cooperative logistics – profit maximization
I need help about this code dealing with a problem of cooperative logistics. I have to maximize profits, that is, demonstrate that with the three carriers together you get a profit greater than the sum of the profits given by the three carriers taken individually. MatLab takes over 30 minutes and gives infeasible. Thank you so much!
clc
clear all
%%%%%%%%%%%%%%%% PARAMETERS %%%%%%%%%%%%%%%%%%%%%
Nr=20; % number of trips
Nc=3; % number of carriers
Vr=22; % number of vehicles
alpha=1; % extra charge on revenue;
cE= 0.2;
beta=0.8;
mu=80;
% dummy quantity
M=1000000;
% data about trips 20
d= [85, 80, 123, 111, 153, 112, 150, 107, 181, 135, 109, 106, 113, 148, 164, 127, 148, 141, 108, 118];
delta=[200, 200, 200, 200, 200, 200, 200, 200, 300, 300, 300, 300, 300, 300, 300, 400, 400, 400, 400, 400];
p=[25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25];
% data about carriers, INVENTATI
I=[3, 3, 3];
cc=[0.8, 1.0, 0.9];
% data about vehicles, 22
T= [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8];
CAP= [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30];
Eempty= [0.3, 0.2, 0.3, 0.3, 0.2, 0.3, 0.3, 0.2, 0.3, 0.2, 0.2, 0.3, 0.2, 0.2, 0.2, 0.2, 0.3, 0.2, 0.2, 0.3, 0.3, 0.2];
Efull= [0.3, 0.4, 0.3, 0.3, 0.3, 0.4, 0.3, 0.4, 0.3, 0.4, 0.4, 0.4, 0.4, 0.4, 0.3, 0.3, 0.3, 0.4, 0.4, 0.3, 0.4, 0.4]; % it is already Efull-Eempty
IsE=[0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]; %1 if the vehicle is electric
Owner= [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3];
% repositioing distances between trips 20×20
eps= [14 16 6 19 26 27 21 10 16 18 29 7 30 27 28 10 8 11 17 10;
27 9 20 11 9 27 22 18 27 14 29 22 5 25 9 21 17 18 11 16;
25 11 10 30 19 14 7 9 19 26 27 22 29 7 12 29 24 7 9 30;
13 16 6 19 7 7 24 5 27 28 6 18 27 9 17 30 24 14 18 10;
22 23 21 13 16 16 25 21 14 8 14 13 18 17 11 7 16 29 6 6;
5 21 9 17 26 30 27 11 24 28 16 6 25 22 27 11 18 30 13 7;
13 11 15 24 20 30 26 11 7 21 7 17 29 5 11 12 22 22 8 5;
28 7 14 20 7 25 20 12 15 5 27 10 5 27 20 26 22 25 14 28;
16 19 11 12 8 25 24 9 26 26 17 15 8 5 20 19 7 21 28 24;
29 8 13 18 17 13 15 12 21 11 10 25 17 29 22 11 28 27 14 13;
10 22 26 16 22 19 7 28 10 14 12 28 27 10 12 6 23 30 28 26;
18 11 15 25 20 7 21 17 21 9 16 5 11 5 18 16 17 26 21 19;
14 15 25 19 11 16 8 25 21 9 11 8 13 5 10 7 5 28 30 8;
26 15 11 19 21 23 9 24 9 26 16 17 9 27 25 27 20 21 15 13;
27 27 14 19 28 9 22 24 18 11 22 15 15 26 27 27 27 19 17 19;
25 11 17 24 6 30 15 23 21 30 16 5 18 25 12 20 9 11 25 27;
29 9 17 11 24 8 29 28 21 16 20 15 6 28 8 22 7 13 26 22;
23 30 28 15 11 20 13 10 25 18 29 13 12 11 16 20 24 11 6 30;
28 23 12 29 16 29 26 22 28 17 20 8 30 22 8 25 12 7 13 9;
7 7 22 11 23 9 17 25 27 26 21 29 23 14 8 6 6 26 24 30];
% 1 if the pair of trips can be combined INVENTATO 20×20
O=[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0];
%O=[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0];
% distances between the depot of vehicle v (column) and
% the origin of trip n (row) 20×22 dati mancanti metto 1000 da 1 a 10
dO= [3 8 4 2 2 4 3 9 3 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
9 3 5 7 8 2 5 9 1 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
8 9 5 1 3 9 5 6 8 5 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 8 2 2 9 2 8 2 7 7 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 6 9 5 6 5 6 3 1 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 5 7 7 4 8 1 5 2 3 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 3 1 5 8 2 6 1 5 2 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 8 7 6 3 7 7 9 1 6 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 8 8 2 7 7 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 7 7 8 2 8 3 9 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 6 7 2 3 3 6 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 6 8 5 4 2 8 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 2 6 5 6 7 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 9 1 2 7 8 8 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 8 9 8 9 8 9 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 8 6 7 9 8;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 5 5 7 9;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 1 8 6 4;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 4 1 3 8;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 8 9 7 3];
% distances between the destination of trip n (row)
% and the depot of vehicle v (column) 20×22 dati mancanti metto 1000 da 1 a 10
dD=[7 5 1 3 9 1 5 2 1 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
7 2 7 3 3 1 5 8 1 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 7 2 5 3 5 8 4 7 8 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
7 7 4 8 3 7 3 1 7 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 1 1 6 7 2 4 9 9 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
6 7 1 1 5 2 4 3 9 5 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
8 7 2 9 5 6 6 5 8 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
