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This paper proposes a new demand response scheduling framework for an array of households, which are grouped into different categories based on socio-economic factors, such as the number of occupants, family decomposition and employment status. Each of the households is equipped with a variety of appliances. The model takes the preferences of participating households into account and aims to minimize the overall production cost and, in parallel, to lower the individual electricity bills. In the existing literature, customers submit binary values for each time period to indicate their operational preferences. However, turning the appliances "on" or "off" does not capture the associated discomfort levels, as each appliance provides a different service and leads to a different level of satisfaction. The proposed model employs integer values to indicate household preferences and models the scheduling problem as a multi-objective mixed integer programming. The main thrust of the framework is that the multi-level preference modeling of appliances increases their "flexibility"; hence, the job scheduling can be done at a lower cost. The model is evaluated by using the real data provided by the Department of Energy & Climate Change, UK. In the computational experiments, we examine the relation between the satisfaction of consumers based on the appliance usage preferences and the electricity costs by exploring the Pareto front of the related objective functions. The results show that the proposed model leads to significant savings in electricity cost, while maintaining a good level of customer satisfaction.

The performance of scintillation detectors for x rays and gamma rays is limited fundamentally by the statistics of the scintillation light and the resulting photoelectrons. This paper presents a new experimental approach to studying these statistics by observing correlations in the signals from two photodetectors. It is shown that the Fano factors (ratios of variance to mean), both for the number the photoelectrons produced on the photocathode of the photomultiplier and for the underlying number of scintillation photons, can be deduced from these correlations. For LaBr3(Ce) and 662 keV gamma rays, the photopeak signals obtained by photomultipliers on opposite faces of a thin sample are negatively correlated, and the Fano factor for the photoelectrons is significantly less than one. The inferred Fano factor for the optical photons is very small, indistinguishable from zero within experimental error.

In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done by using a two stage greedy algorithm, with two corresponding types of heuristics. The solutions acquired in this way are improved by applying a computationally inexpensive, hill climbing like, greedy correction procedure. In our numeric experiments we analyze different heuristic functions for each stage of the greedy algorithm, and show that their performance is highly dependent on the properties of the specific instance. Our tests show that by exploring a relatively small number of solutions generated by combining different heuristic functions, and applying the proposed correction procedure we can find solutions within only a few percent of the optimal ones.