In view of uncertainties caused by sudden accidents (SAs) and affecting retailers' demand in many districts, it is difficult for suppliers to determine when and how many products to procure/produce. Considering a supply chain consisting of two types of competing suppliers and multi-retailer, this work studies the suppliers' optimal emergency procurement/production decision (EPD) with information updating. Firstly, a probability evolution model with information updating to describe the probability of the retailers' procurement behaviour and the occurrence probability of supply disruption (SD) is inferred. Secondly, suppliers' EPDs regarding retailers' procurement behaviour and occurrence probability of SD are discussed and a real-time updated emergency decision-making model (EDM) is proposed based on Stackelberg game and Bayesian inference. Thirdly, the value of information updating and the critical factors that affect the suppliers' optimal EPD are quantitatively analysed. Numerical examples are finally provided to verify the EDM. Results indicate that information is the premise and foundation for the suppliers to deal with SA effectively; suppliers can easily determine when and how many products to procure/produce based on the proposed EDM; it is demonstrated that for any chosen supplier strategy, there exists a corresponding optimal procurement/production quantity for the suppliers that maximises the expected profits. Moreover, the suppliers' EPD with information updating is affected by cost parameters, with the rank of information collection cost coefficient, unit procurement/production cost, unit sales price, unit holding cost and unit shortage cost, from apparently to slightly.

A quick and accurate identification of source information on sudden hazardous chemical leakage accident is crucial for early accident warning and emergency response. This study firstly regards source identification problem of sudden hazardous chemical leakage accidents as an inverse problem and presents a source identification model based on the Bayesian framework. Secondly, a new identification method is designed on the basis of particle swarm optimisation (PSO), differential evolution (DE) and the Metropolis–Hastings (M–H) sampling method. Lastly, the designed method, i.e. PSO-DE-MH, is verified by an outdoor experiment analyses in a section of the South–North Water Transfer Project. Results show that the number of iterations, the average absolute error, the average relative error and the average standard deviations of the identification results obtained by PSO-DE-MH are less than those of PSO-DE and DE-MH. Moreover, the relative error and the sampling relative error of the identification results under five different measurement errors (MEs) (σ = 0.01, 0.05, 0.1, 0.15, 0.2) are less than 9.5% and 0.2%, respectively. The designed method is effective even when the standard deviation of the ME increases to 0.2. Therefore, the designed method can effectively and accurately obtain the source information of sudden hazardous chemical leakage accidents. This study provides a new idea and method to solve the difficult problems of emergency management.