Fairdivide.mod

/* Fair Division Program
 This is a program for dividing up items between people people.
So the minimum satisfaction of any of them is maximised. */
param people, integer,> 0;
/* number of people dividing stuff */
param divi, integer, >= 0;
param indiv, integer, >= 0;
/* number of items to be divided. divi divisible. indiv non divisible */
set I:= 1..people;
/* set of people */
set J := 1..indiv;
/* set of nondivisible items */
set K := 1..divi;
/* set of divisible items */
param indivItems{i in I, j in J}, >= 0;
/*indivisible  amount recieved if item j is given to agent i */
param divItems{i in I, k in K}, >= 0;
/*divisible amount recieved if item k is given to agent i */
var worst;
/*how is the worst person doing?*/
var x{i in I, k in K},>=0;
var y{i in I, j in J}, binary;
/*
here ,>=0; means that the items are divisible.
here , binary; means that items are not divisable.
x[i,j] = 1 means item j is assigned to agent i */
s.t. one{k in K}: sum{i in I} x[i,k] = 1;
s.t. two{j in J}: sum{i in I} y[i,j] = 1;
/* job j must be assigned exactly to one agent */
/*s.t. lim{i in I}: ((sum{j in J} c[i,j] * x[i,j])+(sum{k in K} d[i,k] * y[i,k]) )<= b[i];*/
/*add check person does not get more then 100%. Want to make sure they do not ask for more then 100% */
s.t. wor{i in I}: ((sum{k in K} divItems[1,k] * x[1,k])+(sum{j in J} indivItems[1,j] * y[1,j])) >= worst;
s.t. wor2{i in I}: ((sum{k in K} divItems[2,k] * x[2,k])+(sum{j in J} indivItems[2,j] * y[2,j])) >= worst;
/*Add wo3 3 for 3rd person etc
s.t. wor3{i in I}: ((sum{k in K} divItems[3,k] * x[3,k])+(sum{j in J} indivItems[3,j] * y[3,j])) >= worst;*/