Job Allocation with a Consideration of Fairness
Date Issued
2016
Date
2016
Author(s)
Liu, Chi-Wei
Abstract
Job scheduling is an important issue applied in many fields. In the manufacturing industry, one of the objectives is to assign jobs to machines in order to maximize the minimum profit among machines. Nevertheless, jobs not only bring profits, but also bring in workloads. Each machine cannot be assigned too many jobs due to limited capacity. This characteristic introduces a new challenge to this allocation problem. We would like to propose efficient algorithms to assign jobs by taking fairness issue into consideration. In this study, we consider the aforementioned job allocation problem. Our objective is to assign jobs to bring benefits to all the machines as equally as possible while ensuring that machines cannot be overloaded. In our model, we formulate this problem as a job assignment problem in which a set of jobs is to be assigned to a set of machines to maximize the benefit obtained by the machine earning the minimum benefit. The capacity of all machines are the same. We propose two list scheduling algorithms based on the longest processing time (LPT) rule. We show that the first algorithm guarantees a 1/2 worst-case performance when the job benefit is proportional to job workload. Moreover, our algorithm can have performance guarantees when the relationship between job benefits and workloads is convex or concave. Through numerical experiments, we also show that the algorithm works well when the jobs exhibit economy of scale but not so well when the jobs exhibit diminishing marginal benefits. The second algorithm is then shown to complement the first one in the latter case. Knowing this result, we can decide which algorithm to apply according to the environment.
Subjects
Job scheduling
Approximation algorithms
Fairness
Type
thesis
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