6 8 9 7 6 8 2 5 8 8 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 7 7 6 3 9 1 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 9 7 3 6 9 6 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 4 6 6 5 9 9 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 7 7 1 7 2 1 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 6 7 9 8 6 2 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 4 1 5 4 1 3 3 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 6 6 6 4 6 9 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 5 6 7 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 9 9 6 8 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 9 4 6 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 5 4 9 1;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 4 8 6 9 9];
% operative cost 3×22
c=[0.7, 0.8, 0.8, 0.6, 0.9, 0.8, 0.6, 0.9, 0.6, 0.8, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100;
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0.9, 0.8, 0.8, 1, 0.7, 0.7, 0.8, 100, 100, 100, 100, 100;
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0.9, 0.9, 0.6, 0.7, 0.7];
% 1 if the trip (row) is owned by the carrier (column) INVENTATO 20×3
z=[1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
0 1 0;
0 1 0;
0 1 0;
0 1 0;
0 1 0
0 1 0;
0 1 0;
0 0 1;
0 0 1;
0 0 1;
0 0 1;
0 0 1];
% initial profit of carriers INVENTATO dati ottenuti dal prob1 per ciascun
% carrier
S0= [3380 2382 1561];
%S0 = [1000 1000 1000];
TOA=zeros(Nr,Vr);
% computation of TOA(n,v) for single trips;
for n=1:Nr
for v=1:Vr
TOA(n,v) = dO(n,v)+d(n)+dD(n,v);
end
end
E=zeros(Nr,Vr);
% computation of cost E;
for n=1:Nr
for v=1:Vr
E(n,v)= TOA(n,v)*Eempty(v) + (Efull(v)*d(n)*p(n)/CAP(v));
end
end
TOAC=zeros(Nr,Nr,Vr);
% computation of TOAC(n,k,v) for pairs of trips;
for n=1:Nr
for k=1:Nr
for v=1:Vr
TOAC(n,k,v) = dO(n,v)+d(n)+d(k)+eps(n,k)+dD(k,v);
end
end
end
EC=zeros(Nr,Nr,Vr);
% computation of cost E for combined trips;
for n=1:Nr
for k=1:Nr
for v=1:Vr
EC(n,k,v)= TOAC(n,k,v)*Eempty(v) + (Efull(v)*(d(n)*p(n)+d(k)*p(k))/CAP(v));
end
end
end
% % %%%%%%%%%%%%%%%% MAX %%%%%%%%%%%%%%%%%%%%%
%
%TO BE NOTED: I have not included the carrier in decision variables
% because here we are not includeing vehicles in the data structrue related
% to carriers but we are considering the whole list of vehicles
% than we associate vehicles with carriers by using the parameters Owner(v)
% decision variables with lower and upper bounds
x = optimvar(‘x’,Nr,Vr,’Type’,’integer’,’LowerBound’,0, ‘UpperBound’,1);
y = optimvar(‘y’,Nr,Nr,Vr,’Type’,’integer’,’LowerBound’,0, ‘UpperBound’,1);
% problema definition
prob = optimproblem(‘ObjectiveSense’,’max’);
% objective function computation
obj=0;
% %profit S1 of carriers;
for r=1:Nc
for n=1:Nr
for v=1:Vr
if (Owner(v) == r)
obj=obj+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*x(n,v);
end
end
end
end
%
%profit S2 of carriers;
for r=1:Nc
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (Owner(v) == r)
obj= obj+ (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*y(n,k,v);
end
end
end
end
end
end
%profit S3 of carriers;
for r=1:Nc
%compensation profits and costs for single trips
for n=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
obj=obj+ delta(n)*z(n,r)*x(n,v);
else
if (Owner(v) == r)
obj=obj- delta(n)*z(n,rr)*x(n,v);
end
end
end
end
end
end
%compensation profits and costs for combined trips
for n=1:Nr
for k=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
obj = obj+ y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
else
if (Owner(v) == r)
obj = obj- y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
end
end
end
end
end
end
end
end
%
prob.Objective = obj;
%%% CONSTRAINTS
% profits higher than initial profits
constr_profit = optimineq(Nc,1);
%
for r=1:Nc
S=0;
%S1 computation
for n=1:Nr
for v=1:Vr
if (Owner(v) == r)
S=S+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*x(n,v);
end
end
end
%S2 computation
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (Owner(v) == r)
S= S + (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*y(n,k,v);
end
end
end
end
end
% S3 computation;
%compensation profits and costs for single trips
for n=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
S=S+ delta(n)*z(n,r)*x(n,v);
else
if (Owner(v) == r)
S=S- delta(n)*z(n,rr)*x(n,v);
end
end
end
end
end
end
%compensation profits and costs for combined trips
for n=1:Nr
for k=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
S = S+ y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
else
if (Owner(v) == r)
S = S- y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
end
end
end
end
end
end
end
constr_profit(r)=S>=S0(r);
end
prob.Constraints.constr_profit = constr_profit;
% all demand is executed (14);
constr_demand_sat=optimeq(1,1);
%
for n=1:Nr
temp=0;
for v=1:Vr
temp=temp+x(n,v);
for k=1:Nr
if (k ~= n)
temp=temp+y(n,k,v)+y(k,n,v);
end
end
end
constr_demand_sat(n)=temp==1;
end
prob.Constraints.constr_demand_sat = constr_demand_sat;
% Every vehicle must be assigned to at most one trip;
constr_assign=optimineq(Vr,1);
for v=1:Vr
temp=0;
for n=1:Nr
temp=temp+x(n,v);
for k=1:Nr
