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.
Engebrethsen, Erna S. & Dauzère-Pérès, Stéphane (2022)
Transportation strategies for dynamic lot sizing: single or multiple modes?
The complexity of decision-making for companies buying transportation services has increased due to the presence of more options and pricing schedules for transportation. Many companies make transportation and inventory decisions in an uncoordinated way and select only one transportation mode, missing opportunities for logistics cost savings. The experimental study in this paper is based on a real-world decision problem faced by a Scandinavian company that distributes fast-moving consumer goods and wants to determine its transportation strategy. We propose a novel multi-mode lot-sizing model with dynamic deterministic demand to illustrate the cost impact of accurately modelling piecewise-linear transportation costs and allowing a more flexible usage of transportation modes when planning order replenishments. We compare three transportation strategies with increasing degrees of flexibility: two single mode strategies, where one strategy is more flexible than the other, and a multi-mode strategy. We conclude that managers can significantly reduce costs by increasing the flexibility of mode selection in transportation strategies.
Engebrethsen, Erna S. & Dauzère-Pérès, Stéphane (2019)
Transportation mode selection in inventory models: A literature review
Despite the significant share of transportation costs in logistics costs and the importance of considering transportation in inventory models, the majority of the existing models either neglect or simplify transportation costs and capacities, often assuming that only one transportation option is available. The complexity of modeling and choosing the optimal transportation mode or combination of modes has increased due to the increased variety of transportation options and pricing schedules after deregulation. In this paper, we review and classify inventory models with multiple transportation modes focusing on the freight cost functions, mode characteristics and the methods for modeling multiple modes. To our knowledge, no such review has previously been published. We discuss the benefits and weaknesses of each modeling method and, based on industrial practices, identify new areas for research.
