Mathematical Optimization of the Tactical Allocation of Machining Resources in Aerospace Industry

Licentiate thesis, 2021

In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers (which includes, measures of quality and production lead-times) and to maintain control of the tied-up working capital. We introduce a new multi-item, multi-level capacitated planning model with a medium-to-long term planning horizon. The model can be used by most companies having functional workshops where costly and/or time- and resource demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimizes the maximum excess resource loading above a given loading threshold, while incurring as low qualification costs as possible.

In Paper I (Bi-objective optimization of the tactical allocation of jobtypes to machines), we propose a new bi-objective mathematical optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. Another contribution is a modified version of the bi-directional $\epsilon$ -constraint method especially tailored for our problem. We perform numerical tests on industrial test cases generated for our class of problem which indicates computational superiority of our method over conventional solution approaches.

In Paper II (Robust optimization of a bi-objective tactical resource allocation problem with uncertain qualification costs), we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. We also suggest a solution approach for identifying all the relevant robust efficient (RE) solutions. Our proposed approach is significantly faster than an existing approach for robust bi-objective optimization problems.