if (k ~= n)
temp=temp+y(n,k,v);
end
end
end
constr_assign(v)=temp<=1;
end
prob.Constraints.constr_assign = constr_assign;
% duration of the batteries of electric trucks;
constr_batteries_single=optimineq(Nr,Vr);
for n=1:Nr
for v=1:Vr
if (IsE(v) == 1)
constr_batteries_single(n,v)=x(n,v)*TOA(n,v)<=T(v)*mu;
else
constr_batteries_single(n,v)=x(n,v)*TOA(n,v)<=M;
end
end
end
prob.Constraints.constr_batteries_single = constr_batteries_single;
constr_batteries_combined=optimineq(Nr,Nr,Vr);
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (IsE(v) == 1)
constr_batteries_combined(n,k,v)=y(n,k,v)*TOAC(n,k,v)<=T(v)*mu;
else
constr_batteries_combined(n,k,v)=y(n,k,v)*TOAC(n,k,v)<=M;
end
end
end
end
end
prob.Constraints.constr_batteries_combined = constr_batteries_combined;
% constraints on trips combination;
constr_combined=optimineq(Nr,Nr,Vr,1);
for n=1:Nr
for k=1:Nr
for v=1:Vr
constr_combined(n,k,v)=y(n,k,v)<=O(n,k);
end
end
end
prob.Constraints.constr_combined = constr_combined;
%
% % problem solution
show(prob)
[sol,val] = solve(prob);
% retrieve of optimal values
opt_variables_x=sol.x;
opt_variables_y=sol.y;
opt_obj=val;
% profits higher than initial profits
% %SS=zeros(Nc,1);
% %for r=1:Nc
% SS(r)=0;
% %S1 computation
% for n=1:Nr
% for v=1:Vr
% if (Owner(v) == r)
% SS(r)=SS(r)+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*sol.x(n,v);
% end
% end
% end
%
%
% %S2 computation
% for n=1:Nr
% for k=1:Nr
% if (k ~= n)
% for v=1:Vr
% if (Owner(v) == r)
% SS(r)= SS(r) + (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*sol.y(n,k,v);
% end
% end
% end
% end
% end
%
%
% % S3 computation;
%
% %compensation profits and costs for single trips
% for n=1:Nr
% for rr=1:Nc
% if (rr ~= r)
% for v=1:Vr
% if (Owner(v) == rr)
% SS(r)=SS(r)+ delta(n)*z(n,r)*sol.x(n,v);
% else
% if (Owner(v) == r)
% SS(r)=SS(r)- delta(n)*z(n,rr)*sol.x(n,v);
% end
% end
% end
% end
% end
% end
% %compensation profits and costs for combined trips
% for n=1:Nr
% for k=1:Nr
% for rr=1:Nc
% if (rr ~= r)
% for v=1:Vr
% if (Owner(v) == rr)
% SS(r) = SS(r)+ sol.y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
% else
% if (Owner(v) == r)
% SS(r) = SS(r)- sol.y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
% end
% end
% end
% end
% end
% end
% end
%
% y2=0;
% for i=1:Nr
% for v=1:Vr
% y2=y2+opt_variables_y(i,2,v)+opt_variables_y(2,i,v);
% end;
% end;
%
% end
—-I need help about this code dealing with a problem of cooperative logistics. I have to maximize profits, that is, demonstrate that with the three carriers together you get a profit greater than the sum of the profits given by the three carriers taken individually. MatLab takes over 30 minutes and gives infeasible. Thank you so much!
clc
clear all
%%%%%%%%%%%%%%%% PARAMETERS %%%%%%%%%%%%%%%%%%%%%
Nr=20; % number of trips
Nc=3; % number of carriers
Vr=22; % number of vehicles
alpha=1; % extra charge on revenue;
cE= 0.2;
beta=0.8;
mu=80;
% dummy quantity
M=1000000;
% data about trips 20
d= [85, 80, 123, 111, 153, 112, 150, 107, 181, 135, 109, 106, 113, 148, 164, 127, 148, 141, 108, 118];
delta=[200, 200, 200, 200, 200, 200, 200, 200, 300, 300, 300, 300, 300, 300, 300, 400, 400, 400, 400, 400];
p=[25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25];
% data about carriers, INVENTATI
I=[3, 3, 3];
cc=[0.8, 1.0, 0.9];
% data about vehicles, 22
T= [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8];
CAP= [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30];
Eempty= [0.3, 0.2, 0.3, 0.3, 0.2, 0.3, 0.3, 0.2, 0.3, 0.2, 0.2, 0.3, 0.2, 0.2, 0.2, 0.2, 0.3, 0.2, 0.2, 0.3, 0.3, 0.2];
Efull= [0.3, 0.4, 0.3, 0.3, 0.3, 0.4, 0.3, 0.4, 0.3, 0.4, 0.4, 0.4, 0.4, 0.4, 0.3, 0.3, 0.3, 0.4, 0.4, 0.3, 0.4, 0.4]; % it is already Efull-Eempty
IsE=[0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]; %1 if the vehicle is electric
Owner= [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3];
% repositioing distances between trips 20×20
eps= [14 16 6 19 26 27 21 10 16 18 29 7 30 27 28 10 8 11 17 10;
27 9 20 11 9 27 22 18 27 14 29 22 5 25 9 21 17 18 11 16;
25 11 10 30 19 14 7 9 19 26 27 22 29 7 12 29 24 7 9 30;
13 16 6 19 7 7 24 5 27 28 6 18 27 9 17 30 24 14 18 10;
22 23 21 13 16 16 25 21 14 8 14 13 18 17 11 7 16 29 6 6;
5 21 9 17 26 30 27 11 24 28 16 6 25 22 27 11 18 30 13 7;
13 11 15 24 20 30 26 11 7 21 7 17 29 5 11 12 22 22 8 5;
28 7 14 20 7 25 20 12 15 5 27 10 5 27 20 26 22 25 14 28;
16 19 11 12 8 25 24 9 26 26 17 15 8 5 20 19 7 21 28 24;
29 8 13 18 17 13 15 12 21 11 10 25 17 29 22 11 28 27 14 13;
10 22 26 16 22 19 7 28 10 14 12 28 27 10 12 6 23 30 28 26;
18 11 15 25 20 7 21 17 21 9 16 5 11 5 18 16 17 26 21 19;
14 15 25 19 11 16 8 25 21 9 11 8 13 5 10 7 5 28 30 8;
26 15 11 19 21 23 9 24 9 26 16 17 9 27 25 27 20 21 15 13;
27 27 14 19 28 9 22 24 18 11 22 15 15 26 27 27 27 19 17 19;
25 11 17 24 6 30 15 23 21 30 16 5 18 25 12 20 9 11 25 27;
29 9 17 11 24 8 29 28 21 16 20 15 6 28 8 22 7 13 26 22;
23 30 28 15 11 20 13 10 25 18 29 13 12 11 16 20 24 11 6 30;
28 23 12 29 16 29 26 22 28 17 20 8 30 22 8 25 12 7 13 9;
