Hi, Robust optimization is one of the methods for dealing with uncertainty. You must first model it according to the type of RO approach to your problem (for example, supply chain) and then code the mathematical model in GAMS. This feature is not available by default in GAMS and MATLAB.

Here is an example of a robust optimization model in GAMS for a supply chain management problem:

Sets

i suppliers /1*3/

j customers /1*5/;

Parameters

d(j) demand for customer j

c(i) cost of supplier i

a(i,j) capacity of supplier i to customer j

sigma uncertainty set radius;

Variables

x(i,j) quantity shipped from supplier i to customer j

z total cost of the supply chain

Equations

cost objective function

demand satisfy customer demand

cap respect supplier capacity

robust robustness constraint;

cost.. z =e= sum((i,j), c(i)*x(i,j));

demand(j).. sum(i, x(i,j)) =g= d(j);

cap(i,j).. x(i,j) =l= a(i,j);

robust.. sum((i,j), abs(c(i)*x(i,j))) =l= sigma*z;

Model supply_chain /all/;

solve supply_chain using minlp minimizing z;

In this model, the sets i and j represent the suppliers and customers, respectively. The parameters d(j), c(i), and a(i,j) represent the demand for each customer, the cost of each supplier, and the capacity of each supplier to serve each customer. The parameter sigma represents the uncertainty set radius.

The variable x(i,j) represents the quantity shipped from supplier i to customer j, and the variable z represents the total cost of the supply chain.

The objective function cost minimizes the total cost of the supply chain. The equation demand ensures that customer demand is satisfied, and the equation cap ensures that supplier capacity is respected.

The robustness constraint robust ensures that the supply chain is robust to uncertainty in the cost of each supplier. The constraint limits the total cost of the supply chain to be within sigma times the optimal cost.

To use this model, you would need to input your specific data for the demand, cost, and capacity parameters, as well as specify the uncertainty set radius sigma. You can then solve the model using a suitable solver in GAMS.

Note that this is just a basic example, and the specific details of your supply chain problem may require additional constraints and modifications to the model.