  Luminosities of muon-proton and muon-nucleus collisions at a recently
proposed muon-ion collider (MuIC) at Brookhaven National Laboratory (BNL) in
the USA have been estimated using A Luminosity Optimizer for High Energy
Physics (AloHEP) software keeping in mind beam-beam tune-shift values. It is
shown that L$_{\mu p}$ = 3.6x10$^{31}$ cm$^{-2}$s$^{-1}$ and L$_{\mu{\rm -Au}}$
= 2.84x10$^{27}$ cm$^{-2}$s$^{-1}$ values can be achieved at MuIC. The physics
search potential of the collider is superior to HERA. However, LHeC will
provide 2 orders of higher luminosities at approximately same center-of-mass
(CoM) energies.
