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luboxing
Obsidian | Level 7

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
2 REPLIES 2
ballardw
Super User

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

luboxing
Obsidian | Level 7

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).

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