To reduce the inventory cost and ensure product quality while meeting the diverse demands of customers, manufacturers yield products in batches. However, the raw materials required for manufacturing need to be obtained from suppliers in advance, making it necessary to understand beforehand how to best structure the pickup routes so as to reduce the cost of picking up and stocking while also ensuring the supply of raw materials required for each batch of production. To reduce the transportation and inventory costs, therefore, this paper establishes a mixed integer programming model for the joint optimization of multibatch production and vehicle routing problems involving a pickup. Following this, a two-stage hybrid heuristic algorithm is proposed to solve this model. In the first stage, an integrated algorithm, combining the Clarke-Wright (CW) algorithm and the Record to Record (RTR) travel algorithm, was used to solve vehicle routing problem. In the second stage, the Particle Swarm Optimization (PSO) algorithm was used to allocate vehicles to each production batch. Multiple sets of numerical experiments were then performed to validate the effectiveness of the proposed model and the performance efficiency of the two-stage hybrid heuristic algorithm.

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This paper considers the ship size optimization problem for a liner shipping company that provides feeder service between one hub port and one feeder port. In the maritime market with uncertainty, this problem becomes more challenging. This research first analyzes the decision behaviors of the shipping company. Then, a stochastic dynamic programming method is proposed to calculate the expected total volume of containers transported within the planning horizon. Using the calculated volumes as input parameters calculate the profit of each ship sizes and then determine the suitable ship size for the feeder route. Numerical experiments are performed to validate the effectiveness of the proposed method and the efficiency of the proposed algorithm.