Multi-item dynamic lot sizing with multiple transportation modes and item fragmentation

This paper addresses a tactical joint inventory and transportation planning problem for multiple items with deterministic and time-varying demand, considering different transportation modes and item fragmentation. The latter corresponds to the splitting of the same item ordered quantity between several trucks or containers. On the one hand, fragmenting the items potentially reduces the number of containers used. On the other hand, loading the item lot fragments on several containers may negatively impact the handling and shipping operations. This new problem is proposed as a way to tackle such conflict. Several Mixed Integer Linear Programming models are proposed for the problem, which rely on two multi-item lot-sizing models with mode selection and two bin-packing models with item fragmentation. A relax-and-fix heuristic is also proposed. Using realistic instances, computational experiments are first conducted to identify the most efficient model in terms of computational time, to study the impact of key parameters on the computational complexity and to analyze the efficiency of the heuristic. Then, managerial insights are derived through additional computational experiments, in particular, to identify contexts requiring joint optimization of lot-sizing and bin-packing decisions, as well as the impact of item fragmentation constraints. Directions for future research are finally proposed.

Automated summary

This paper addresses the tactical joint inventory and transportation planning problem for multiple items with deterministic and time-varying demand, considering different transportation modes and item fragmentation. The proposed problem tackles the conflict between potentially reducing the number of containers used and negatively impacting handling and shipping operations. Several Mixed Integer Linear Programming models are suggested and a relax-and-fix heuristic is proposed for solving the problem. Realistic instances are used for computational experiments to identify the most efficient model, study the impact of key parameters, and analyze the efficiency of the heuristic. Managerial insights are derived to identify contexts requiring joint optimization and the impact of item fragmentation constraints, and future research directions are proposed.