Simultaneous Spacing and Duration Constraints with time gaps in Gekko

Question

I'm trying to simultaneously enforce sequential duration and spacing constraints to vector solution output in Gekko. Normally, this would be fairly straightforward using window logic, but my time array (in weeks) has gaps per the "week" array below (e.g., it goes [13, 14, 17...]).

I was able to get the spacing requirement (s) in weeks to work by looking up the index of the next sequential week using the code below (seems to work for all values of "s"), but I'm unsure how to factor in "d" (the number of consecutive weeks that must be run) into the existing solution (complete reproducible example below).

The general solution output I'm looking for would look like this for s=1 and d=2: [13, 14, 17, 18, 33, 34, 50, 51...]

import numpy as np
import pandas as pd
from gekko import GEKKO
m = GEKKO(remote=False)
m.options.NODES = 3
m.options.IMODE = 3
m.options.MAX_ITER = 1000

lnuc_weeks = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]

min_promo_price = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,3]

max_promo_price = [3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5,3.5, 3.5, 3.5, 3.5, 3.5, 3.5]

base_srp = [3.48, 3.48, 3.48, 3.48, 3.0799, 3.0799, 3.0799, 3.0799,3.0799, 3.0799, 3.0799, 3.0799, 3.0799, 3.0799, 3.0799, 3.0799, 3.0799, 3.0799, 3.0799]

lnuc_min_promo_price = 1.99

lnuc_max_promo_price = 1.99

coeff_fedi = [0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589,0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589, 0.022589]

coeff_feao = [0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995, 0.02929995]

coeff_diso = [0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338, 0.05292338]

sumproduct_base = [0.20560305, 0.24735297, 0.24957423, 0.23155435, 0.23424058,0.2368096 , 0.27567109, 0.27820648, 0.2826393 , 0.28660598, 0.28583971, 0.30238505, 0.31726649, 0.31428312, 0.31073792, 0.29036779, 0.32679041, 0.32156337, 0.24633734]

neg_ln = [[0.14842000515],[0.14842000512],[0.14842000515],[0.14842000512],[-0.10407483058],[0.43676249024],[0.43676249019],[0.43676249024],[0.43676249019],[0.43676249024],[0.43676249019], [0.026284840258],[0.026284840291],[0.026284840258],[0.026284840291], [0.026185109811],[0.026284840258],[0.026284840291],[0.026284840258]]

neg_ln_ppi_coeff = [1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879,1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879, 1.22293879,1.22293879, 1.22293879, 1.22293879, 1.22293879]

base_volume = [124.38, 193.2, 578.72, 183.88, 197.42, 559.01, 67.68, 110.01,60.38, 177.11, 102.65, 66.02, 209.83, 81.22, 250.44, 206.44, 87.99, 298.95, 71.07]

week = pd.Series([13, 14, 17, 18, 19, 26, 28, 33, 34, 35, 39, 42, 45, 46, 47, 48, 50, 51, 52])


n = 19

x1 = m.Array(m.Var,(n), integer=True) #LNUC weeks

i = 0
for xi in x1:
    xi.value = lnuc_weeks[i]
    xi.lower = 0
    xi.upper = lnuc_weeks[i]
    i += 1

x2 = m.Array(m.Var,(n)) #Blended SRP

i = 0
for xi in x2:
    xi.value = 5
    m.Equation(xi >= m.if3((x1[i]) - 0.5, min_promo_price[i], lnuc_min_promo_price))
    m.Equation(xi <= m.if3((x1[i]) - 0.5, max_promo_price[i], lnuc_max_promo_price))
    i += 1
x3 = m.Array(m.Var,(n), integer=True) #F&D
x4 = m.Array(m.Var,(n), integer=True) #FO
x5 = m.Array(m.Var,(n), integer=True) #DO
x6 = m.Array(m.Var,(n), integer=True) #TPR

#Default to F&D
i = 0
for xi in x3:
    xi.value = 1
    xi.lower = 0
    xi.upper = 1
    i += 1

i = 0
for xi in x4:
    xi.value = 0
    xi.lower = 0
    xi.upper = 1
    i += 1

i = 0
for xi in x5:
    xi.value = 0
    xi.lower = 0
    xi.upper = 1
    i += 1

i = 0
for xi in x6:
    xi.value = 0
    xi.lower = 0
    xi.upper = 1
    i += 1

x7 = m.Array(m.Var,(n), integer=True) #Max promos

i = 0
for xi in x7:
    xi.value = 1
    xi.lower = 0
    xi.upper = 1
    i += 1

x = [x1,x2,x3,x4,x5,x6,x7]

neg_ln=[m.Intermediate(-m.log(x[1][i]/base_srp[i])) for i in range(n)]

total_vol_fedi  =[m.Intermediate(coeff_fedi[0]+ sumproduct_base[i] + (neg_ln[i]*neg_ln_ppi_coeff[0])) for i in range(n)]
total_vol_feao  =[m.Intermediate(coeff_feao[0]+ sumproduct_base[i] + (neg_ln[i]*neg_ln_ppi_coeff[0])) for i in range(n)]
total_vol_diso  =[m.Intermediate(coeff_diso[0]+ sumproduct_base[i] + (neg_ln[i]*neg_ln_ppi_coeff[0])) for i in range(n)]
total_vol_tpro  =[m.Intermediate(sumproduct_base[i] + (neg_ln[i]*neg_ln_ppi_coeff[0])) for i in range(n)]

simu_total_volume = [m.Intermediate((
(m.max2(0,base_volume[i]*(m.exp(total_vol_fedi[i])-1)) * x[2][i] +
m.max2(0,base_volume[i]*(m.exp(total_vol_feao[i])-1)) * x[3][i] +
m.max2(0,base_volume[i]*(m.exp(total_vol_diso[i])-1)) * x[4][i] +
m.max2(0,base_volume[i]*(m.exp(total_vol_tpro[i])-1)) * x[5][i]) + base_volume[i]) * x[6][i]) for i in range(n)]


[m.Equation(x3[i] + x4[i] + x5[i] + x6[i] == 1) for i in range(i)]

#Limit max promos
m.Equation(sum(x7)<=10)

#Enforce spacing and duration
d=2
s=1
for s2 in range(1, s+1):
    for i in range(0, n-s2):
        f = week[week == week[i] + s2].index
        if len(f) > 0:
            m.Equation(x7[i] + x7[f[0]]<=1)

m.Maximize(m.sum(simu_total_volume))

m.options.SOLVER=1
m.solve(disp = True)

df = pd.concat([pd.Series(week), pd.Series([i[0] for i in x7]), pd.Series([i[0] for i in simu_total_volume])], axis=1)
df.columns = ['week', 'x7', 'total_volume']
df[df['x7']>0]