Deterministic multiprocessor scheduling with multiple objectives

One common job scheduling objective is to minimize makespan. The problem can be modeled as integer linear programming (ILP) and will often have multiple alternative optimal solutions. However, secondary considerations, e.g. minimizing the second latest completion time, may very well dictate a preference between solutions with identical makespans. Because of the nature of the primary objective, standard approaches for optimizing a prioritized set of multiple objectives will not work. In this paper we prove that for unit time problems, an appropriate objective function can be formulated, which, when optimized, satisfies both the primary and secondary objectives. Moreover, the new formulation can be modeled as a classical assignment problem (AP). This has the added advantage of efficiency of solution and availability of software. Applications to computer processor scheduling and the military are presented.