A new Approach based on Ant Colony Optimization (ACO) to Determine the Supply Chain (SC) Design for a Product Mix

Manufacturing supply chain(SC) faces changing business environment and various customer demands. Pareto Ant Colony Optimisation (P-ACO) in order to obtain the non-dominated set of different SC designs was utilized as the guidance for designing manufacturing SC. PACO explores the solution space on the basis of applying the Ant Colony Optimisation algorithm and implementing more than one pheromone matrix, one for every objective. The SC design problem has been addressed by using Pareto Ant Colony Optimisation in which two objectives are minimised simultaneously. There were tested two ways in which the quantity of pheromones in the PM is incremented. In the SPM, the pheromone increment is a function of the two objectives, cost and time, while in MPM the pheromone matrix is divided into two pheromones, one for the cost and another one for the time. It could be concluded that the number of solutions do not depend on if the pheromone is split or is a function of the two variables because both method explore the same solution space. Although both methods explore the same solution space, the POS generated by every one is different. The POS that is generated when the pheromone matrix is split got solutions with lower time and cost than SMP because in the probabilistic decision rule a value of λ = 0.2 is used. It means that the ants preferred solution with a low cost instead of solutions with low time. The strategy of letting the best-so-far ant deposit pheromone over the PM accelerates the algorithm to get the optimal POS although the number of ants in the colony is small. An experimental example is used to test the algorithm and show the benefits of utilising two pheromone matrices and multiple ant colonies in SC optimisation problem.