A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

Abstract

This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors' previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of singlemachine scheduling problems: the total weighted earlinesstardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.

Scheduling jobs with release dates on identical parallel machines by minimizing the total weighted completion time

“…With this framework the authors were able to solve instances with up to 200 jobs to the proven optimality. Later, Tanaka and Fujikuma (2012) developed a DP based algorithm that considers state elimination, dominance rules and Lagrangean relaxation concepts. To the best of our knowledge, this method represents the state-of-the-art approach for solving the 1|r j | w j C j , being able to solve to the proven optimality instances with up to 200 jobs much faster than Pan and Shi's method.…”

API-based two-dimensional dispatching decision-making approach for semiconductor wafer fabrication with operation due date–related objectives

“…The best result for this problem to date is achieved by dynamic-programming-based exact algorithm (Tanaka and Fujikuma 2012). An initial lower bound is calculated by solving a Lagrangian relaxation of the original problem via dynamic programming.…”

A Strong Preemptive Relaxation for Weighted Tardiness and Earliness/Tardiness Problems on Unrelated Parallel Machines

“…Several heuristics with excellent empirical performance are available for both 1// j π j T j and 1// j π j T j + ǫ j E j to perform the latter task. However, in this work we rely on the recent powerful optimal algorithms of Tanaka et al (2009) and Tanaka and Fujikuma (2012) to handle the single machine problems as we mentioned in Section 1. Our computational experiments in Section 5 ultimately support this decision.…”

“…That is, we recognize that the main practical difficulty of solving Rm-TWT and Rm-TWET to (near-) optimality is determining a good job partition, and we directly incorporate this aspect of the problem into our rationale for developing this particular relaxation. Once a job partition is available, we rely on recent advances by Tanaka et al (2009) and Tanaka and Fujikuma (2012) to solve m independent single machine TWT or TWET problems, respectively, to construct a non-preemptive solution of high quality to the original unrelated parallel machine scheduling problem. The downside of our preemptive relaxation is that it is formulated as a difficult mixed integer linear program.…”