The Sum of a Linear and a Linear Fractional Function: Pseudoconvexity on the Nonnegative Orthant and Solution Methods

The aim of the paper is to present sequential methods for a pseudoconvex optimization problem whose objective function is the sum of a linear and a linear fractional function and the feasible region is a polyhedron, not necessarily compact. Since the sum of a linear and a linear fractional function is not in general pseudoconvex, we first derive conditions characterizing its pseudoconvexity on the nonnegative orthant. We prove that the sum of a linear and a linear fractional function is pseudoconvex if and only if it assumes particular canonical forms. Then, theoretical properties regarding the existence of a minimum point and its location are established, together with necessary and sufficient conditions for the infimum to be finite. The obtained results allow us to suggest simplex- like sequential methods for solving optimization problems having as objective function the proposed canonical forms

Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions

The issue of the pseudoconvexity of a function on a closed set is addressed. It is proved that if a function has no critical points on the boundary of a convex set, then the pseudoconvexity on the interior guarantees the pseudoconvexity on the closure of the set. This result holds even when the boundary of the set contains line segments, and it is used to characterize the pseudoconvexity, on the nonnegative orthant, of a wide class of generalized fractional functions, namely the sum between a linear one and a ratio which has an affine function as numerator and, as denominator, the p-th power of an affine function. The relationship between quasiconvexity and pseudoconvexity is also investigated

Generating the efficient frontier of a class of bicriteria generalized fractional programming

In this paper, a particular class of bicriteria maximization problems over a compact polyhedron is considered. The first component of the objective function is the ratio of powers of affine functions and the second one is linear. Several theoretical properties are provided, such as the pseudoconcavity of the first criterium of the objective function, the connectedness and compactness of both the efficient frontier and the set of efficient points. The obtained results allow us to propose a new simplex-like solution method for generating the whole efficient frontier; to better clarify the use of the suggested algorithm, several examples are described and the results of a computational test are presented

Simplex-like sequential methods for a class of generalized fractional programs

A sequential method for a class of generalized fractional programming problems is proposed. The considered objective function is the ratio of powers of affine functions and the feasible region is a polyhedron, not necessarily bounded. Theoretical properties of the optimization problem are first established and the maximal domains of pseudoconcavity are characterized. When the objective function is pseudoconcave in the feasible region, the proposed algorithm takes advantage of the nice optimization properties of pseudoconcave functions; the particular structure of the objective function allows to provide a simplex-like algorithm even when the objective function is not pseudoconcave. Computational results validate the nice performance of the proposed algorithm

Environmental sustainability and service quality beyond economic and financial indicators: A performance evaluation of Italian water utilities

As water utilities operate as natural monopolists and they provide essential services for human life, their activities are regulated by public authorities. The sustainable use of water resources and a specific attention on social needs should be essential goals for this kind of firms, so that the evaluation of their business should go beyond their profitability and their financial solvency. Keeping pace with the new Circular Economy paradigm and the evolution of the water regulatory framework, in this paper we suggest a global composite indicator apt to evaluate in a novel way the water utilities performance, encompassing financial and economic indexes together with environmental sustainability and service quality measures. To show its empirical implementation we evaluate the performance of Italian water utilities. The operating context is also under scrutiny focusing on specific water utility features such as size, geographical location, degree of diversification and ownership. In this light, operating in the Center and being large are considered favourable background conditions, while the South and the medium size display a significant unfavourable influence on the water utility performance. Multi-utilities are more advantaged with respect to the mono-utilities and no significant distinction can be made among the different ownership models. ispartof: Socio-Economic Planning Sciences status: Published onlin

A reduced formulation for pseudoinvex vector functions

Vector pseudoinvexity is characterized in the current literature by means of a suitable functional which depends on two variables. In this paper, vector pseudoinvexity is characterized by means of a functional which depends on one variable only. For this very reason, the new characterizing conditions are easier to be verified

Water pollution in wastewater treatment plants: An efficiency analysis with undesirable output

