Two branch‐and‐bound algorithms for the robust parallel machine scheduling problem

Two branch‐and‐bound algorithms for the robust parallel machine scheduling problem

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Article ID: iaor201111468
Volume: 39
Issue: 7
Start Page Number: 1652
End Page Number: 1660
Publication Date: Jul 2012
Journal: Computers and Operations Research
Authors: , ,
Keywords: production, scheduling, combinatorial optimization, stochastic processes
Abstract:

Uncertainty is an inevitable element in many practical production planning and scheduling environments. When a due date is predetermined for performing a set of jobs for a customer, production managers are often concerned with establishing a schedule with the highest possible confidence of meeting the due date. In this paper, we study the problem of scheduling a given number of jobs on a specified number of identical parallel machines when the processing time of each job is stochastic. Our goal is to find a robust schedule that maximizes the customer service level, which is the probability of the makespan not exceeding the due date. We develop two branch‐and‐bound algorithms for finding an optimal solution; the two algorithms differ mainly in their branching scheme. We generate a set of benchmark instances and compare the performance of the algorithms based on this dataset.

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