POOLING PROBLEMS: THE NEW HYBRIDISED MODELS (NPQAND NHYB- ) AND ASYMPTOTIC SOLUTION METHODS.

ABSTRACT

Pooling problem explains a situation in which products having different qualities are mixed in a set of pools in such a way that the qualities of the blended products of the end pools must satisfy given quality requirements before transporting further downstream or to the targeted audience on demand. The blending process results to bilinear optimization problem which has resulted to different models and solution methods. Different complex problems are always encountered in the mixing and transportation process of pooling problems. However, different models and solution methods have been formulated to handle the associated blending & transportation process problems. Specifically, we identified the challenges of some recent models not able to handle large instances of dataset within a reasonable short time, the challenge of optimizing the quality of the products and improving the lower bound of the relaxation solution methods used. Thus, two new hybridized reformulations (NPQ - & NHYB- ) and their associated solution methods are presented to handle the above challenges. Also, some Mathematical properties are considered via propositions of the formulated models. To illustrate the flexibility, robustness and smart nature of the proposed new hybridized models (NPQ- and NHYB-), simulation study that generate large instances of dataset is carried out. Again, the applications of the simulated and lifetime data from the literature to the two new hybridized reformulations (NPQ & NHYB) of standard pooling problems are carried out with graphical illustrations Results show that our formulated NPQ and NHYB perform better than the existing ones. By implication, our models demonstrate strengths in the area of time management, optimal solution and tenacity to handle larger instances which others could not handle.