Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

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.

Congruence Between Leadership Gender and Organizational Claims Affects the Gender Composition of the Applicant Pool: Field Experimental Evidence

The extent to which men and women sort into different jobs and organizations—namely, gender differences in supply-side labor market processes—is a key determinant of workplace gender composition. This study draws on theories of congruence to uncover a unique organization-level driver of gender differences in job seekers’ behavior. We first argue and show that congruence between leadership gender and organizational claims is a key mechanism that drives job seekers’ interest. Specifically, many organizational claims are gender-typed, such that social claims activate the female stereotype, whereas business claims activate the male stereotype. Thus, whereas female-led organizations making social claims are gender-congruent, male-led firms making the same claims are gender-incongruent. Beyond demonstrating a general preference among job seekers for congruence, we also find that female job seekers are most interested in working for organizations that are simultaneously congruent and provide credible signals that they are fair and equitable employers. The congruence of leadership gender and organizational claims thus affects the gender composition of applicant pools for otherwise identical jobs.

Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines

In the paper we consider the problem of scheduling n identical jobs on 4 uniform machines with speeds s1 ≥ s2 ≥ s3 ≥ s4, respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are subject to some kind of mutual exclusion constraints modeled by a bipartite incompatibility graph of degree Δ, where two incompatible jobs cannot be processed on the same machine. We show that the general problem is NP-hard even if s1 = s2 = s3. If, however, Δ ≤ 4 and s1 ≥ 12s2, s2 = s3 = s4, then the problem can be solved to optimality in time O(n1.5). The same algorithm returns a solution of value at most 2 times optimal provided that s1 ≥ 2s2. Finally, we study the case s1 ≥ s2 ≥ s3 = s4 and give a 32/15-approximation algorithm running also in O(n1.5) time.