Jianming Dong

An FPTAS for the parallel two-stage flowshop problem

We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the ( m , 2 ) -PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The ( m , 2 ) -PFS problem can be decomposed into two subproblems: to assign the n jobs to the m parallel flowshops, and for each flowshop to schedule the jobs assigned to the flowshop. We first present a pseudo-polynomial time dynamic programming algorithm to solve the ( m , 2 ) -PFS problem optimally, for any fixed m, based on an earlier idea for solving the ( 2 , 2 ) -PFS problem. Using the dynamic programming algorithm as a subroutine, we design a fully polynomial-time approximation scheme (FPTAS) for the ( m , 2 ) -PFS problem.

Single-server parallel-machine scheduling with loading and unloading times

We consider a scheduling problem in which jobs are processed on two identical parallel machines that share a common server that loads and unloads jobs on them. Each job has to be loaded by the server before being processed on one of the machines and unloaded immediately by the server after its processing. The goal is to minimize the makespan. We study non-preemptive variants of the problem where the loading and unloading times are both equal to one time unit. Since the non-preemptive variant of the problem is NP-hard, we apply two classical heuristics, namely list scheduling (LS) and longest processing time (LPT),to tackle the problem. We show that LS and LPT have tight worst-case ratios of 12/7 and 4/3, respectively.

A note on the algorithm LPT-FF for a flowshop scheduling with two batch-processing machines

A flowshop scheduling problem with two batch-processing machines is investigated in this paper, with the optimization goal to minimize the makespan. When the job processing times on the two machines are positively correlated, a

Machine scheduling with a maintenance interval and job delivery coordination

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Single machine scheduling with job delivery to multiple customers

4-approximation algorithm for this NP-hard problem was previously proposed. We show that this algorithm has a worst-case performance guarantee of

Corrigendum to “An FPTAS for the parallel two-stage flowshop problem” [Theoret. Comput. Sci. 657 (2017) 64–72]

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