	4	2022	8	7	3,256.24	3,613.85
2022	3	4	2022	9	8	3,123.72	3,506.88
2022	3	4	2022	10	9	3,494.57	2,894.91
2022	3	4	2022	11	10	3,665.44	2,818.28
2022	3	4	2022	12	11	3,946.23	3,105.49
2022	3	4	2022	13	12	3,801.13	3,436.77
2022	3	4	2022	14	13	4,145.82	3,608.90
2022	3	4	2022	15	14	4,193.16	3,579.46
2022	3	4	2022	16	15	3,660.22	3,740.13
2022	3	4	2022	17	16	3,764.65	3,778.65
2022	3	4	2022	18	17	3,819.29	3,409.57
2022	3	4	2022	19	18	3,546.83	3,455.49
2022	3	4	2022	20	19	4,045.83	3,596.81
2022	3	4	2022	21	20	4,197.98	3,244.33
2022	3	4	2022	22	21	3,476.33	3,635.28
2022	3	4	2022	23	22	3,451.32	3,780.78
2022	3	4	2022	24	23	3,513.11	3,002.59
2022	3	4	2022	25	24	3,769.57	3,064.38
2022	3	4	2022	26	25	3,588.74	3,116.02
2022	3	4	2022	27	26	4,063.67	3,503.90
2022	3	4	2022	28	27	4,319.61	3,308.17
2022	3	4	2022	29	28	4,127.35	3,703.07
2022	3	4	2022	30	29	4,143.08	3,796.24
2022	3	4	2022	31	30	4,084.32	3,711.78

[ballardw]

An example of what the expected output given a set of conditions for at least some of that data would help.

[luboxing]

Thanks for looking into it, Ballardw! Sure -- for example, if I pick

1/14/2022 as begining day for January, implying 1/13/2022 as ending day

MWE = 2875.82

2/12/2022 as begining day for February, implying 2/11/2022 as ending day

MWB = 2849.19 and MWE = 3120.61

3/9/2022 as begining day for March, implying 3/8/2022 as ending day

MWB = 3123.72

So the total distance is (2849.19-2875.82)**2 + (3123.72-3120.61)**2 = 718.829 and is the optima (min).