Optimal Scheduling for Vector or Scalar Criterion on Parallel Machines with Arbitrary Due Dates of Tasks

Abstract

We examine the problem of constructing a feasible schedule for parallel machines of equal or various productivities with various due dates of tasks and arbitrary start times of machines. We consider two optimality criteria: maximizing the earliest start time of machines (scalar criterion) or obtaining optimal start times of machines subject to a direct lexicographical order of their assignment (vector criterion). In fact, in this chapter we examine four intractable combinatorial optimization problems (for each one there are no efficient polynomial algorithms for its solving). Each of four presented PSC-algorithms contains separate sufficient signs of optimality of a feasible solution, the first polynomial component that checks the sufficient signs of optimality, and an approximation algorithm. Since the formulated problems are quite complex, each component of the PSC-algorithms contain many subalgorithms, each of which implements a separate original heuristic. We give examples of the problems solving.