A COMPARISON OF AN CP AND MIP APPROACH FOR SCHEDULING JOBS IN PRODUCTION AREAS WITH TIME CONSTRAINTS AND UNCERTAINTIES

This research is motivated by the expensive cost of scraps because of timelink misses in a semiconductor manufacturing line due to tool downs. A timelink is a time constraint between defined process steps. This paper presents a mixed integer programming model (MIP) and a constraint programming model (CP) with downscaled time constraints. With the assistance of the survival analysis, a safety value will be computed and included as a constant in the MIP and as a dynamic expression in the CP, to downscale the allowed time between two specific operations. The MIP and CP models are tested on a realistic production area example with different problem sizes. The quality of the solution and the performance of these two approaches are compared with each other. The test results show that the CP model outperforms the MIP and quickly finds much earlier usable schedules for large problem sizes.

[1]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[2]  Philippe Laborie,et al.  Reasoning with Conditional Time-Intervals , 2008, FLAIRS.

[3]  Andy Ham,et al.  Scheduling of Dual Resource Constrained Lithography Production: Using CP and MIP/CP , 2018, IEEE Transactions on Semiconductor Manufacturing.

[4]  Irem Ozkarahan,et al.  A constraint programming-based solution approach for medical resident scheduling problems , 2011, Comput. Oper. Res..

[5]  Louis-Martin Rousseau,et al.  A constraint programming approach for a batch processing problem with non-identical job sizes , 2012, Eur. J. Oper. Res..

[6]  Philippe Baptiste,et al.  Constraint - based scheduling : applying constraint programming to scheduling problems , 2001 .

[7]  Erwin Pesch,et al.  Ablaufplanung: Einführung in Scheduling , 2019 .

[8]  Andreas Klemmt,et al.  Ablaufplanung in der Halbleiter- und Elektronikproduktion , 2012 .

[9]  Gabriel A. Wainer,et al.  ROBUSTNESS ANALYSIS OF AN MIP FOR PRODUCTION AREAS WITH TIME CONSTRAINTS AND TOOL INTERRUPTIONS IN SEMICONDUCTOR MANUFACTURING , 2017 .

[10]  Andreas Klemmt,et al.  Scheduling jobs with time constraints between consecutive process steps in semiconductor manufacturing , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[11]  Philippe Laborie,et al.  IBM ILOG CP Optimizer for Detailed Scheduling Illustrated on Three Problems , 2009, CPAIOR.

[12]  Toby Walsh,et al.  Handbook of Constraint Programming , 2006, Handbook of Constraint Programming.

[13]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[14]  Xian Liu,et al.  Survival Analysis: Models and Applications , 2012 .

[15]  Tao Wang,et al.  Scheduling operating theatres: Mixed integer programming vs. constraint programming , 2015, Eur. J. Oper. Res..

[16]  John W. Fowler,et al.  Constraint Programming Approach for Scheduling Jobs With Release Times, Non-Identical Sizes, and Incompatible Families on Parallel Batching Machines , 2017, IEEE Transactions on Semiconductor Manufacturing.

[17]  Jennifer K. Ryan,et al.  Production Scheduling with Queue-time Constraints: Alternative Formulations , 2014 .

[18]  Gerald Weigert,et al.  Robustness analysis of an MIP for production areas with time constraints and tool interruptions in semiconductor manufacturing , 2017, 2017 Winter Simulation Conference (WSC).

[19]  Andreas Klemmt,et al.  From dispatching to scheduling: Challenges in integrating a generic optimization platform into semiconductor shop floor execution , 2017, 2017 Winter Simulation Conference (WSC).

[20]  Peter Brucker,et al.  Scheduling Algorithms , 1995 .

[21]  Christian Maleck,et al.  A comparison of control methods for production areas with time constraints and tool interruptions in semiconductor manufacturing , 2017, 2017 40th International Spring Seminar on Electronics Technology (ISSE).