Several Linearisations of the Quadratic Formulation (DOMP)

Abstract

In the previous chapter we defined the DOMP and proposed a nonlinear mixed-integer programme to model it. This formulation, (DOMP), has a quadratic objective function as well as a quadratic group of constraints. In this chapter we propose equivalent mixed-integer linear programmes to handle (DOMP), see Nickel [56] and Boland et al. [6]. In other words, we look for linear reformulations (linearisations) of (DOMP) which provide the same feasible solutions and the same optimal objective function value as the original programme. In this chapter we propose three linearisations that are motivated on linearisations developed for the Quadratic Assignment Problem, see Burkard [7] and Rendi [62]. In addition, we show how properties of optimal solutions can be used to strengthen these models, and discuss relationships between them. Furthermore, computational results and an exhaustive statistical study are presented in order to compare the different linearisations.