7 7 22 11 23 9 17 25 27 26 21 29 23 14 8 6 6 26 24 30];
% 1 if the pair of trips can be combined INVENTATO 20×20
O=[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0];
%O=[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0];
% distances between the depot of vehicle v (column) and
% the origin of trip n (row) 20×22 dati mancanti metto 1000 da 1 a 10
dO= [3 8 4 2 2 4 3 9 3 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
9 3 5 7 8 2 5 9 1 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
8 9 5 1 3 9 5 6 8 5 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 8 2 2 9 2 8 2 7 7 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 6 9 5 6 5 6 3 1 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 5 7 7 4 8 1 5 2 3 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 3 1 5 8 2 6 1 5 2 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 8 7 6 3 7 7 9 1 6 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 8 8 2 7 7 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 7 7 8 2 8 3 9 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 6 7 2 3 3 6 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 6 8 5 4 2 8 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 2 6 5 6 7 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 9 1 2 7 8 8 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 8 9 8 9 8 9 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 8 6 7 9 8;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 5 5 7 9;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 1 8 6 4;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 4 1 3 8;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 8 9 7 3];
% distances between the destination of trip n (row)
% and the depot of vehicle v (column) 20×22 dati mancanti metto 1000 da 1 a 10
dD=[7 5 1 3 9 1 5 2 1 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
7 2 7 3 3 1 5 8 1 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 7 2 5 3 5 8 4 7 8 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
7 7 4 8 3 7 3 1 7 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 1 1 6 7 2 4 9 9 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
6 7 1 1 5 2 4 3 9 5 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
8 7 2 9 5 6 6 5 8 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
6 8 9 7 6 8 2 5 8 8 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 7 7 6 3 9 1 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 9 7 3 6 9 6 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 4 6 6 5 9 9 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 7 7 1 7 2 1 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 6 7 9 8 6 2 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 4 1 5 4 1 3 3 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 6 6 6 4 6 9 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 5 6 7 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 9 9 6 8 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 9 4 6 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 5 4 9 1;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 4 8 6 9 9];
% operative cost 3×22
c=[0.7, 0.8, 0.8, 0.6, 0.9, 0.8, 0.6, 0.9, 0.6, 0.8, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100;
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0.9, 0.8, 0.8, 1, 0.7, 0.7, 0.8, 100, 100, 100, 100, 100;
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0.9, 0.9, 0.6, 0.7, 0.7];
% 1 if the trip (row) is owned by the carrier (column) INVENTATO 20×3
z=[1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
0 1 0;
0 1 0;
0 1 0;
0 1 0;
0 1 0
0 1 0;
0 1 0;
0 0 1;
0 0 1;
0 0 1;
0 0 1;
0 0 1];
% initial profit of carriers INVENTATO dati ottenuti dal prob1 per ciascun
% carrier
S0= [3380 2382 1561];
%S0 = [1000 1000 1000];
TOA=zeros(Nr,Vr);
% computation of TOA(n,v) for single trips;
for n=1:Nr
for v=1:Vr
TOA(n,v) = dO(n,v)+d(n)+dD(n,v);
end
end
E=zeros(Nr,Vr);
% computation of cost E;
for n=1:Nr
for v=1:Vr
E(n,v)= TOA(n,v)*Eempty(v) + (Efull(v)*d(n)*p(n)/CAP(v));
end
end
TOAC=zeros(Nr,Nr,Vr);
% computation of TOAC(n,k,v) for pairs of trips;
for n=1:Nr
for k=1:Nr
for v=1:Vr
TOAC(n,k,v) = dO(n,v)+d(n)+d(k)+eps(n,k)+dD(k,v);
end
end
end
EC=zeros(Nr,Nr,Vr);
% computation of cost E for combined trips;
for n=1:Nr
for k=1:Nr
for v=1:Vr
EC(n,k,v)= TOAC(n,k,v)*Eempty(v) + (Efull(v)*(d(n)*p(n)+d(k)*p(k))/CAP(v));
end
end
end
% % %%%%%%%%%%%%%%%% MAX %%%%%%%%%%%%%%%%%%%%%
%
%TO BE NOTED: I have not included the carrier in decision variables
% because here we are not includeing vehicles in the data structrue related
% to carriers but we are considering the whole list of vehicles
% than we associate vehicles with carriers by using the parameters Owner(v)
% decision variables with lower and upper bounds
x = optimvar(‘x’,Nr,Vr,’Type’,’integer’,’LowerBound’,0, ‘UpperBound’,1);
y = optimvar(‘y’,Nr,Nr,Vr,’Type’,’integer’,’LowerBound’,0, ‘UpperBound’,1);
% problema definition
prob = optimproblem(‘ObjectiveSense’,’max’);
% objective function computation
obj=0;
% %profit S1 of carriers;
for r=1:Nc
for n=1:Nr
for v=1:Vr
