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.
Highlights
Introduction & literature reviewIn the recent years, Batch-Processing (BP) operation has been a critical solution to eliminate of the production bottlenecks in the most industries
The proposed scheduling problem can be partitioned in two sub-problems; i.e., grouping the jobs in the batches and scheduling of the batches on the machines, based on this strategic, this paper considers two categories of the heuristics algorithms; in first category, batching of the jobs is done by a Modified Full Batch Largest Process Time (FBLPT) role and the allocation of the batches on the machines takes place with considering various the machine’s scenarios; Earliest Idle time (EI), Shortest Completion time (SC) and Shortest Processing time (SP)
The assigned jobs to the machine k must be batched according to Full Batch Largest Processing Time (FBLPT) role, such that the size of the batches on the machine k don’t exceed of the machine’s capacity (Bk) and the created batches on the machine k must be arranged according to the Shortest Ready Time (SRT) role which in the numerical example, the sequence of the batch on the machines is equal to: M1 = {J1, J2}, {J6}, {J3, J7}, M2 = {J4, J5}, and M3 = {J10}, {J8, J9}
Summary
Batch-Processing (BP) operation has been a critical solution to eliminate of the production bottlenecks in the most industries. Jose Elias et al [10] considered the unrelated parallel batch processing machine scheduling problem with different speed and capacity of the machines and unequal job ready time They proposed an Iterated Greedy algorithm to minimize total flow time as the objective function. The cutting machines have the capability of cutting the batches of the sheets metal with different thicknesses (job size) at the same time, that leads to eliminate production bottlenecks and higher productivity This problem is shown as Rm|p-batch, pjk, sj, rj, Bk|Cmax in the classical symbolic of the scheduling literature, where first section of the symbolization shows machinery environment (Rm indicates m machines in the unrelated parallel environment).
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