Termination

Our solution receives the fmincon exitflag of 1, which indicates that a local minimum is found that satisfies the constraints.

Local optimality

The solution is a local minima as indicated by the exitflag of 1. fmincon yielding an exit flag of 1 also indicates that KKT conditions and the second order conditions are met. The Lagrange multiplier values in Table 4 are further evidence that the solution meets these requirements.

Global optimality

Table 2 and Figure 2 above show our best solution. This solution was found 19% of the time, so we are confident that this is the global solution. We also ran a parametric study of the parameter N, which is addressed later in the investigation. This only makes us more confident that the solution presented is the global optimum.

Uniqueness

Our global solution is non-unique for N = 6, since the locations of our stations are not unique. This means we have some several cases of the same overall supply with the same locations but different supplies at each station. As addressed latter when N values of 7 or greater are used we see several solutions where stations are co-located. These solutions have identical values for overall supply and since their values are identical these solutions can be seen as the same global solution. We are fairly certain we have arrived at a global solution, but there are some local minima we found. These would represent stations with sub-globally optimal placements that necessitate larger supply to fulfill demand.