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The inventory routing problem with stochastic demand includes the inventory control, product transportation and scheduling decisions, considering an estimation of customer demands. This problem appears in several real situations, playing a fundamental role in reducing costs and improving the efficiency and reliability of the service. In practice, there are often restrictions on the "time window", which corresponds to a certain period of the day on which deliveries can be made. Despite the great relevance of this type of constraint, there are no results in the literature that combine stochastic demand and time window constraints. In this work, we propose a system, using advanced techniques of operational research, to solve the inventory routing problem with stochastic demand, considering time window constraints, as well as additional constraints of maximum inventory capacities in both the client and the depot and individual confidence level of the customer service.

The integration of inventory management, vehicle routing, and scheduling decisions is known as Inventory Routing Problem (IRP). In this problem, the main objective is to determine: (i) the quantity of products to be delivered based on customer's demand; (ii) the delivery periods and (iii) the route of vehicles. IRPs that include time window service constraints are found in real scenarios and the attendance of this type of constraints brings benefits to both the supplier and the customer. This systematic review of the literature aims to identify trends in the area that studies Inventory Routing Problems with time windows. We identify and analyze the proposed approaches, the characteristics of the solved problems and the type of experiments performed in 9 primary studies.

Fornecedores necessitam atender a demanda de seus clientes da forma mais otimizada possível e mantendo a qualidade de seu serviço. Porém, em muitos casos essa demanda é desconhecida. O problema conhecido como problema de roteirização e inventário com demanda estocástica combina: (i) o controle de estoque; (ii) o transporte do produto; e (iii) decisões de agendamento da entrega considerando essa classe de demanda. Este trabalho tem como objetivo melhorar o algoritmo estado da arte baseado em programação matemática e relaxação lagrangeana visando encontrar soluções com custo menor. Para tal, foram propostas três variantes do algoritmo considerando diferentes heurísticas. Foram realizados experimentos com instâncias de teste contendo 15, 25 e 50 clientes; e foram analisados o custo final da solução e o tempo computacional para a solução convergir.