Single machine interfering jobs problem with flowtime objective

Interfering jobs problems (or multi agents scheduling problems) are an emergent topic in the scheduling literature.In these decisión problems,two or more sets of jobs have to be scheduled, each one with its own criteria. More specifically, we focus on a problem in which jobs belonging to two sets have to be scheduled in a single machine in order to minimize the total flowtime of the jobs in one set, while the total flowtime of the jobs in the other set should not exceed a given constant €. This problem is known to be weakly NP- hard, and, in the literature, a dynamic programming (DP) algorithm has been proposed to find optimal solutions. In this paper, we first analyse the distribution of solutions of the problem in order to establish its empirical hardness. Next, a novel encoding scheme and a set of properties associated to the neighbourhood of this scheme are presented. These properties are used to develop both exact and approximate methods, i.e. a branch and bound (B&B) method, several constructive heuristics, and different versions of a genetic algorithm (GA). The computational experience carried out shows that the proposed B&B is more efficient than the exist- ing DP algorithm. The results also show the advantages of the proposed encoding scheme, as the approximate methods yield close-to-optimum solutions for big-sized instances where exact methods are not feasible.Ministerio de Economía y Competitividad DPI2013-44461-P/DPIMinisterio de Economía y Competitividad DPI2010-15573/DP