Development of a method to linearize the quadratic assignment problem

The paper presents a new powerful technique to linearize the quadratic assignment problem. There are so many techniques available in literature that used In all these linear formulations, both number of variables and constraints significantly increase. problem (QAP) is well-known whereby set facilities allocated locations such way cost function distance flow between facilities. this problem, costs associated with facility being placed at certain location. objective minimize each three main categories methods for solving These heuristics, bounding exact algorithms. Heuristics quickly give near-optimal solutions five types heuristics construction methods, limited enumeration improvement simulated annealing genetic For every formulated QAP, lower bound can be calculated. We have Gilmore-Lawler bounds, eigenvalue related bounds based on reformulations as techniques. four classes exactly, which dynamic programming, cutting plane techniques, branch procedures hybrids last two. QAP has application computer backboard wiring, hospital layout, dartboard design, typewriter keyboard production process, scheduling, etc. proposed strength increases by only one after linearization process.