Unreliable manufacturing supply chain optimisation based on an infinitesimal perturbation analysis

This paper studies the optimisation of a manufacturing/remanufacturing system, which produces one type of product and is composed of a serviceable inventory, two parallel machines, a recovery inventory, two quality inspection centres and customers who demand a constant quantity of product. The proposed system takes into account the withdrawn products and the return of the used products from the market. The manufacturing and remanufacturing products are stored in the serviceable inventory. The used products are inspected then disposed of or stored in the recovery inventory for remanufacturing. The withdrawn products are inspected and stored in the serviceable inventory for selling or stored in the recovery inventory for remanufacturing. The objective of this work is to find the optimal serviceable inventory level that minimises the cost function, then to study the influence of withdrawn products and used products on the value of the optimal serviceable inventory level. Infinitesimal perturbation analysis method is used to derive gradient estimators of the total cost with respect to inventory levels. These estimators are used in an optimisation algorithm that computes the optimal serviceable inventory level. Numerical results and influence analysis are presented to illustrate the usefulness of the proposed approach.