Application of “Einstein's Riddle” in Solving Construction Machine Allocation Problems

Abstract

"Einstein's riddle" is a popular example of constraints satisfaction problem. Since its introduction, different forms and variations of the riddle have been presented. Regardless of the variant of the riddle, its solution is considered a tough challenge for humans. Researchers have developed and are still developing mathematical models, as well as computational simulation models for solving it. In this article, the authors have modified a previously published mathematical model and developed a computational spreadsheet model for solving the riddle, which provides a unique solution for the riddle. The model was also tested in a small and medium-scaled form for solving constraint satisfaction problems regarding the allocation of construction machines. The authors have also highlighted the model's limitations for solving such problems and made suggestions regarding necessary modifications in the model to solve more complex problems in the same domain.

Route Optimization of Multiple-Agent Travelling Salesman Problem

“…Excel add-inn solver is a useful tool, however it is limited by the size of the problem (i.e. 200 decision variables and constraints) by which it is applicable for small and medium size problems [25]. In order to avoid this limitation, author used basic functions in Excel.…”