Bi-objective project portfolio selection in Lean Six Sigma

There are many aspects of a successful implementation of Lean Six Sigma techniques. Typically, decision-makers have to consider multiple conflicting objectives, and in many cases, they lack a formal approach for selecting projects. To meet the organization's requirements, some studies have proposed the use of multi-objective combinatorial optimization techniques. However, such formulations are notoriously difficult and complex to solve in reasonable computational time. In contrast to previous works, the present study proposes a novel integrated methodology to formulate and solve the Lean Six Sigma project portfolio as a 0-1 Bi-objective Quadratic Programming Problem. The model considers interdependent project effects (quadratic objectives) and is subject to resource limitations and constraints regarding mutually exclusive projects and mandatory projects. The approach permits tackling the problem as a Mixed-Integer Quadratically-Constrained Programming Problem and thus to use the branch-and-bound algorithms implemented by the standard optimization solvers such as CPLEX or Gurobi. Numerical examples are provided to verify the efficiency and added value of the methodology.