Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

Abstract

This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.

Novel Approaches to the Formulation of Scheduling Problems

“…Finally, we are going to focus on the problems with objectives P m ||Σw j C j and P m ||Σw j T j . Other objectives for the study of identical parallel machines were considered in [11][12][13].…”

Identical Parallel Machine Scheduling Considering Workload Smoothness Index

“…Calculate the difference between the maximum and the minimum workload, denoted Δ max For example, suppose there are seven jobs to be processed on two machines. The corresponding processing times of the jobs are (8,9,8,6,8,7,6). Let the maximum workload constraint be 29.…”

“…Various optimization objectives, including the makespan and the total completion time, have been well addressed in previous studies [4][5][6][7]. In addition to the above classical objectives, workload balance between the machines together with the corresponding operators is also a major aspect of decision making in manufacturing industry [8][9][10]. It contributes to reducing the idleness and work-in-process and removing bottlenecks [8,11].…”

Robust Appointment Scheduling in Healthcare

“…This model proposed in this paper generates a workforce schedule that minimizes overtime and balances a doctor's workload over a year, satisfying weekly patient demand. The objective function minimizes the addition between the workload of each pair of patients and the number of yearly overtime hours of the workforce as well [40][41][42][43][44]. By assuming that the input is only patients with a single session and that consultation and installation time are zero, the considered problem without resource constraints is reduced to the two stages as given in the flow shop problem, which is NP-hard [45].…”