if (Owner(v) == r)
obj=obj+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*x(n,v);
end
end
end
end
%
%profit S2 of carriers;
for r=1:Nc
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (Owner(v) == r)
obj= obj+ (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*y(n,k,v);
end
end
end
end
end
end
%profit S3 of carriers;
for r=1:Nc
%compensation profits and costs for single trips
for n=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
obj=obj+ delta(n)*z(n,r)*x(n,v);
else
if (Owner(v) == r)
obj=obj- delta(n)*z(n,rr)*x(n,v);
end
end
end
end
end
end
%compensation profits and costs for combined trips
for n=1:Nr
for k=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
obj = obj+ y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
else
if (Owner(v) == r)
obj = obj- y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
end
end
end
end
end
end
end
end
%
prob.Objective = obj;
%%% CONSTRAINTS
% profits higher than initial profits
constr_profit = optimineq(Nc,1);
%
for r=1:Nc
S=0;
%S1 computation
for n=1:Nr
for v=1:Vr
if (Owner(v) == r)
S=S+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*x(n,v);
end
end
end
%S2 computation
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (Owner(v) == r)
S= S + (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*y(n,k,v);
end
end
end
end
end
% S3 computation;
%compensation profits and costs for single trips
for n=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
S=S+ delta(n)*z(n,r)*x(n,v);
else
if (Owner(v) == r)
S=S- delta(n)*z(n,rr)*x(n,v);
end
end
end
end
end
end
%compensation profits and costs for combined trips
for n=1:Nr
for k=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
S = S+ y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
else
if (Owner(v) == r)
S = S- y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
end
end
end
end
end
end
end
constr_profit(r)=S>=S0(r);
end
prob.Constraints.constr_profit = constr_profit;
% all demand is executed (14);
constr_demand_sat=optimeq(1,1);
%
for n=1:Nr
temp=0;
for v=1:Vr
temp=temp+x(n,v);
for k=1:Nr
if (k ~= n)
temp=temp+y(n,k,v)+y(k,n,v);
end
end
end
constr_demand_sat(n)=temp==1;
end
prob.Constraints.constr_demand_sat = constr_demand_sat;
% Every vehicle must be assigned to at most one trip;
constr_assign=optimineq(Vr,1);
for v=1:Vr
temp=0;
for n=1:Nr
temp=temp+x(n,v);
for k=1:Nr
if (k ~= n)
temp=temp+y(n,k,v);
end
end
end
constr_assign(v)=temp<=1;
end
prob.Constraints.constr_assign = constr_assign;
% duration of the batteries of electric trucks;
constr_batteries_single=optimineq(Nr,Vr);
for n=1:Nr
for v=1:Vr
if (IsE(v) == 1)
constr_batteries_single(n,v)=x(n,v)*TOA(n,v)<=T(v)*mu;
else
constr_batteries_single(n,v)=x(n,v)*TOA(n,v)<=M;
end
end
end
prob.Constraints.constr_batteries_single = constr_batteries_single;
constr_batteries_combined=optimineq(Nr,Nr,Vr);
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (IsE(v) == 1)
constr_batteries_combined(n,k,v)=y(n,k,v)*TOAC(n,k,v)<=T(v)*mu;
else
constr_batteries_combined(n,k,v)=y(n,k,v)*TOAC(n,k,v)<=M;
end
end
end
end
end
prob.Constraints.constr_batteries_combined = constr_batteries_combined;
% constraints on trips combination;
constr_combined=optimineq(Nr,Nr,Vr,1);
for n=1:Nr
for k=1:Nr
for v=1:Vr
constr_combined(n,k,v)=y(n,k,v)<=O(n,k);
end
end
end
prob.Constraints.constr_combined = constr_combined;
%
% % problem solution
show(prob)
[sol,val] = solve(prob);
% retrieve of optimal values
opt_variables_x=sol.x;
opt_variables_y=sol.y;
opt_obj=val;
% profits higher than initial profits
% %SS=zeros(Nc,1);
% %for r=1:Nc
% SS(r)=0;
% %S1 computation
% for n=1:Nr
% for v=1:Vr
% if (Owner(v) == r)
% SS(r)=SS(r)+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*sol.x(n,v);
% end
% end
% end
%
%
% %S2 computation
% for n=1:Nr
% for k=1:Nr
% if (k ~= n)
% for v=1:Vr
% if (Owner(v) == r)
% SS(r)= SS(r) + (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*sol.y(n,k,v);
% end
% end
% end
% end
% end
%
%
% % S3 computation;
%
% %compensation profits and costs for single trips
% for n=1:Nr
% for rr=1:Nc
% if (rr ~= r)
% for v=1:Vr
% if (Owner(v) == rr)
% SS(r)=SS(r)+ delta(n)*z(n,r)*sol.x(n,v);
% else
% if (Owner(v) == r)
% SS(r)=SS(r)- delta(n)*z(n,rr)*sol.x(n,v);
% end
% end
% end
% end
% end
% end
% %compensation profits and costs for combined trips
% for n=1:Nr
% for k=1:Nr
% for rr=1:Nc
% if (rr ~= r)
% for v=1:Vr
% if (Owner(v) == rr)
% SS(r) = SS(r)+ sol.y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
% else
% if (Owner(v) == r)
% SS(r) = SS(r)- sol.y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
% end
% end
% end
% end
% end
% end
% end
%
% y2=0;
% for i=1:Nr
% for v=1:Vr
% y2=y2+opt_variables_y(i,2,v)+opt_variables_y(2,i,v);
% end;
% end;
%
% end
—- I need help about this code dealing with a problem of cooperative logistics. I have to maximize profits, that is, demonstrate that with the three carriers together you get a profit greater than the sum of the profits given by the three carriers taken individually. MatLab takes over 30 minutes and gives infeasible. Thank you so much!
