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In the planning phase of district energy systems, optimization models based on mathematical programming are a widely used approach. Most optimization models determine the optimal energy system design based on a single representative year. However, this approach is unable to consider changing economic and technological boundary conditions over the system's lifetime. As a result, these one-period models fall short for districts with 5th generation district heating and cooling (5GDHC) networks, which are typically developed over long time periods and are built in multiple construction phases. In this paper, we present two multi-period optimization approaches for designing 5GDHC districts: The first approach is a forward-looking model which determines the optimal investment pathway by using a perfect foresight of future parameter developments. In the second approach, a one-period model is solved repeatedly for every investment period without knowledge of future parameter developments. Both approaches are compared to a one-period model for a real-world 5GDHC district in Germany. In comparison with a one-period design approach, the forward-looking method leads to total cost savings of up to 17 % and the sequential method of up to 11 %. By using a forward-looking model, gas-fired technologies are sized smaller while the capacity of electricity-driven technologies in the energy hub as well as photovoltaic modules and thermal energy storages in buildings increases compared to a one-period model. The case study shows that a multi-period modeling approach is an important addition to design optimization models for 5GDHC networks and can have a significant impact on the optimal design. [ABSTRACT FROM AUTHOR]

The Luenberger productivity indicator applies directional distance functions which allow to specifying in what direction (i.e. direction of measurement) the operating units will be evaluated. In the presence of a change in the direction of measurement, the standard components of the existing Luenberger productivity indicator may provide values which are not compatible with reality. In order to eliminate this pitfall, the so-called bottoms-up approach is used to revisit the definition of the indicator and its components. We start with a list of selected sources of productivity change, namely efficiency change, technical change and direction change, then examine the best possible way of measuring each of the sources and combine them to derive a new measure of productivity change. The proposed indicator will be illustrated by means of an empirical application to a panel of 417 German savings banks over the time period 2006–2012. The example explains how the proposed approach is able to properly measure efficiency change, technical change and direction change. The results also provide conclusive evidence about the effect of the change in direction of measurement on the results of the productivity over time in a centralised management scenario. [ABSTRACT FROM PUBLISHER]