  A microscopic approach has been employed to study the kaon productions in
heavy ion collisions. The momentum integrated Boltzmann equation has been used
to study the evolution of strangeness in the system formed in heavy ion
collision at relativistic energies. The kaon productions have been calculated
for different centre of mass energies ($\sqrt{s_{\mathrm {NN}}}$) ranging from
AGS to RHIC. The results have been compared with available experimental data.
We obtain a non-monotonic horn like structure for $K^+/\pi^+$ when plotted with
$\sqrt{s_{\mathrm {NN}}}$ with the assumption of an initial partonic phase
beyond a certain threshold in $\sqrt{s_{NN}}$. However, a monotonic rise of
$K^+/\pi^+$ is observed when a hadronic initial state is assumed for all
$\sqrt{s_{\mathrm {NN}}}$. Experimental values of $K^-/\pi^-$ are also
reproduced within the ambit of the same formalism. Results from scenarios where
the strange quarks and hadrons are formed in equilibrium and evolves with and
without secondary productions have also been presented.
