Scheduling family jobs on an unbounded parallel-batch machine to minimize makespan and maximum flow time

Abstract

This paper investigates the scheduling of family jobs with release dates on an unbounded parallel-batch machine. The involved objective functions are makespan and maximum flow time. It was reported in the literature that the single-criterion problem for minimizing makespan is strongly NP-hard when the number of families is arbitrary, and is polynomially solvable when the number of families is fixed. We first show in this paper that the singlecriterion problem for minimizing maximum flow time is also strongly NP-hard when the number of families is arbitrary. We further show that the Pareto optimization problem (also called bicriteria problem) for minimizing makespan and maximum flow time is polynomially solvable when the number of families is fixed, by enumerating all Pareto optimal points in polynomial time. This implies that the single-criterion problem for minimizing maximum flow time is also polynomially solvable when the number of families is fixed.2010 Mathematics Subject Classification. Primary: 58F15, 58F17; Secondary: 53C35.

Role of batch size in scheduling optimization of flexible manufacturing system using genetic algorithm

“…Cheng et al (2012) developed a mixed integer linear programming model to address scheduling problem of parallel batch processing of jobs to minimize makespan and completion time using polynomial time algorithm. Geng and Yuan (2018) investigated the unbounded parallel batching machine to minimize makespan and completion time using pareto optimization. Matin et al (2017) proposed PSO to optimize batch size in flow shop to minimize makespan and completion time.…”