Heuristic Algorithm to Minimize Total Weighted Tardiness on the Unrelated Parallel Machine with Sequence Dependent Setup and Future Ready Time
Date of Award
Master of Science
David Yu, Otieno A Wilkistar
ATC-based rule, Look-ahead, total weighted tardiness
This study presents a heuristic algorithm to minimize total weighted tardiness on unrelated parallel machines with sequence-dependent setup time and future ready time. We propose a new rule based on Apparent Tardiness Cost (ATC). The performance of the rule is evaluated on unrelated parallel machines. In order to solve a problem, we use a look-ahead method and a job-swap method. When a machine becomes idle, the heuristic compares the jobs on the machine and selects the one with the smallest total tardiness value to carry out a process.
The propose heuristic is divided into three stages: The first stage employs the newly introduced dispatching rule, ATC with continuous setup and ready time for unrelated parallel machines (ATCSR_UP), along with a look-ahead heuristic to select the initial job for each machine. The second stage, consisting of several iterations, schedules the rest of the job on the machine. Each iteration starts by finding the job with the smallest tardiness. The ATCSR_Rm rule proposed by Lin and Hsieh (2013) concerns the unrelated-parallel-machine scheduling which this study examines, so we compare our ATC-based rule with their proposed rule. Although they study a separable setup time in their research, no other paper than Lin and Hsieh (2003) focus on unrelated parallel machine with future ready times. In their WSPT term, they consider the processing time for each job; our own rule considers processing time, setup time, job ready time, and machine time. We consider the setup time, job ready time, and machine time because — according to the continuous sequence-dependent setup rule — setup time should be included in processing time (Yue and Jang 2013). In addition, job ready time and machine time should also be included in the processing time. Adding setup time 〖(s〗_(i,j)), job ready time (r_j), and machine time (t_m) to the formula thus makes the formula more accurate.
Lin and Hsieh (2013) use max(r_j,t_i+s_(i,j) ) for the slack term, and they compare the ready time with the sum of the machine available time 〖(t〗_i) and the setup time 〖(s〗_(i,j)). However, in our formula, we consider ready time, machine time, and current time. Current time (t) is used when a job might come at a future time when the machine in question is idle or has finished the job.
The last term of the propose heuristic is the ready term, which uses both ready time (r_j) and machine time (t_m), because it needs to specify whether ready time (r_j) or machine time (t_m) goes first. If a job is ready to be processed but the machine is not ready, the job has to wait. We use ready time (r_j) and machine time (t_m) because this makes the formula more suitable for practical, real-world use
Li, Tzu Yi, "Heuristic Algorithm to Minimize Total Weighted Tardiness on the Unrelated Parallel Machine with Sequence Dependent Setup and Future Ready Time" (2018). Theses and Dissertations. 1997.