In this paper, we consider dynamic congestion pricing in the presence of demand uncertainty. In particular, we apply a robust optimization (RO) approach based on a bi-level cellular particle swarm optimization (BCPSO) to optimal congestion pricing problems when flows correspond to dynamic user...

A random variable (RV) X is given aminimum selling price $$S_U \left( X \right):=\mathop {\sup }\limits_x \left\{ {x + EU\left( {X - x} \right)} \right\}$$ and amaximum buying price $$B_p \left( X \right):=\mathop {\inf }\limits_x \left\{ {x + EP\left( {X - x} \right)} \right\}$$ whereU(·)...

This paper presents an approximate affinely adjustable robust counterpart for conic quadratic constraints. The theory is applied to obtain robust solutions to the problems of subway route design with implementation errors and a supply chain management with uncertain demands. Comparison of the...

In this paper we focus on robust linear optimization problems with uncertainty regions defined by [phi]-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on [phi]-divergences arise in a natural way as confidence sets if the uncertain...

This paper presents an approximate affinely adjustable robust counterpart for conic quadratic constraints. The theory is applied to obtain robust solutions to the problems of subway route design with implementation errors and a supply chain management with uncertain demands. Comparison of the...

A random variable (RV) X is given aminimum selling price <Equation ID="E1"> <EquationSource Format="TEX"> $$S_U \left( X \right):=\mathop {\sup }\limits_x \left\{ {x + EU\left( {X - x} \right)} \right\}$$ </EquationSource> </Equation> and amaximum buying price <Equation ID="E2"> <EquationSource Format="TEX"> $$B_p \left( X \right):=\mathop {\inf }\limits_x \left\{ {x + EP\left( {X - x} \right)} \right\}$$ </EquationSource> </Equation>...</equationsource></equation></equationsource></equation>