Given the following formula



with the table below encode the relationship of `x_0`, `x_1` and `r` for Objective 2':





For objective 2, we can code it as following with Docplex, where we have either 0 or 1 for priority `p`.

CPriorityInFreight = mdl.binary_var_matrix(catPriorities, freights, name='CPriorityInFreight')
FreightMixture = mdl.binary_var_dict(freights, name='FreightMixture')
for p in catPriorities:
for f in freights:
# CPriorityInFreight[c, f] = 1 <-> priority c is in freight f
CPriorityInFreight[p, f] = (
1 <= mdl.sum(Assignment[o, f] for o in orders if get_order(o).CategoryPriority == p))

for f in freights:
# sums == 2 <-> we have both cat 0 and cat 1
FreightMixture[f] = (2 == mdl.sum(CPriorityInFreight[c, f] for c in catPriorities))


o2 = mdl.sum(FreightMixture[f] for f in freights)


In Objective 2', we now have the following code for decision variable declaration (with `FreightMixture` containing value `0,1,2`) and first formula

CPriorityInFreight = mdl.binary_var_matrix(catPriorities, freights, name='CPriorityInFreight')
FreightMixture = mdl.integer_var_dict(freights, name='FreightMixture')
for p in catPriorities:
for f in freights:
# CPriorityInFreight[c, f] = 1 <-> priority c is in freight f
CPriorityInFreight[p, f] = (
1 <= mdl.sum(Assignment[o, f] for o in orders if get_order(o).CategoryPriority == p))


But how do we translate these relationship on second formula of Objective 2' into Docplex?

(Of course if there are simpler way to achieve semantically equivalent formulas with Objective 2', feel free to suggest)

#DecisionOptimization

Hi,

similar question at https://stackoverflow.com/questions/72947402/logical-formula-in-docplex/72948601#72948601

from docplex.mp.model import Model

mdl = Model(name='logical')

x = mdl.binary_var(name='x')
y = mdl.binary_var(name='y')
obj= mdl.integer_var(name='obj')

R=[[0,0],[2,1]]


decisionVars=[x,y,obj]

for i in range(0,2):
    for j in range(0,2):
        mdl.add_constraint(mdl.if_then((x==i)+(y==j)==2,(obj==R[i][j])))
            

mdl.maximize(obj)

mdl.solve()

for v in decisionVars:
    print(v.name," = ",int(v.solution_value))​

gives

x  =  1
y  =  0
obj  =  2

------------------------------
[Alex] [Fleischer]
[Data and AI Technical Sales]
[IBM]
------------------------------

Original Message:
Sent: Tue July 12, 2022 01:40 AM
From: Jack Tan
Subject: Logical formula in docplex

Given the following formula



with the table below encode the relationship of `x_0`, `x_1` and `r` for Objective 2':





For objective 2, we can code it as following with Docplex, where we have either 0 or 1 for priority `p`.

CPriorityInFreight = mdl.binary_var_matrix(catPriorities, freights, name='CPriorityInFreight')
FreightMixture = mdl.binary_var_dict(freights, name='FreightMixture')
for p in catPriorities:
for f in freights:
# CPriorityInFreight[c, f] = 1 <-> priority c is in freight f
CPriorityInFreight[p, f] = (
1 <= mdl.sum(Assignment[o, f] for o in orders if get_order(o).CategoryPriority == p))

for f in freights:
# sums == 2 <-> we have both cat 0 and cat 1
FreightMixture[f] = (2 == mdl.sum(CPriorityInFreight[c, f] for c in catPriorities))


o2 = mdl.sum(FreightMixture[f] for f in freights)


In Objective 2', we now have the following code for decision variable declaration (with `FreightMixture` containing value `0,1,2`) and first formula

CPriorityInFreight = mdl.binary_var_matrix(catPriorities, freights, name='CPriorityInFreight')
FreightMixture = mdl.integer_var_dict(freights, name='FreightMixture')
for p in catPriorities:
for f in freights:
# CPriorityInFreight[c, f] = 1 <-> priority c is in freight f
CPriorityInFreight[p, f] = (
1 <= mdl.sum(Assignment[o, f] for o in orders if get_order(o).CategoryPriority == p))


But how do we translate these relationship on second formula of Objective 2' into Docplex?

(Of course if there are simpler way to achieve semantically equivalent formulas with Objective 2', feel free to suggest)

#DecisionOptimization