Coupled Task Scheduling With Exact Delays: Literature Review and Models

Abstract

The coupled task scheduling problem concerns scheduling a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. While research on the problem dates back to the 1980s, interests in the computational complexity of variants of the problem and solution methodologies have been evolving in the past few years. This motivates us to present an up-to-date and comprehensive literature review on the topic. Aiming to provide a complete road map for future research on the coupled task scheduling problem, we discuss all the relevant studies and potential research opportunities. In addition, we propose several sets of benchmark instances for the problem in various settings and provide a detailed evaluation of all the available models with a view to facilitating future research on the solution methods.

Scheduling coupled tasks with exact delays for minimum total job completion time

“…This basic model of scheduling coupled tasks has been studied for various radar tracking systems of multiple targets and/or multiple functionalities with various objective functions (Elshafei et al 2004;Farina and Neri 1980;Izquierdo-Fuente and Casar-Corredera 1994;Orman et al 1996Orman et al , 1998). This scheduling model has also found many other applications, ranging from improving performance of submarine torpedoes to chemistry manufacturing processes, to scheduling systems of robotic cells and to patient appointments in a chemotherapy outpatient clinic, as documented by Khatami et al (2020). Various solution approaches have been proposed.…”

A simple heuristic for the coupled task scheduling problem

“…The same instances are also solved by the solver Gurobi version 8.0.0 (Gurobi Optimization 2018) and utilising the model presented as Problem P earlier. As discussed, the model presented in P is shown to outperform all available mixed integer programs (MIPs) for the coupled task scheduling problem (Khatami et al 2019). The MIP model and algorithms are implemented in the programming language Python version 3.6 and all computational experiments are performed on a PC with Intel R Core TM i5-7500 CPU clocked at 3.40GHz with 8GB of memory under Linux Ubuntu 18.04 operating system.…”

“…A number of mathematical programs are available in the literature for the coupled task scheduling problem. We utilise the model proposed by Békési et al (2014) that according to Khatami et al (2019) is among the top performing models. Linear ordering variables are used in this formulation and the sequence is generated by ordering the tasks rather than jobs.…”

“…To investigate the performance of the proposed heuristic, we use the benchmark instances proposed in Khatami et al (2019) for the general case of the coupled task scheduling problem, denoted as the "general set". For the number of jobs we use the instances with n ∈ {10, 20, 25, 40, 50}, and for the choice of processing time of tasks and the duration of delays, three types of small, medium and large jobs are considered as small jobs: 25,200); and, large jobs:…”

“…These studies utilised instances with different characteristics and did not make them publicly available, making therefore difficult to conduct a comparison study. We refer the interested reader to Khatami et al (2019) for a comprehensive review of the coupled task studies, applications and models.…”