The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers' demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles' capacities. In this paper, its features are analyzed. A mathematical model and tabu search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature.

In this paper, by taking the outsourcing transportation mode into account, a bilevel programming model is proposed to formulate the static bike repositioning (SBR) problem, which can be used to determine the number of bikes loaded and unloaded at each station and the optimal truck routes in bike sharing systems (BSS). The upper-level BSS providers determine the optimal loading and unloading quantities at stations to minimize the total penalties. The lower-level truck owner pursues the minimum transportation route cost. An iterated local search and tabu search are developed to solve the model. Computational tests on a set of instances from 20 to 200 bikes demonstrate the effectiveness of the model and algorithms proposed, together with some insightful findings.

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This research discusses the sequence of inbound and outbound aircrafts on a mixed operation single runway at an airport. Influenced by the climate, the target airport cannot meet landing conditions. As a result, aircrafts have to land at other nearby airports. Since the sequence for considering both normal and alternate aircrafts arriving in a fixed time window becomes difficult, few studies have considered this situation. Therefore, in this article, we propose a mixed integer programming model for formulating and possibly solving this problem to minimize total delay time. Since the problem is NP-hard, we propose an Improved Immunoglobulin-based Artificial Immune System (IIAIS) to find an optimal or near optimal solution to the considered aircraft scheduling problem. Using the problem instances from the OR library and a real-life practical case, we empirically evaluate the performance of the proposed algorithm. The results show that the proposed algorithm performs better than other existing algorithms.INDEX TERMS Air transportation, mixed operation runway, total delay time, constraint position shifting, artificial immune system.

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