Study on Assumptions, Techniques and Notation to Minimize Total Cost of Inter Cell and Intra Cell Flows

Nitish, Dr. Ravindra Kumar Sharma, Dr. Harish Kumar

Minimize, machines, annealing, comprehensive, applications.

Our objective is to minimize total cost of inter-cell and intra-cell flows subject to a cell size constraint, i.e., the maximum number of machines allowed in each cell. We consider a center-to center linear distance measure and for simplification, we do not consider any other spatial constraint. However, one may note that such constraints can also be added to the model by some simple modifications to the will-be proposed procedure.

As the problem of partitioning a manufacturing system into several subsystems, with the objective of minimizing inter-cell flow movement cost is NP-complete (Garey and Johnson (1979)), most researchers have focused on developing heuristics or metaheuristics. In this work, as well, we 100 Saghafian and Akbari Jokar propose an enhanced Simulated Annealing (SA) in which the crossover and mutation operators of Genetic Algorithm (GA) are used as generation mechanism to generate neighborhood solution.

Kirkpatrick, Gelatt and Vecchi (1983) introduced simulated Annealing (SA) and Creny (1985) considered the analogy between the annealing process of solids and the process of solving combinatorial optimization problems. However, it was originally developed as a simulation model for a physical annealing process of condensed matter (Metropolis et al. (1953)). Laarhoven and Aarts (1987) gave a comprehensive discussion of the theory and review of various applications.

Also, they showed that the simulated annealing process converges to the set of global optimal solutions under certain conditions. It starts from an initial solution to the problem, and then generates a new trial solution from the neighborhood at the current solution. If the new solution is better than the current solution it is accepted and used as the new current solution.