clc
clear all
%%%%%%%%%%%%%%%% PARAMETERS %%%%%%%%%%%%%%%%%%%%%
Nr=20; % number of trips
Nc=3; % number of carriers
Vr=22; % number of vehicles
alpha=1; % extra charge on revenue;
cE= 0.2;
beta=0.8;
mu=80;
% dummy quantity
M=1000000;
% data about trips 20
d= [85, 80, 123, 111, 153, 112, 150, 107, 181, 135, 109, 106, 113, 148, 164, 127, 148, 141, 108, 118];
delta=[200, 200, 200, 200, 200, 200, 200, 200, 300, 300, 300, 300, 300, 300, 300, 400, 400, 400, 400, 400];
p=[25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25];
% data about carriers, INVENTATI
I=[3, 3, 3];
cc=[0.8, 1.0, 0.9];
% data about vehicles, 22
T= [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8];
CAP= [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30];
Eempty= [0.3, 0.2, 0.3, 0.3, 0.2, 0.3, 0.3, 0.2, 0.3, 0.2, 0.2, 0.3, 0.2, 0.2, 0.2, 0.2, 0.3, 0.2, 0.2, 0.3, 0.3, 0.2];
Efull= [0.3, 0.4, 0.3, 0.3, 0.3, 0.4, 0.3, 0.4, 0.3, 0.4, 0.4, 0.4, 0.4, 0.4, 0.3, 0.3, 0.3, 0.4, 0.4, 0.3, 0.4, 0.4]; % it is already Efull-Eempty
IsE=[0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]; %1 if the vehicle is electric
Owner= [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3];
% repositioing distances between trips 20×20
eps= [14 16 6 19 26 27 21 10 16 18 29 7 30 27 28 10 8 11 17 10;
27 9 20 11 9 27 22 18 27 14 29 22 5 25 9 21 17 18 11 16;
25 11 10 30 19 14 7 9 19 26 27 22 29 7 12 29 24 7 9 30;
13 16 6 19 7 7 24 5 27 28 6 18 27 9 17 30 24 14 18 10;
22 23 21 13 16 16 25 21 14 8 14 13 18 17 11 7 16 29 6 6;
5 21 9 17 26 30 27 11 24 28 16 6 25 22 27 11 18 30 13 7;
13 11 15 24 20 30 26 11 7 21 7 17 29 5 11 12 22 22 8 5;
28 7 14 20 7 25 20 12 15 5 27 10 5 27 20 26 22 25 14 28;
16 19 11 12 8 25 24 9 26 26 17 15 8 5 20 19 7 21 28 24;
29 8 13 18 17 13 15 12 21 11 10 25 17 29 22 11 28 27 14 13;
10 22 26 16 22 19 7 28 10 14 12 28 27 10 12 6 23 30 28 26;
18 11 15 25 20 7 21 17 21 9 16 5 11 5 18 16 17 26 21 19;
14 15 25 19 11 16 8 25 21 9 11 8 13 5 10 7 5 28 30 8;
26 15 11 19 21 23 9 24 9 26 16 17 9 27 25 27 20 21 15 13;
27 27 14 19 28 9 22 24 18 11 22 15 15 26 27 27 27 19 17 19;
25 11 17 24 6 30 15 23 21 30 16 5 18 25 12 20 9 11 25 27;
29 9 17 11 24 8 29 28 21 16 20 15 6 28 8 22 7 13 26 22;
23 30 28 15 11 20 13 10 25 18 29 13 12 11 16 20 24 11 6 30;
28 23 12 29 16 29 26 22 28 17 20 8 30 22 8 25 12 7 13 9;
7 7 22 11 23 9 17 25 27 26 21 29 23 14 8 6 6 26 24 30];
% 1 if the pair of trips can be combined INVENTATO 20×20
O=[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0];
%O=[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1;
%1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0];
% distances between the depot of vehicle v (column) and
% the origin of trip n (row) 20×22 dati mancanti metto 1000 da 1 a 10
dO= [3 8 4 2 2 4 3 9 3 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
9 3 5 7 8 2 5 9 1 4 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
8 9 5 1 3 9 5 6 8 5 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 8 2 2 9 2 8 2 7 7 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 6 9 5 6 5 6 3 1 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 5 7 7 4 8 1 5 2 3 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 3 1 5 8 2 6 1 5 2 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 8 7 6 3 7 7 9 1 6 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 8 8 2 7 7 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 7 7 8 2 8 3 9 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 6 7 2 3 3 6 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 6 8 5 4 2 8 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 2 6 5 6 7 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 9 1 2 7 8 8 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 8 9 8 9 8 9 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 8 6 7 9 8;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 5 5 7 9;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 1 8 6 4;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 4 1 3 8;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 8 9 7 3];
% distances between the destination of trip n (row)
