Principles of Performance and Reliability Modeling and Evaluation by Lance Fiondella & Antonio Puliafito

Author:Lance Fiondella & Antonio Puliafito
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

3 Formal Problem Definition

In this section, we consider simplified versions of the combinatorial optimization problem to be addressed in Sect. 4. Accordingly, we aim to (a) show that even under simplified assumptions the problem is already NP-hard and (b) illustrate further simplifications and alternative formulations that yield tractable analysis motivating the heuristics evaluated in Sect. 5. Generally, the optimization problem goal is to allocate a given budget in order to maximize the expected energy supplied under a failure occurrence. The allocation process consists of two main decisions, namely which equipment to invest in and where to install the investment.

The topology considered consists of auto-loops, where each loop comprises two feeder lines (also referred to simply as lines). Let N be the number of feeder lines. Each line starts at a source and ends at a sink, and comprises M sections. We assume that lines are independent of each other. Each section j of line n is associated with two parameters, namely a probability of failure and a load . If a section k fails, all sections between k and the sink of that line are not supplied. Therefore, a failure on a specific section affects succeeding sections in the direction of the sink. Let be the indicator variable that characterizes whether an investment is applied in the j-th section of line n. Let be the price of an investment in section j of line n, whereas is the additive increase in the probability of success due to the investment. Table 1 summarizes the previous definitions.Table 1Table of notation

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