Stability of scheduling with random processing times on one machine

Abstract

We consider a strong NP-hard single-machine scheduling problem with deadlines and minimizing the total weight of late jobs on a single machine (1 w i U i ). Processing times are deterministic values or random variables having Erlang distributions. For this problem we study the tolerance to random parameter changes for solutions constructed according to tabu search metaheuristics. We also present a measure (called stability) that allows an evaluation of the algorithm based on its resistance to random parameter changes. Our experiments prove that random model solutions are more stable than the deterministic model ones.

Parallel Algorithm with Blocks for a Single-Machine Total Weighted Tardiness Scheduling Problem

“…A comprehensive review of the literature on scheduling problems with critical lines is presented in the following papers: Chenga, et al [8], Adamu and Adewumi [9]. Single-machine scheduling problems with random execution times or desired completion dates are also considered in the literature (Rajba and Wodecki [10], Bożejko et al [11,12]). In turn, the parallel algorithms for the single-machine scheduling problems are considered: parallel dynasearch algorithm [13], parallel population training algorithm [14], parallel path relinking for the problem version with setups [15].…”

Sampling Method for the Flow Shop with Uncertain Parameters

“…By the lack of the solutions stability in the fixed schedule there may occur a big mistake, which makes such a schedule unacceptable. That's why a necessity exists to construct such models and methods of their solutions that would take into account potential changes in the course of parameters process realisation and generate stable solutions ( [4], [9], [15]).…”