Erratum to: TOP DOI 10.1007/s11750-012-0253-9

Correction to Figs. 1, 2 and 3;

Fig. 1
figure 1

2D and 3D simplices removing the minimum dose region

Fig. 2
figure 2

Pareto optimality

Fig. 3
figure 3

Example of division according to the raw material costs

We regret by mistake Figs. 1, 2 and 3 in the Original published article were inappropriate as these were from outdated manuscript version, unfortunately used by Springer typesetters. The mistake made is clearly not due to the authors.

Sincerely yours, The Editors