  In the absence of randomized controlled and natural experiments, it is
necessary to balance the distributions of (observable) covariates of the
treated and control groups in order to obtain an unbiased estimate of a causal
effect of interest; otherwise, a different effect size may be estimated, and
incorrect recommendations may be given. To achieve this balance, there exist a
wide variety of methods. In particular, several methods based on optimization
models have been recently proposed in the causal inference literature. While
these optimization-based methods empirically showed an improvement over a
limited number of other causal inference methods in their relative ability to
balance the distributions of covariates and to estimate causal effects, they
have not been thoroughly compared to each other and to other noteworthy causal
inference methods. In addition, we believe that there exist several unaddressed
opportunities that operational researchers could contribute with their advanced
knowledge of optimization, for the benefits of the applied researchers that use
causal inference tools. In this review paper, we present an overview of the
causal inference literature and describe in more detail the optimization-based
causal inference methods, provide a comparative analysis of the prevailing
optimization-based methods, and discuss opportunities for new methods.
