Problem definition: International Humanitarian Organizations (IHOs) prepare a detailed annual allocation plan for the operations to be conducted in the countries they serve. The annual plan is strongly affected by the available financial budget. Budget of IHOs comes from donations, which are...

We consider a new combinatorial optimization problem that combines network design and facility location aspects. Given a graph with two types of customers and two technologies that can be installed on the edges, the objective is to find a minimum cost subtree connecting all customers while the...

Given a point on the standard simplex, we calculate a proximal point on the regular grid which is closest with respect to any norm in a large class, including all <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell ^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-norms for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p\ge 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>p</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>. We show that the minimal <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\ell ^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-distance to the...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We consider a network design problem that arises in the cost-optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design...