## 1 Introduction
This model makes it possible to compare the results of a time schedule set based on the needs of the public regulator, which takes into account the needs of the community indicated in the Area Plan (PdA), the planning tool that defines the quality objectives of the integrated water service management (IWSM) and the infrastructural interventions necessary to satisfy them, with another time schedule calibrated based on the objectives of optimizing the entrepreneurial return typical of private management. In this way, an attempt is made to balance the interests of the stakeholders involved. The proposed model is based on the application of the analytic hierarchy process (AHP) within an innovative logical scheme designed in compliance with the current national legislation established by the Regulatory Authority for Energy, Networks and the Environment (ARERA), an independent body that carries out regulation and control activities in the areas of energy, natural gas, water services, the waste cycle and district heating. The ultimate goal of the proposed model is to guarantee the sustainable management of water resources and the protection of the fundamental rights of the populations concerned. The proposed model is in continuity with a previous study, in which the AHP technique was used to choose the best design alternatives (which mainly concerned restoration/replacement interventions or extraordinary maintenance interventions) capable of mitigating the impacts of the main infrastructural, managerial, economic and environmental criticalities found at a territorial level (the choice problem) [20]. Instead, in the present work, the AHP technique is used to organize the optimal design alternatives previously selected in a ranking that indicates the chronological priorities to be respected in the investments to be made (the ranking problem). The approach adopted is innovative for several reasons: first, although the AHP method is among those recommended by the ARERA for the selection of investments to be included in the PdA, the proposed model innovates the regulatory approach by proposing and configuring a final hierarchization route of the selected interventions; second, unlike ordinary applications in the context of the IWSM, the model does not limit itself to ranking the technical solutions under a temporal profile, but returns a flexible classification concerning both the social interests of the regulatory entity and the industrial interests of the water operator; finally, differing from the other operational approaches present in the literature, the model fits into a broader water investment evaluation protocol which distinguishes and integrates the investment choice phase from the investment ranking phase. The model was tested by applying it to a concrete case of the IWSM of the Campania region (Italy). Among the main results, it was found that the results placed at the two extremes of the ranking are shared between the two players in the investment strategy (the private operator and public territorial body). Furthermore, both actors considered interventions on purification plants a priority. The model, therefore, is proven to be a sufficiently effective tool in identifying shared planning strategies between public and private operators. The work is structured as follows: Section 2 is dedicated to the analysis of the reference literature on the application of multiple-criteria decision analyses (MCDA) and, specifically, on the AHP technique for the selection and temporal hierarchization of investments typical of the sector; in Section 3, the model is described in detail and subsequently applied to a real manager of the IWSM of the Campania region (in Southern Italy); in Section 4, the obtained results are presented and discussed; Section 5 shows the main conclusions and possible future research ideas; and finally, Appendix A provides a theoretical insight into the AHP, the technique used in this work within the temporal hierarchy model of investments in the water sector.