We wall want happy employees. Our client had a complex set of rules and constraints governing the deployment of employees across a set of sites. These rules were conditioned on employee specialization, unique characteristics of the site, and the prior history of employee deployments to a site. Employees, on the other hand had their preferences for shift selection, vacation dates, and constraints for the accommodation of certain planned life events requiring employee absence.
The end result is a highly complex constrained optimization problem than could not be solved using off-the-shelf softwares. Even finding a single solution that satisfies all hard constraints was for our client a difficult and time consuming process, and adding in a ‘happiness’ factor (satisfying employee preferences to the greatest extent permitted by the constraints) seemed like an unattainable goal. The end result was a system that was in perpetual risk of collapse compounded by low employee satisfaction due to the perpetual fire-fighting.
Using our unique background as physicists and mathematicians we were able to develop a custom optimizer which efficiently and reliably solved the hard constraints, and optimized happiness to an impressive extent. Nearly 99.5% of the preferences could be satisfied 95% or more of the time. It turned out that the solution space satisfying the hard constraints was ample enough, and the employee preferences varied enough, that the vast majority could indeed be accommodated. All it took was for a few creative and experienced mathematical minds to look at the problem, and go a bit beyond the box of off-the-shelf software.