Obsidian | Level 7

Least distance day-matching

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
Super User

Re: Least distance day-matching

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

Obsidian | Level 7

Re: Least distance day-matching

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).

Discussion stats
• 2 replies
• 599 views
• 0 likes
• 2 in conversation