## File project.mod

#Load parameters from .dat file
param supply{i in 1..8};
param sugar_cost{i in 1..8};
param to_charleston{i in 1..8};
param to_atlanta{i in 1..8};
param transit_return;

param molasses_production{i in 1..2};
param sugar_production{i in 1..2};
param bagasse_production{i in 1..2};

param operating_costs_variable{i in 1..2};
param operating_costs_flat{i in 1..2};
param capacity{i in 1..2};

param sugar_profit{i in 1..2};
param molasses_profit;
param bagasse_profit;

param from_charleston{i in 1..7};
param from_atlanta{i in 1..7};
param demand{i in 1..7};

#amount of sugar bought from each plant and sent to each refinery
var raw_sugar{i in 1..8, j in 1..2} >= 0;

#Amount of molasses to produce in each refinery
#var molasses{i in 1..2} >= 0;

#Amount of refined sugar to produce in each refinery
#var sugar{i in 1..2} >= 0;

#Amount of bagasse to produce in each refinery
#var bagasse{i in 1..2} >= 0;

#Amount of molasses shipped from each plant to each customer
var sold_molasses{i in 1..2, j in 1..7} >= 0;

maximize profit:

#profit from selling sugar to market
sum{i in 1..2} sugar_profit[i]*(transit_return*sugar_production[i]*(sum{j in 1..8} raw_sugar[j,i]))

#profit from selling molasses to customers 6 and 7 and to market
+ molasses_profit*(sum{i in 1..2} transit_return*molasses_production[i]*(sum{j in 1..8} raw_sugar[j,i])) - molasses_profit*(sum{i in 1..2, j in 1..5} sold_molasses[i,j])

#profit from selling bagasse to market
+ bagasse_profit*(sum{j in 1..2} transit_return*(1-molasses_production[j]-sugar_production[j])*(sum{i in 1..8} raw_sugar[i,j]))

#cost of buying raw sugar
- sum{i in 1..8, j in 1..2} sugar_cost[i]*raw_sugar[i,j]

#cost of shipping raw sugar to refineries
- sum{i in 1..8} to_charleston[i]*raw_sugar[i,1]
- sum{i in 1..8} to_atlanta[i]*raw_sugar[i,2]

#variable cost of operating refineries
- sum{i in 1..8, j in 1..2} operating_costs_variable[j]*transit_return*raw_sugar[i,j]

#fixed cost of operating refineries
- sum{i in 1..2} operating_costs_flat[i]

#cost of shipping molasses to customers
- sum{j in 1..7} from_charleston[j]*sold_molasses[1,j]
- sum{j in 1..7} from_atlanta[j]*sold_molasses[2,j];

subject to

#We can only buy so much sugar from each supplier
sugar_supply_con {i in 1..8}: sum{j in 1..2} raw_sugar[i,j] <= supply[i];

#Each refinery must operate between 50% and 100% capacity
maximum_capacity {j in 1..2}: transit_return*(sum{i in 1..8} raw_sugar[i,j]) <= capacity[j];
minimum_capacity {j in 1..2}: transit_return*(sum{i in 1..8} raw_sugar[i,j]) >= .5*capacity[j];

#Charleston can only produce 2250000 pounds of purified sugar
charleston_sugar_con: transit_return*sugar_production[1]*(sum{j in 1..8} raw_sugar[j,1]) <= 2250;

#We produce certain amounts of sugar, molasses depending on how much raw sugar we get
#molasses_con {j in 1..2}: molasses[j] = transit_return*molasses_production[j]*(sum{i in 1..8} raw_sugar[i,j]);
#sugar_con {j in 1..2}: sugar[j] = transit_return*sugar_production[j]*(sum{i in 1..8} raw_sugar[i,j]);

#Whatever we don't use for sugar or molasses, we use for bagasse
#bagasse_con {j in 1..2}: bagasse[j] = transit_return*(sum{i in 1..8} raw_sugar[i,j]) - molasses[j] - sugar[j];

#We must meet all demand for molasses from our customers
molasses_demand_con {j in 1..7}: sum{i in 1..2} sold_molasses[i,j] >= demand[j];

#We only have so much molasses at each refinery to ship out
total_molasses_con {k in 1..2}: sum{j in 1..7} sold_molasses[k,j] <= transit_return*molasses_production[k]*(sum{i in 1..8} raw_sugar[i,k]);