Joint Product and Fulfillment Optimization

Hello I am trying to create a Joint Pricing and fulfillment Model on Matlab. Using the Demand curve as one of the decision Variable however I am getting an error. I know it has something to do with the demand curve but I can't figure out how to reformulate it .

Error using optim.internal.problemdef.Times.getTimesOperator
At least one argument must be numeric.

Error in .*

Error in *

Error in JPF (line 9)

p.Objective =  g*(116-2*g) +18*x('IltoMi') + 38.25*x('IltoOR') + 41.75*x('CatoMi') + 20.71*x('CatoOr');
Please let me know if further information is required Thank 

p = optimproblem;
  vars = {'Price','IltoMi','IltoOR','CatoMi','CatoOr'};

    x= optimvar('x',vars,'LowerBound',0);

    optimvar('y',3,'Type','integer','LowerBound',0,'UpperBound',1);
    p.ObjectiveSense = 'maximize';

    p.Objective =  g*(116-2*g) + g*(116-2*g) +18*x('IltoMi') + 38.25*x('IltoOR') + 41.75*x('CatoMi') + 20.71*x('CatoOr');

    p.Constraints.c1 = x('IltoMi') + x('IltoOR') + x('CatoMi')+ x('CatoOr') == 116-2*x('Price');
    p.Constraints.c2 = x('IltoOR') + x('IltoMi') <= 60;
    p.Constraints.c3 = x('CatoMi')+ x('CatoOr') <= 56;

[PATEL ZEEL BHARATKUMAR]

Sir , if you find the solution of this then please tell me because i am getting this error also in my program.

Thank you.

Answer 1

[Mark McBroom]

The error message is coming from the first two terms in the Objective. I believe the problem is that the Objective is not a linear expression. It is complaining about the first two terms involving "g". See this link .

[john canry]

Thank you Mark. Would QUADPROG OR FMINCON or a different solve be a fit for this problem?

[Alan Weiss]

Sorry, at the moment we do not have an integer solver for quadratic objectives.

If your problem is convex, you might be able to use the approach shown in this example, but I don't really know whether it applies to your case.

Alan Weiss

MATLAB mathematical toolbox documentation

[Sanyam Maheshwari]

I am also facing the issue with my optimization problem.

global SL V p r k m n C Z s 
SL = [0.75 0.75 0.75 0.75];
V = 94100;
p = [0.07,0.18,0.2,0.3];
r = [55 55 55 55;
     47 47 47 47;
     45 45 45 45;
     49 49 49 49];
k = [33 33 33 33;
     28 28 28 28;
     29 29 29 29;
     30 30 30 30];
m = 4;
n= 4;
C = [78,69,70,73;
    64,68,56,59;
    34,39,42,41;
    52,47,48,45];
Z =[250	250	250	250;
    320	320	320	320;
    440	440	440	440;
    350	350	350	350];
s = [110,95,99,100];
global SL V r k m n C Z s 
% Generating Variables
Q = optimvar('Q',m,n,'LowerBound',0,'UpperBound',Z);
b = optimvar('b',m,n,'Type','integer','LowerBound',0,'UpperBound',1);
rng
y = rand(4);
x = sym('x',[4,1]);
% limit of integration
l = y*Q; 
q = sum(l(:));
% Constraints
% Budget Constraint
B = C*b*y*Q;
budget = sum(B(:)) <= V;
% normal constraint
normal = int(normpdf(x, 400, 100),q,Inf) <=SL;
% each product connects to exactly one supplier
con4 = sum(b,1) == ones(m,1)';
% Objective Function:-
% optimization problem
demandprob = optimproblem;
% Revenue 
revenue = sum(s*b*x,1);
% Cost
cost = sum(sum(C*b*y*Q,1),2);
%Salvage
salvage = sum(b*r*(sum(sum(y*Q - x,1),2)),1);
% Revenue when demand is more
revenue2 = sum(s*b*y*Q,2);
% Salvage when demand is more
salvage2 = sum(b*k*(x - sum(sum(y*Q,1),2)),1);
% The objective function to maximize the below Expected Profit
demandprob.Objective = int(((revenue - cost + salvage).*normpdf(x, 400, 100)),0,q); + int(((revenue2 - cost - salvage2).*normpdf(x, 400, 100)),q,Inf);
% Include the constraints in the problem.
demandprob.Constraints.budget = budget;
demandprob.Constraints.normal = normal;
demandprob.Constraints.con4 = con4;
opts = optimoptions('intlinprog','Display','off','PlotFcn',@optimplotmilp);
% Call the solver to find the solution.
[sol,fval,exitflag,output] = solve(demandprob,'options',opts);

Also I want to maximize this optimization problem

What should I do further.

please help