A multi-objective intelligent water drop algorithm to minimise cost Of goods sold and time to market in logistics networks

Abstract

The Intelligent Water Drop (IWD) algorithm is inspired by the movement of natural water drops (WD) in a river. A stream can find an optimum path considering the conditions of its surroundings to reach its ultimate goal, which is often a sea. In the process of reaching such destination, the WD and the environment interact with each other as the WD moves through the river bed. Similarly, the supply chain problem can be modelled as a flow of stages that must be completed and optimised to obtain a finished product that is delivered to the end user. Every stage may have one or more options to be satisfied such as suppliers, manufacturing or delivery options. Each option is characterised by its time and cost. Within this context, multi–objective optimisation approaches are particularly well suited to provide optimal solutions. This problem has been classified as NP hard; thus, this paper proposes an approach aiming to solve the logistics network problem using a modified multi–objective extension of the IWD which returns a Pareto set.Artificial WD, flowing through the supply chain, will simultaneously minimise the cost of goods sold and the lead time of every product involved by using the concept of Pareto optimality. The proposed approach has been tested over instances widely used in literature yielding promising results which are supported by the performance measurements taken by comparison to the ant colony meta-heuristic as well as the true fronts obtained by exhaustive enumeration. The Pareto set returned by IWD is computed in 4 s and the generational distance, spacing, and hyper–area metrics are very close to those computed by exhaustive enumeration. Therefore, our main contribution is the design of a new algorithm that overcomes the algorithm proposed by Moncayo-Martínez and Zhang (2011).This paper contributes to enhance the current body of knowledge of expert and intelligent systems by providing a new, effective and efficient IWD-based optimisation method for the design and configuration of supply chain and logistics networks taking into account multiple objectives simultaneously.