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A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

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posted on 2021-03-03, 22:03 authored by Anbang LiuAnbang Liu, Peter LuhPeter Luh, Bing YanBing Yan, Mikhail BraginMikhail Bragin
ob-shop scheduling is an important but difficult problem arising in low-volume high-variety manufacturing. It is usually solved at the beginning of each shift with strict computational time requirements. For fast resolution of the problem, a promising direction is to formulate it in an Integer Linear Programming (ILP) form so as to take advantages of widely available ILP methods such as Branch-and-Cut (B&C). Nevertheless, computational requirements on ILP methods for existing ILP formulations are high. In this paper, a novel ILP formulation is presented. In the formulation, a set of binary indicator variables indicating whether an operation begins at a time slot on a machine group or not is selected as decision variables, and all constraints are innovatively formulated based on this set of variables. For fast resolution of large problems, our recent decomposition-and-coordination method “Surrogate Absolute-Value Lagrangian Relaxation” (SAVLR) is enhanced by using a 3-segment piecewise linear penalty function, which more accurately approximates a quadratic penalty function as compared to an absolute-value function. Testing results demonstrate that our new formulation drastically reduces the computational requirements of B&C as compared to our previous formulation. For large problems where B&C has difficulties, near-optimal solutions are efficiently obtained by using the enhanced SAVLR under the new formulation.


Email Address of Submitting Author

Submitting Author's Institution

Center for Intelligent and Networked System (CFINS), Department of Automation, Tsinghua University

Submitting Author's Country

  • China