Efficient algorithms to minimize makespan of the unrelated parallel batch-processing machines scheduling problem with unequal job ready times

Abstract

This paper considers the minimization of makespan in the unrelated parallel batch processing machines scheduling problem with considering non-identical job size and dynamic job ready time. The considered unrelated machines have different capacity and different processing speed. Each machine processes a number of the jobs as a batch at the same time so that the machine’s capacity is not exceeded. The batch processing time and the batch ready time are equal to the largest processing time and the largest ready time of jobs in the same batch, respectively. In this paper, a Mixed Integer Linear Programming (MILP) model, two categories of the heuristic procedures (six heuristics) and a meta-heuristic algorithm are proposed to solve the problem. A lower bound is also presented by relaxing of the original problem to evaluate the quality of the proposed algorithms. The computational experiments show the performance of the proposed algorithms under the considered measures.

An Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Batch Processing and Time-of-Use Electricity Prices

“…Shahidi-Zadeh et al [19] proposed a multi-objective harmony search algorithm to minimize the makespan, tardiness or earliness penalties and the purchasing cost of machines. Zarook et al [20] proposed a mixed-integer linear programming model, two categories of the heuristic procedures and a meta-heuristic algorithm to solve the problem.…”

Heuristic and Metaheuristic Methods for the Unrelated Machines Scheduling Problem: A Survey

“…Four data sets with different job and machine heterogeneity properties were used for testing. A batch scheduling problem with releasee times and unequal job sizes is investigated in [59]. Several simple DRs used for creating batches and scheduling them on machines are proposed.…”

“…[141] M d [163], [211], [251] Mm [188], [211], [215], [220], [231], [246], [251] js [57], [59], [197], [209], [210], [221], [234] Q k [57], [59], [197], [209], [210], [221], [234] Ms [200], [225], [265] studies will focus even more on optimising problems with several different constraints, and that even more new constraint variants will be defined. Finally, Table IV shows the application of different methods in the reviewed papers.…”