Consider k random samples which are independently drawn from k shifted-exponential distribution, with different scale parameters and a common location parameter. On the basis of the given samples and in a Bayesian framework, we address the problem of point and interval estimation of the location parameter under the conjugate priors. Moreover, we also address the problem of testing the equality of the location parameters. We propose Bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Our proposed Bayesian procedures are compared and contrasted, via a comparison study, a simulation study, and a real-world data analysis, to the existing exact classical procedures and the generalized variable procedures.