% and the depot of vehicle v (column) 20×22 dati mancanti metto 1000 da 1 a 10
dD=[7 5 1 3 9 1 5 2 1 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
7 2 7 3 3 1 5 8 1 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1 7 2 5 3 5 8 4 7 8 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
7 7 4 8 3 7 3 1 7 1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
5 1 1 6 7 2 4 9 9 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
6 7 1 1 5 2 4 3 9 5 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
8 7 2 9 5 6 6 5 8 9 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
6 8 9 7 6 8 2 5 8 8 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 7 7 6 3 9 1 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 9 7 3 6 9 6 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3 4 6 6 5 9 9 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 7 7 1 7 2 1 7 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 6 7 9 8 6 2 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 4 1 5 4 1 3 3 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 6 6 6 4 6 9 5 1000 1000 1000 1000 1000;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1 5 6 7 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 9 9 6 8 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2 9 4 6 2;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 5 5 4 9 1;
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 4 8 6 9 9];
% operative cost 3×22
c=[0.7, 0.8, 0.8, 0.6, 0.9, 0.8, 0.6, 0.9, 0.6, 0.8, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100;
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0.9, 0.8, 0.8, 1, 0.7, 0.7, 0.8, 100, 100, 100, 100, 100;
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0.9, 0.9, 0.6, 0.7, 0.7];
% 1 if the trip (row) is owned by the carrier (column) INVENTATO 20×3
z=[1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
1 0 0;
0 1 0;
0 1 0;
0 1 0;
0 1 0;
0 1 0
0 1 0;
0 1 0;
0 0 1;
0 0 1;
0 0 1;
0 0 1;
0 0 1];
% initial profit of carriers INVENTATO dati ottenuti dal prob1 per ciascun
% carrier
S0= [3380 2382 1561];
%S0 = [1000 1000 1000];
TOA=zeros(Nr,Vr);
% computation of TOA(n,v) for single trips;
for n=1:Nr
for v=1:Vr
TOA(n,v) = dO(n,v)+d(n)+dD(n,v);
end
end
E=zeros(Nr,Vr);
% computation of cost E;
for n=1:Nr
for v=1:Vr
E(n,v)= TOA(n,v)*Eempty(v) + (Efull(v)*d(n)*p(n)/CAP(v));
end
end
TOAC=zeros(Nr,Nr,Vr);
% computation of TOAC(n,k,v) for pairs of trips;
for n=1:Nr
for k=1:Nr
for v=1:Vr
TOAC(n,k,v) = dO(n,v)+d(n)+d(k)+eps(n,k)+dD(k,v);
end
end
end
EC=zeros(Nr,Nr,Vr);
% computation of cost E for combined trips;
for n=1:Nr
for k=1:Nr
for v=1:Vr
EC(n,k,v)= TOAC(n,k,v)*Eempty(v) + (Efull(v)*(d(n)*p(n)+d(k)*p(k))/CAP(v));
end
end
end
% % %%%%%%%%%%%%%%%% MAX %%%%%%%%%%%%%%%%%%%%%
%
%TO BE NOTED: I have not included the carrier in decision variables
% because here we are not includeing vehicles in the data structrue related
% to carriers but we are considering the whole list of vehicles
% than we associate vehicles with carriers by using the parameters Owner(v)
% decision variables with lower and upper bounds
x = optimvar(‘x’,Nr,Vr,’Type’,’integer’,’LowerBound’,0, ‘UpperBound’,1);
y = optimvar(‘y’,Nr,Nr,Vr,’Type’,’integer’,’LowerBound’,0, ‘UpperBound’,1);
% problema definition
prob = optimproblem(‘ObjectiveSense’,’max’);
% objective function computation
obj=0;
% %profit S1 of carriers;
for r=1:Nc
for n=1:Nr
for v=1:Vr
if (Owner(v) == r)
obj=obj+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*x(n,v);
end
end
end
end
%
%profit S2 of carriers;
for r=1:Nc
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (Owner(v) == r)
obj= obj+ (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*y(n,k,v);
end
end
end
end
end
end
%profit S3 of carriers;
for r=1:Nc
%compensation profits and costs for single trips
for n=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
obj=obj+ delta(n)*z(n,r)*x(n,v);
else
if (Owner(v) == r)
obj=obj- delta(n)*z(n,rr)*x(n,v);
end
end
end
end
end
end
%compensation profits and costs for combined trips
for n=1:Nr
for k=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
