Hägglunds, part of the Bosch Rexroth group, manufactures hydraulic motors used in industries such as renewable energy, construction and infrastructure, pulp and paper, logistics, and transportation. A few years ago, the company implemented a system in which their motors were categorized based on the time from customer order to final delivery. Three categories were created: category 10, 20, and 30 with corresponding lead times of 6, 10, and 16 weeks. This categorization reflects both inventory management and production strategy. The company wants to achieve greater precision regarding which motors belong to each lead time category. The company also wants to achieve better control over different motors and their respective lead times. This thesis aims to optimize this categorization in order, if possible, to allow motors that are frequently sold to be offered with short lead times to customers. An integer programming model was constructed with the logical expression that the motor must be complete in order for the components belonging to the motor to be selected. The condition is non-linear, which led to the implementation of a pseudo-Boolean transformation.

Two different optimizations were carried out. One minimizes the number of components used to manufacture the motors selected for inventory holding, and the other optimization minimizes the inventory value required to provide the correct lead times for the motors. The optimization based on inventory value generated many selected components, while the optimization based on minimizing components resulted in a high inventory value. A combination of the two optimizations was carried out where the number of different components was minimized under the condition that the inventory value may not increase by more than 20\% above the inventory value obtained from minimizing inventory value. The results show that an optimization model is possible to implement for problems containing logical expressions. A solution with minimized inventory value results in a large number of motors and components. A solution with a minimized number of components results in a high inventory value. Minimizing the number of components under the condition that the inventory value may not be more than 20\% higher than the minimum inventory value balances the relationship between capital binding and inventory size. The work shows that a binary integer programming model is a possible solution for inventory management problems with this level of complexity.