The problem of simultaneous estimation of location/scale parameters \(\theta _1\) and \(\theta _2\) of a general bivariate location/scale model, when the ordering between the parameters is known a priori (say, \(\theta _1\le \theta _2\) ), has been considered. We consider isotonic regression estimators based on the best location/scale equivariant estimators (BLEEs/BSEEs) of \(\theta _1\) and \(\theta _2\) with general weight functions. Let \(\mathcal {D}\) denote the corresponding class of isotonic regression estimators of \((\theta _1,\theta _2)\) . Under the sum of the weighted squared error loss function, we characterize admissible estimators within the class \(\mathcal {D}\) , and identify estimators that dominate the BLEE/BSEE of ( \(\theta _1\) , \(\theta _2\) ). Our study unifies several studies reported in the literature for specific probability distributions having independent marginals. We also report a generalized version of the Katz (Ann Math Stat 34:967–972, 1963) result on the inadmissibility of certain estimators under a loss function that is weighted sum of general loss functions for component problems. A simulation study is carried out to validate the findings of the paper, and to compare different competing estimators.