Optimal placement of gas detectors: A P‐median formulation considering dynamic nonuniform unavailabilities

Abstract

A stochastic programming formulation (SPqt), based on the P‐median problem, is proposed for determining the optimal placement of detectors in mitigation systems while considering nonuniform dynamic detector unavailabilities. Unlike previously proposed formulations, SPqt explicitly considers backup detection levels. This allows the modeller to determine the maximum degree of the nonlinear products to be used based on the trade‐off between computational complexity and solution accuracy. We analyze this trade‐off on formulation SPqt results by using 4 real data sets for the gas detector placement problem while using unavailability values obtained from real industry gas detector data. For this data, our results show that two detection levels are sufficient to find objective values within 1% of the optimal solution. Using two detection levels reduces the nonlinear formulation to a quadratic formulation. Three solution strategies are proposed for this quadratic formulation and then compared from the computational efficiency perspective. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2728–2739, 2016