The Total Earliness/Tardiness Minimization on a Single Machine with Arbitrary Due Dates

Abstract

We solve a single machine problem of constructing a schedule of tasks with arbitrary due dates on a single machine that minimizes the total earliness/tardiness in relation to their due dates. This problem is solved in three different formulations: (1) the start time of the machine is fixed. In this case the problem is NP-hard; (2) the start time of the machine belongs to a specified time segment. The problem is intractable because there is no exact polynomial algorithm for its solving; (3) the start time of the machine is arbitrary. The problem is intractable because there is no exact polynomial algorithm for its solving. For the first two problems we give PSC-algorithms, each of them contains sufficient signs of a feasible solution optimality and is based on the optimal solution for the single machine problem to minimize the total tardiness of tasks in relation to their various due dates (with equal weights). We show that the PSC-algorithm of its solving is a simplified modification of the PSC-algorithm presented in Chap. 4. For the third problem solving we build an efficient approximation algorithm.