Optimization models and solution methods for inventory routing problems

Abstract

Inventory management and distribution planning are essential activities for an efficient performance in the supply chain, especially for companies operating under the vendor-managed inventory business model. In this model, suppliers are allowed to manage the inventory levels and purchasing orders of their customers with the aim of reducing logistics and improving the supply chain performance. When inventory management and distribution planning are addressed in an integrated way in the vendor-managed inventory context, a challenging optimization problem arises, the inventory routing problem (IRP). In the IRP, a supplier is responsible for simultaneously determining the replenishment plan for its customers throughout a planning horizon as well as the vehicle routing and scheduling plan in each period such that a given performance measure is optimized.

The integrated optimization of inventory management and distribution planning activities can provide significant competitive advantages for companies. However, despite its practical appeal and benefits, the IRP has received increasing attention only in the last years. Consequently, there is still a considerable lack of research regarding optimization models and specific solution methods for relevant practical variants of this problem. Thus, the objective of this thesis is to develop comprehensive mathematical models and effective solution methods for several IRPs. Relevant variants are considered to make the addressed problems as realistic as possible.

Firstly, we describe the basic variant of the IRP and present a mathematical formulation for this problem. We then present two metaheuristic algorithms based on iterated local search and simulated annealing to solve this variant. Two different objective functions are considered. The results of extensive computational experiments using problem instances from the literature show that the presented metaheuristic algorithms effectively handle both objective functions, providing high-quality solutions within relatively short running times. In addition, the metaheuristics were able to find new best solutions for some of the benchmark instances.

Then we shift to a practical variant of the IRP considering product perishability. This feature has a substantial relevance in the supply chain context given that in several industries, the raw materials, as well as intermediate and final products, are often perishable. Moreover, perishability may appear in more than one activity throughout the supply chain. We study a variant in which the product is assumed to have a fixed shelf-life with age-dependent revenues and inventory holding costs. We first introduce four different mathematical formulations and branch-and-cut algorithms to solve them. We also propose a hybrid heuristic based on the combination of an iterated local search metaheuristic and two mathematical programming components. The results of computational experiments show the different advantages of the introduced formulations and the effectiveness of our hybrid method when dealing with this variant as well as the basic variant of the problem.

Finally, we focus on a stochastic variant of the IRP. Uncertainty plays a crucial role in supply chain management given that critical input data that are required for effective planning often are not known in advance. We address the basic variant of the IRP under the consideration that both the product supply and the customer demands are uncertain. We introduce a two-stage stochastic programming formulation and a heuristic solution method for this problem. From the results of extensive computational experiments, we show the response mechanisms of the optimal solutions under different uncertainty levels and cost configurations. We also show that the heuristic method effectively solves instances with a large number of scenarios.

By investigating different practical constraints for the IRP and providing tailored effective solution methods for the studied variants, this thesis addresses problems arising in several logistics contexts and shows the adaptability of the basic variant of the IRP and how it can be used as a basis to study richer practical IRPs. It brings contributions for the supply chain optimization literature and for the development of tools for supporting decision-making in practice.