Single machine batch scheduling problem with family setup times and release dates to minimize makespan

Authors:
J. J. Yuan;Z. H. Liu;C. T. Ng;T. C. Cheng
Affiliations:
Aff1 Aff3;Aff2 Aff3;Department of Logistics, The Hong Kong Polytechnic University, Hong Kong, People's Republic of China;Department of Logistics, The Hong Kong Polytechnic University, Hong Kong, People's Republic of China
Venue:
Journal of Scheduling
Year:
2006

Citing 4
Cited 3

Scheduling Algorithms

Scheduling Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
The single machine batching problem with family setup times to minimize maximum lateness is strongly NP-hard

Journal of Scheduling
Batch scheduling to minimize maximum lateness

Operations Research Letters

A hybrid genetic algorithm for the single machine maximum lateness problem with release times and family setups

Computers and Operations Research
Single-machine scheduling with advanced process control constraints

Journal of Scheduling
Vehicle scheduling with combinable delivery and pickup operations

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the single machine batch scheduling problem with family setup times and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an $$O(n (\frac{n}{m}+1)^m)$$ time dynamic programming algorithm and an $$O(mk^{k}P^{2k-1})$$ time dynamic programming algorithm for the problem, where n is the number of jobs, m is the number of families, k is the number of distinct release dates and P is the sum of the setup times of all the families and the processing times of all the jobs. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme (PTAS) for the problem.