Multitasking Scheduling Problems with Deterioration Effect

Abstract

Multitasking scheduling problems with a deterioration effect incurred by coexisting behavioral phenomena in human-related scheduling systems including deteriorating task processing times and deteriorating rate-modifying activity (DRMA) of human operators are addressed. Under the assumption of this problem, the processing of a selected task suffers from the joint effect of available but unfinished waiting tasks, the position-dependent deterioration of task processing time, and the DRMA of human operators. Traditionally, these issues have been considered separately; herein, we address their integration. We propose optimal algorithms to solve the problems to minimize makespan and the total absolute differences in completion time, respectively. Based on the analysis, some special cases and extensions are also discussed.

A branch‐and‐price algorithm for identical parallel machine scheduling with multiple milestones

“…They analyze the computational complexity of these models and develop algorithms. Subsequently, researchers explore several extensions of Hall et al's multitasking model (Hall et al, 2015), introducing deterioration effects and rate‐modifying activities (Ji et al, 2019; Zhu et al, 2019; Zhu, Li, & Chu, 2017; Zhu, Zheng, & Chu, 2017). Liu et al (2017) further expand Hall et al's model by incorporating a common due date‐related objective.…”

A branch‐and‐price approach to the multitasking scheduling with batch control on parallel machines

“…Multitasking is a common phenomenon that can be frequently observed in administrative planning, production environment, and business processes (Jez, 2011;Goes et al, 2018). In recent years, multitasking-related issues have attracted great attentions in the literature (Hall et al, 2015(Hall et al, , 2016Liu et al, 2017;Zhu et al, 2017aZhu et al, , 2017bJi et al, 2019;Xiong et al, 2019;Zhu et al, 2019;Wang et al, 2020). Multitasking is quickly switching and performing more than one task at a same time (Lin, 2013).…”

“…Zhu et al (2017bZhu et al ( , 2019 studied multitasking scheduling with a rate-modifying activity (RMA), which considered that the operator takes regularly engages rest breaks during work shifts to recover/mitigate some negative effects. Zhu et al (2017a) also integrated the effect of available but unfinished waiting tasks, the position-dependent deterioration of task processing time, and the deteriorating ratemodifying activity (DRMA) of human operators. An optimal algorithm was proposed to minimize the makespan and the total absolute differences in completion time.…”

“…Developing an effective approach to the pricing problem is the key point of branch-and-price algorithm. Incorporating fast approaches in the B&P framework, such as greedy randomized adaptive search (Bard and Rojanasoonthon, 2006), binary decision diagram (Kowalczyk and Leus, 2018), labeling-set algorithm (Bulhoes et al, 2020), and heuristic (Xiong et al, 2019;Pereira et al, 2020), is an efficient way to deal Hall et al (2015Hall et al ( , 2016 Single machine None Zhu et al (2017aZhu et al ( , 2017bZhu et al ( , 2019 Single machine Rate-modifying activities, Deterioration effect Liu et al (2017) Single machine Due date assignment Wang et al (2020) Single machine Deterioration effect, Efficiency promotion Ji et al (2019) Parallel machines Slack due-window assignment Xiong et al (2019) Parallel machines None with large-size problems and achieved good results. Here we consider developing an artificial bee colony (ABC) algorithm to fast obtain the solutions of the pricing problem while the reduced cost is minimized.…”

“…Zhu et al. (2017a) also integrated the effect of available but unfinished waiting tasks, the position‐dependent deterioration of task processing time, and the deteriorating rate‐modifying activity (DRMA) of human operators. An optimal algorithm was proposed to minimize the makespan and the total absolute differences in completion time.…”