The environmental efficiency of 96 Tuscan (Italian) wastewater treatment plants (WWTPs) is investigated taking into account the quality of the outgoing water in terms of pollutant. In this regard, the presence of the residual nitrogen in the outgoing treated water is considered as undesirable output. The efficiency analysis is performed by applying a novel integrated Analytic Hierarchy Process/Non-radial Directional Distance Function (AHP/NDDF) approach, combining the benefits of the two techniques. Similarly to the standard NDDF approach, the suggested model allows to include simultaneously inputs, desirable and undesirable outputs and not to overestimate the efficiency scores. At the same time, the AHP inclusion gives the possibility to directly take into account the decision maker preferences in the weighting system and to encompass some existing directional distance function models as special cases.The obtained results are then used to identify the efficiency explanatory variables: among them, the facilities' capacity, the percentage of wastewater discharged by the industrial and agricultural activities and the level of compliance with the pollutant concentration threshold set by the legislator have a significant impact on the WWTP performance. The integrated performance assessment allows the water authorities to combine the WWTP efficiency together with the environmental sustainability issue and it has the potential for further promising environmental inspections

A Matheuristic for Integrated Timetabling and Vehicle Scheduling

Planning a public transportation system is a complex process, which is usually broken down in several phases, performed in sequence. Most often, the trips required to cover a service with the desired frequency (headway) are decided early on, while the vehicles needed to cover these trips are determined at a later stage. This potentially leads to requiring a larger number of vehicles (and, therefore, drivers) that would be possible if the two decisions were performed simultaneously. We propose a multicommodity-flow type model for integrated timetabling and vehicle scheduling. Since the model is large-scale and cannot be solved by off-the-shelf tools with the efficiency required by planners, we propose a diving-type matheuristic approach for the problem. We report on the efficiency and effectiveness of two variants of the proposed approach, differing on how the continuous relaxation of the problem is solved, to tackle real-world instances of bus transport planning problem originating from customers of M.A.I.O.R., a leading company providing services and advanced decision-support systems to public transport authorities and operators. The results show that the approach can be used to aid even experienced planners in either obtaining better solutions, or obtaining them faster and with less effort, or both

Heterogeneity and penetration of HIV-1 non-subtype B viruses in an Italian province: Public health implications

SUMMARYThis study assessed changes in prevalence and distribution of HIV-1 non-subtype B viruses in Italian and immigrant patients over two decades in a province in Italy. All HIV-positive patients who underwent genotypic resistance testing were selected. Prevalence of non-subtype B viruses in 3-year periods was calculated. All sequences of non-subtype B and those provided by REGA as unassigned were analysed for phylogenetic relationships. In total, 250/1563 (16%) individuals were infected with a non-subtype B virus. Prevalence increased over time, reaching a peak (31·5%) in 2004–2006. In Italian patients, the most frequent subtypes were B (92·5%) and F1 (4%). F1 subtype was also prevalent in patients from South America (13·6%); in patients of African origin, CRF02_AG (54·9%) and G (12·3%) were the most frequent. HIV-1 non-subtype B infections in Italians were mostly found in patients who acquired HIV sexually. A phylogenetic relationship between F subtypes in Italian and representative HIV-1 sequences from Brazil was found. C subtypes in Italians were phylogenetically related to subtypes circulating in Brazil. Inter-subtype recombinants were also found in the latest years. The HIV-1 epidemic in Brescia province evolved to the point where about 1/3 patients recently diagnosed harboured non-B HIV subtypes. The distribution of HIV-1 non-B subtypes in Italian patients resembled that in South American patients and phylogenetic relatedness between some Italian and South American HIV-1 strains was found. The possible epidemiological link between these two populations would have been missed by looking only at risk factors for HIV acquisition declared by patients. The evidence of inter-subtype recombinants points to significant genetic assortment. Overall our results support phylogenetic analysis as a tool for epidemiological investigation in order to guide targeted prevention strategies