T.B. Klos
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1
This paper concerns networks of precedence constraints between tasks with random durations, known as stochastic task networks, often used to model uncertainty in real-world applications. In some applications, we must associate tasks with reliable start-times from which realized start-times will (most likely) not deviate too far. We examine a dispatching strategy according to which a task starts as early as precedence constraints allow, but not earlier than its corresponding planned release-time. As these release-times are spread farther apart on the time-axis, the randomness of realized start-times diminishes (i.e. stability increases). Effectively, task start-times becomes less sensitive to the outcome durations of their network predecessors. With increasing stability, however, performance deteriorates (e.g. expected makespan increases). Assuming a sample of the durations is given, we define an LP for finding release-times that minimize the performance penalty of reaching a desired level of stability. The resulting LP is costly to solve, so, targeting a specific part of the solution-space, we define an associated Simple Temporal Problem (STP) and show how optimal release-times can be constructed from its earliest-start-time solution. Exploiting the special structure of this STP, we present our main result, a dynamic programming algorithm that finds optimal release-times with considerable efficiency gains.
We present a visualization of bargaining processes between a seller and a buyer (or buyers) where negotiations take place over the composition and price of bundles of goods. The negotiations themselves are simulated by software specific for the kind of negotiations. The visualization collects information from the simulation steps in a simulation-specific way and visualizes those steps in a general way. We demonstrate the visualization for two cases: a seller who offers bundles of linearly dependent items to many customers and a seller who repeatedly offers a bundle of non linearly dependent goods to a specific customer meanwhile learning this customers preferences.