Convex Quadratic Reformulations for Unrelated Parallel Machines Scheduling Problems

In this paper, we focus on three unrelated parallel machines scheduling problems in order to minimize sum of earliness and tardiness penalties. We consider the Plateau and Rios- Solis’s model for formulating these problems as 0-1 quadratic (non-convex) programs under linear constraints. First of all, we illustrate some defections on this model and then some modifications to obviate these defections are provided. We then apply the Skutella and the DPM methods to make a convex reformulation of two kinds of three problems. We finally discuss about how to make conic reformulation for all three problems, and how to solve them in order to obtain parameters that used for convex reformulation with QCR method. Indeed, this method gets a high-quality continuous lower bound