Optimising safety stock placement and lead time in an assembly supply chain using bi-objective MAX-MIN ant system

The problem of placing safety inventory over a network, which assembles a product, is a challenging issue in supply chain design (SCD) because manufacturers always want to reduce inventory all over the supply chain (SC). Moreover, the process of designing a SC and then placing inventory, to offer high service level at the lowest possible cost, across a complex SC, is not an easy task for decision makers. In this paper we use the SC representation proposed by Graves and Willems (2000), Manufacturing & Service Operations Management 2 (1), 68-83, where a SC is divided into many supplying, manufacturing, and delivering stages. Our problem is to select one resource option to perform each stage, and based on the selected options to place an amount of inventory (in-progress and on-hand) at each stage, in order to offer a satisfactory customer service level with as low as possible total supply chain cost. A resource option here represents a supplier, a manufacturing plant (production line), or a transport mode in a supplying, manufacturing, or delivering stage, respectively. We developed an approach based on ant colony optimisation (ACO) to minimise simultaneously the total supply chain cost and the products' lead time to ensure product deliveries without delays. What are new in our approach are the bi-objective function and the computational efficiency of our ACO-based approach. In addition, ACO has not been applied to solve the inventory placement problem. As a validation of the model, we: (a) describe a successful application at CIFUNSA, one of the largest iron foundry in the world, and (b) compare different CPU time instances and metrics about multi-objective optimisation.