The {0,1}-knapsack problem with qualitative levels

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.

A multiple criteria methodology for prioritizing and selecting portfolios of urban projects

This paper presents an integrated methodology supporting decisions in urban planning. In particular, it deals with the prioritization and the selection of a portfolio of projects related to buildings of some values for the cultural heritage in cities. In particular, our methodology has been validated to the historical center of Naples, Italy. Each project is assessed on the basis of a set of both quantitative and qualitative criteria with the purpose to determine their level of priority for further selection. This step was performed through the application of the Electre Tri-nC method. This method is a multiple criteria outranking based model for ordinal classification (or sorting) problems and allows to assign a priority level to each project as an analytical `recommendation' tool. A set of resources (namely budgetary constraints) as well as some logical constraints related to urban policy requirements have to be taken into consideration together with the priority of projects in a portfolio analysis model permitting to identify the efficient portfolios and to support the selection of the most adequate set of projects to activate. The process has been conducted thanks to the interaction between analysts, municipality representative and experts. The proposed methodology is generic enough to be applied in other territorial or urban planning problems. More precisely, given the increasing interest of historical cities to restore their cultural heritage the integrated multiple criteria decision aiding analytical tool proposed in this paper has an important potential of being used in the future.