Results

The optimal solution of this problem has cost 4727.17. Tables Production of LIN and Production of LOX give the optimal levels of production required in order to satisfy the demands regardless of when the interruptions occur, if ever. Note that the production levels are higher at the beginning and then, for liquid oxygen, they equal the demand. This depends on the fact that production at the initial time periods must assume for worst-case scenarios such as K=4 consecutive interruptions early in the planning horizon. The inventory levels equal the balance between demand and production as they must account for the event that no interruption occurs.

Note that this is the result of the optimization problem solved at the beginning of the time period. Using a rolling horizon approach, i.e., re-solving the model at every time period while taking into account the interruptions that already occurred, would allow us to obtain a less expensive production plan although the planned production levels might have to change.

Finally, since the interruption of a plant at a given period affects the production of both gases, the retrieval of uncertains needs to be done for each gas and getsol takes both interruption and the robust constraint RobProd as arguments. As would be expected, most worst-case interruptions are at the initial time periods, since those are critical moments when the LIN and LOX tanks need to be built up.

Worst-case interruptions for LIN:
2 3 4 5 6 14

Worst-case interruptions for LOX:
2 3 4 5 6 8 10 15