# Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops Doctoral thesis, 2023

In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item, multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to 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 minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory.

In Paper I, we propose a new bi-objective mixed-integer (linear) 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. In Paper II, 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. In Paper III, we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV, using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap.

Decision-making

Robust efficient solutions

Discrete bi-objective optimization

Capacity planning

Discrete tri-objective optimization

Production planning

Coverage gap

Pascal, Chalmers Tvärgata 3, Göteborg
Opponent: Prof. Kathrin Klamroth, Institute of Mathematical Modelling, Analysis and Computational Mathematics, University of Wuppertal, Germany

## Author

### Sunney Fotedar

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Fotedar,S., Strömberg,A.-B. A method to identify a representation of the set of non-dominated points for discrete tri-objective optimization problems.

Making Aerospace Manufacturing Smarter and More Efficient

In the aerospace world, every component, from the tiniest screw to the largest engine part, plays a vital role. Ensuring these parts are produced both efficiently and cost-effectively is essential. It's not just about keeping costs down; it's about delivering quality products on time, each time.

The Challenges: Production in aerospace involves the production resources, the materials, and the finished products. One needs to ensure that the resources are always ready for the task at hand, while not spending too much money getting prepared. There's also an inventory to manage—not having too many unused parts lying around. Hence, there is a balancing act to manage.

Our Solution: We developed a series of mathematical models to tackle these challenges. Our first model aimed to tell manufacturers how to allocate resources to get the most out of these, while also minimising costs. In the real world, things don't always go as planned—our second model helps manufacturers remain flexible and prepare for unforeseen challenges. Our third model ensures a balanced inventory, helping manufacturers to hold just the right amount of semi-finished as well as finished parts. Finally, we took all our learnings and used these to create a general model that could be applied to any complex multi-objective decision-making problem.

In Conclusion: It's about working smarter, reducing waste, and ensuring that the aerospace industry can continue to soar to new heights both efficiently and cost-effectively.

### Tactical resource allocation for efficient capacity Utilization

VINNOVA (2017-04845), 2017-11-10 -- 2022-12-31.

### Subject Categories

Production Engineering, Human Work Science and Ergonomics

Mathematics

Computational Mathematics

Other Mathematics

Discrete Mathematics

### Driving Forces

Sustainable development

Transport

Production

Basic sciences

### ISBN

978-91-7905-902-6

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5368

### Publisher

Chalmers

Pascal, Chalmers Tvärgata 3, Göteborg

Opponent: Prof. Kathrin Klamroth, Institute of Mathematical Modelling, Analysis and Computational Mathematics, University of Wuppertal, Germany