A Two-Level Optimization Approach For Engineer-To-Order Project Scheduling*

Abstract

This paper presents a new formulation of the flexible job-shop scheduling problem with outsourcing options adapted for Engineer-To-Order (ETO) products. Our formulation enables modeling complex product structures with flexible precedence relations between elements and operations. Having a significant role in the ETO context, the specificity of non-physical operations (design and engineering) is taken into account. Indeed, non-physical operations are subject to a validation stage, can be iterated in case of non-validation, and are executed once for several identical elements. The proposed approach is governed by a new ETO strategy to overcome the impact of the design uncertainty and element cancellations (time and financial wastes). First, the production and purchase of the most uncertain elements are delayed at the latest while their design is validated early. Besides, in the presence of similar elements, an element can be saved when cancelled by being used as a sub-part of another one. The proposed approach sequentially solves two mathematical models. The first model aims to minimise the makespan and outsourcing costs. The second model maximizes the solution robustness and the ability of saving elements while being governed by the completion time and project cost, output of the first model. The obtained results and a comparative study show the efficiency and robustness of the proposal.