obj = obj+ y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
else
if (Owner(v) == r)
obj = obj- y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
end
end
end
end
end
end
end
end
%
prob.Objective = obj;
%%% CONSTRAINTS
% profits higher than initial profits
constr_profit = optimineq(Nc,1);
%
for r=1:Nc
S=0;
%S1 computation
for n=1:Nr
for v=1:Vr
if (Owner(v) == r)
S=S+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*x(n,v);
end
end
end
%S2 computation
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (Owner(v) == r)
S= S + (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*y(n,k,v);
end
end
end
end
end
% S3 computation;
%compensation profits and costs for single trips
for n=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
S=S+ delta(n)*z(n,r)*x(n,v);
else
if (Owner(v) == r)
S=S- delta(n)*z(n,rr)*x(n,v);
end
end
end
end
end
end
%compensation profits and costs for combined trips
for n=1:Nr
for k=1:Nr
for rr=1:Nc
if (rr ~= r)
for v=1:Vr
if (Owner(v) == rr)
S = S+ y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
else
if (Owner(v) == r)
S = S- y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
end
end
end
end
end
end
end
constr_profit(r)=S>=S0(r);
end
prob.Constraints.constr_profit = constr_profit;
% all demand is executed (14);
constr_demand_sat=optimeq(1,1);
%
for n=1:Nr
temp=0;
for v=1:Vr
temp=temp+x(n,v);
for k=1:Nr
if (k ~= n)
temp=temp+y(n,k,v)+y(k,n,v);
end
end
end
constr_demand_sat(n)=temp==1;
end
prob.Constraints.constr_demand_sat = constr_demand_sat;
% Every vehicle must be assigned to at most one trip;
constr_assign=optimineq(Vr,1);
for v=1:Vr
temp=0;
for n=1:Nr
temp=temp+x(n,v);
for k=1:Nr
if (k ~= n)
temp=temp+y(n,k,v);
end
end
end
constr_assign(v)=temp<=1;
end
prob.Constraints.constr_assign = constr_assign;
% duration of the batteries of electric trucks;
constr_batteries_single=optimineq(Nr,Vr);
for n=1:Nr
for v=1:Vr
if (IsE(v) == 1)
constr_batteries_single(n,v)=x(n,v)*TOA(n,v)<=T(v)*mu;
else
constr_batteries_single(n,v)=x(n,v)*TOA(n,v)<=M;
end
end
end
prob.Constraints.constr_batteries_single = constr_batteries_single;
constr_batteries_combined=optimineq(Nr,Nr,Vr);
for n=1:Nr
for k=1:Nr
if (k ~= n)
for v=1:Vr
if (IsE(v) == 1)
constr_batteries_combined(n,k,v)=y(n,k,v)*TOAC(n,k,v)<=T(v)*mu;
else
constr_batteries_combined(n,k,v)=y(n,k,v)*TOAC(n,k,v)<=M;
end
end
end
end
end
prob.Constraints.constr_batteries_combined = constr_batteries_combined;
% constraints on trips combination;
constr_combined=optimineq(Nr,Nr,Vr,1);
for n=1:Nr
for k=1:Nr
for v=1:Vr
constr_combined(n,k,v)=y(n,k,v)<=O(n,k);
end
end
end
prob.Constraints.constr_combined = constr_combined;
%
% % problem solution
show(prob)
[sol,val] = solve(prob);
% retrieve of optimal values
opt_variables_x=sol.x;
opt_variables_y=sol.y;
opt_obj=val;
% profits higher than initial profits
% %SS=zeros(Nc,1);
% %for r=1:Nc
% SS(r)=0;
% %S1 computation
% for n=1:Nr
% for v=1:Vr
% if (Owner(v) == r)
% SS(r)=SS(r)+(alpha* d(n)*I(r) – TOA(n,v)*c(r,v)-(1-IsE(v))*beta*cE*E(n,v))*sol.x(n,v);
% end
% end
% end
%
%
% %S2 computation
% for n=1:Nr
% for k=1:Nr
% if (k ~= n)
% for v=1:Vr
% if (Owner(v) == r)
% SS(r)= SS(r) + (alpha*(d(n)+d(k))*I(r)-TOAC(n,k,v)*c(r,v)-(1-IsE(v))*beta*cE*EC(n,k,v))*sol.y(n,k,v);
% end
% end
% end
% end
% end
%
%
% % S3 computation;
%
% %compensation profits and costs for single trips
% for n=1:Nr
% for rr=1:Nc
% if (rr ~= r)
% for v=1:Vr
% if (Owner(v) == rr)
% SS(r)=SS(r)+ delta(n)*z(n,r)*sol.x(n,v);
% else
% if (Owner(v) == r)
% SS(r)=SS(r)- delta(n)*z(n,rr)*sol.x(n,v);
% end
% end
% end
% end
% end
% end
% %compensation profits and costs for combined trips
% for n=1:Nr
% for k=1:Nr
% for rr=1:Nc
% if (rr ~= r)
% for v=1:Vr
% if (Owner(v) == rr)
% SS(r) = SS(r)+ sol.y(n,k,v)*(delta(n)*z(n,r)+delta(k)*z(k,r));
% else
% if (Owner(v) == r)
% SS(r) = SS(r)- sol.y(n,k,v)*(delta(n)*z(n,rr)+delta(k)*z(k,rr));
% end
% end
% end
% end
% end
% end
% end
%
% y2=0;
% for i=1:Nr
% for v=1:Vr
% y2=y2+opt_variables_y(i,2,v)+opt_variables_y(2,i,v);
% end;
% end;
%
% end
—- #logistics #cooperation MATLAB Answers — New Questions
