Near optimal furnace tool allocation with batching and waiting time constraints

Yu Ting Kao, Shun Cheng Zhan, Shi Chung Chang, Jen Hsuan Ho, Peng Wang, Peter B. Luh, Simon Wang, Fenix Wang, Joey Chang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations

Abstract

Furnace tools often constitute a bottleneck of a semiconductor wafer fab. They are characterized by long processing times with batching requirements. The problem is further complicated by stringent limitations on waiting times before furnace processing and the heterogeneous tool configuration. A novel integer programming model of allocating furnace tools to process steps over time for achieving production targets is first formulated. The formulation adopts difference equations to describe flows of wafers-in-process (WIPs) and availability of individual tools. Waiting time limitation is captured by an inequality for every time slot that the number of wafers processed in the next time slots within the limitation must be no less than the available WIPs of the current time slot. Constraints on batching decision couple among constraints of wafer flow, tool availability and bounds of batch size. After converting all the constraints to linear forms, an optimization tool suite is then applied to solving test problems derived from a real fab with a stopping criterion of no more than 5% difference from optimality. Comparisons with a currently practiced heuristic show that the near optimal furnace allocations lead to 18.5% more processing in average and 39.6% shorter average waiting time in certain cases than those of the heuristic. Computation times are all within 30 seconds over a personal computer with a Intel [email protected] GHz CPU. Such computation efficiency indicates a strong potential for applications to dynamic allocations in a fab.

Original languageEnglish
Title of host publication2011 IEEE International Conference on Automation Science and Engineering, CASE 2011
Pages108-113
Number of pages6
DOIs
StatePublished - 2011
Event2011 7th IEEE International Conference on Automation Science and Engineering, CASE 2011 - Trieste, Italy
Duration: Aug 24 2011Aug 27 2011

Publication series

NameIEEE International Conference on Automation Science and Engineering
ISSN (Print)2161-8070
ISSN (Electronic)2161-8089

Conference

Conference2011 7th IEEE International Conference on Automation Science and Engineering, CASE 2011
Country/TerritoryItaly
CityTrieste
Period8/24/118/27/11

Keywords

  • Furnace
  • batching
  • heuristic
  • integer linear programming
  • optimization
  • waiting time limitation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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