Abstract
This research deals with a multi-job Integer batch scheduling problem on a single machine with different due dates. Every job demanded one or more parts, and the single machine processed the job into a number of batches. The objective is to minimize total actual flow time, defined as the total flow time of all jobs starting from the arrival to the common due date. The decisions are to determine the sequence of jobs, the number of batches, batch size, and sequence of all batches on a single machine. This research proposes three algorithms, developed based on the longest due date rule (The P1-LDD Algorithm), the adjacent pairwise interchange method (The P2-API Algorithm), and the permutation method (The P3-PM Algorithm). The numerical experience shows that the three algorithms produce an outstanding solution. The P1-LDD Algorithm fits to solve a simple problem. The P2-API Algorithm has superior to solve a big complicated problem. The P3-PM Algorithm has the best performance to solve small complicated problems.
Highlights
We discuss a batch scheduling of multi-job with multiple delivery dates on a single machine where every job consists of a number of parts along with a respective due date
The objective is to minimize the total actual flow time, defined by Halim et al (1994) as the time interval of all parts on all batches to flow on the shop, starting from when that arrives until the due date
The problem of batch scheduling with multiple jobs and multiple due dates can be viewed as a single job batch scheduling problem with recurring common due dates
Summary
We discuss a batch scheduling of multi-job with multiple delivery dates on a single machine where every job consists of a number of parts along with a respective due date. This research is relevant to the company that adopts the Just-In-Time system where the company can manage the arrival of the part when the machine is already to process it. This problem is categorized as the serial batch problem where the length of a batch is equal to the sum of processing time of part in it, and common setup time is needed before the machine processes a new batch (Baptiste, 2000). The company should minimize the time of jobs flowing in the shop and keep on-time delivery (It is the same as minimizing the total actual flow time). The problems determine the number of batches for every job, the arrival time of the baches, the batch sizes, the schedule of the resulting batches, and the schedule of the jobs
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