Two-Machine Open Shop Scheduling with Proportionally Deteriorating Jobs and Makespan Objective

Document Type : Original Manuscript


Department of Industrial Engineering and Management, Chaoyang University of Technology, Taichung, Taiwan


This manuscript examines the two-machine open shop scheduling problem where the latter a job is scheduled the longer it takes to process this job. The performance is measured by minimizing the makespan. By modifying existing algorithms for the corresponding problem with fixed processing times, two new algorithms are developed for the problem under consideration. The proofs of optimality of both algorithms are presented. The execution of these algorithms is illustrated by two numerical examples. Finally, both algorithms are further modified to solve a more generalized problem where the time demanded to process a job is a general linear function of its beginning time.

Graphical Abstract

Two-Machine Open Shop Scheduling with Proportionally Deteriorating Jobs and Makespan Objective


  • Existing algorithms for the problem O2//Cmax with fixed processing times are reviewed.
  • New algorithms for the problem O2/pij=bijt/Cmax with proportionally deteriorating processing times are developed.
  • Proofs of optimality of the developed algorithms are provided.
  • Generalization of the developed algorithms for solving the problem O2/pij=bij(a+ct)/Cmax is presented.


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