Optimizing automotive inbound logistics: A mixed-integer linear programming approach

The optimization of inbound logistics from first-tier suppliers at the aggregation level of a factory is a challenging coordination problem. In practice, different transport modes and multiple constraints exist and need to be taken into account: the available number of storage places, capacity of goods-entry, delivery profile and transportation pattern constraints, truck utilization, demand satisfaction, and the reverse flow of empty load carriers. A scalable solution method that is tailored to an automotive factory is currently not available. Optimization is usually carried out manually, e.g. experience-based or by using decision trees that follow an iterative optimization approach. Most of the mathematical models in the literature only deal with parts of the requirements and do not validate results in the required complexity. We present a mixed-integer linear programming approach to solve this complex problem using Gurobi. The solution capability and quality are enhanced by the introduction of a cyclic inventory constraint and valid inequalities. The evaluation of the approach is based on a case study of a German automotive factory with 570 suppliers and 3927 stock keeping units and reduces the as-is total cost by 33.86%. Additionally, CO₂ emissions are reduced by 74.66%. We further show that variable order quantities, along with a courier and express service as an additional transport mode, are of high economic relevance. As part of a sensitivity analysis, we show how the total costs change, when (a) goods-entry handling constraints, (b) truck utilization, (c) storage constraints, or (d) transportation costs vary, and (e) the effect of a cyclic inventory constraint.