Optimizing performance of rigid polyurethane foam using FGP models

  • Abbas Al-Refaie
  • Raghed Aldwairi
  • Toly Chen
Original Research


This research proposes and implements fuzzy goal programming (FGP) models to optimize the performance of rigid polyurethane foam (RPF) for four quality characteristics. At initial process factor settings, the RPF process was found incapable for density, shrinkage ratio, and expanding ratio. However, it was found highly capable for compressive strength at 10% deformation. As a result, costly nonconforming products were produced and delivered. For this reason, fuzzy goal programming models were proposed and implemented to determine the combination of optimal factors settings followed by confirmation experiments. The results showed that: (1) for density the capability index is enhanced from −1.72 to (0.66, 0.62, and 0.85) at lower, middle and upper optimal factor setting levels, respectively, (2) for compressive stress at 10% deformation, the capability index is improved from 5.32, to (6.98, 5.45, and 6.02), (3) for shrinkage ratio the process capability is highly capable; \({{\widehat{C}}_{pu}}\) becomes (4.56, 4.62, and 5.91), and (4) for expanding ratio the capability index becomes highly capable; \({{\widehat{C}}_{pu}}\), equals to (6.37, 6.30, and 6.88). Such improvements in process capability result in significant savings in quality, maintenance, and production costs. In conclusions, implementing fuzzy goal programming model is found an efficient technique to optimal RPF performance for four quality responses.


Rigid polyurethane foam Fuzzy goal programming Process capability Optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of JordanAmmanJordan
  2. 2.Department of Industrial Engineering and Systems ManagementFeng Chia UniversityTaichungTaiwan, Republic of China

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