Reliability and risk controlled by the simultaneous presence of random events on a time interval

The paper treats the important problem related to risk controlled by the simultaneous presence of critical events, randomly appearing on a time interval and shows that the expected time fraction of simultaneously present events does not depend on the distribution of events durations. In addition, the paper shows that the probability of simultaneous presence of critical events is practically insensitive to the distribution of the events durations. These counter-intuitive results provide the powerful opportunity to evaluate the risk of overlapping of random events through the mean duration times of the events only, without requiring the distributions of the events durations or their variance. A closed-form expression for the expected fraction of unsatisfied demand for random demands following a homogeneous Poisson process in a time interval is introduced for the first time. In addition, a closed-form expression related to the expected time fraction of unsatisfied demand, for a fixed number of consumers initiating random demands with a specified probability, is also introduced for the first time. The concepts stochastic separation of random events based on the probability of overlapping and the average overlapped fraction are also introduced. Methods for providing stochastic separation and optimal stochastic separation achieving balance between risk and cost of risk reduction are presented

Going beyond perfect rationality: drought risk, economic choices and the influence of social networks

Theoretical and experimental studies from psychological and behavioral sciences show that heuristics and social networks play an important role in decision-making under risk. The goal of this paper is to investigate the effects of empirical social networks and different behavioral rules on farmers’ irrigation adoption under drought risk and its impacts on several macroeconomic indicators such as the rate of adaptation, water demand and regional agricultural income. We present an application of a spatial economic ABM which is able to simulate the effect of droughts on crop production, farm income and farm decision-making. The agents’ population is parameterized using survey data, including data on social networks. Four experiments are conducted combining two climate scenarios with two behavioral scenarios (maximizers vs. heuristic-based agents). The results show that the adoption process follows a different path in the scenario with heuristic-based farmers. The adoption of irrigation is slower in the short run due to reliance on information from social networks and farmers’ uncertainty regarding drought events. This results in agricultural income loss and a lower water demand in the short run compared to the scenario with maximizing agent

The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches

We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branch's individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.Comment: 22 pages, 15 figure