In bike sharing systems the quality of the service to the users strongly depends on the strategy adopted to reposition the bikes. The bike repositioning problem is in general very complex as it involves different interrelated decisions: the routing of the repositioning vehicles, the scheduling of their visits to the stations, the number of bikes to load or unload for each station and for each vehicle that visits the station. In this paper we study the problem of optimally loading/unloading vehicles that visit the same station at given time instants of a finite time horizon. The goal is to minimize the total lost demand of bikes and free stands in the station. We model the problem as a mixed integer linear programming problem and present an optimal algorithm that runs in linear time in the size of the time horizon.

Long-haul truck transportation is concerned with freight transportation from shipments' origins to destinations, with vehicle trips lasting from some hours to several days. Drivers performing long-haul transportation are subject to strict rules derived from Hours of Service (HoS) regulations. There exists a large body of literature integrating HoS regulations within long-haul transportation. The optimization problems in this context generally deal with routing and scheduling decisions aimed at determining where a driver should stop and how long a rest should be. However, the overwhelming majority of the literature on long-haul transportation ignores refueling decisions and treats fuel costs as proportional to the traveled distance. In this talk we analyze a long-haul truck scheduling problem where a path has to be determined for a vehicle traveling from a specified origin to a specified destination. We consider refueling decisions along the path while accounting for heterogeneous fuel prices in a road network. Furthermore, the path has to comply with Hours of Service (HOS) regulations. Therefore, a path is defined by the actual road trajectory traveled by the vehicle, as well as the locations where the vehicle stops due to refueling, compliance with HOS regulations, or a combination of the two. This setting is cast in a bi-objective optimization problem, considering the minimization of fuel cost and the minimization of path duration. An algorithm is proposed to solve the problem on a road network. The algorithm builds a set of non-dominated paths with respect to the two objectives. Given the enormous theoretical size of the road network, the algorithm follows an interactive path construction mechanism. Specifically, the algorithm dynamically interacts with a geographic information system to identify the relevant potential paths and stop locations. Computational tests are made on real-sized instances where the distance covered ranges from 500 to 1500 km. The algorithm is compared with solutions obtained from a policy mimicking the current practice of a logistics company. The results show that the non-dominated solutions produced by the algorithm significantly dominate the ones generated by the current practice, in terms of fuel costs, while achieving similar path durations. The average number of non-dominated paths is 2.7, which allows decision-makers to ultimately visually inspect the proposed alternatives.

We consider the inventory routing problem, in which a supplier has to replenish a set of customers by means of a limited fleet of capacitated vehicles over a discrete time horizon. The goal is to minimize the total cost of the distribution that comprises the inventory cost at the supplier and at the customers and the routing cost. We present a matheuristic that combines a tabu search and mathematical programming formulations. When compared with two exact methods on 640 small instances, the matheuristic finds 192 (48%) optima over the 402 instances with known optima and improves 125 upper bounds. Tested on 240 large instances (with up to 200 customers) for which no optimal solutions are known, it improves the best solution for 220 (92%) of the 240 instances. The online supplement is available at https://doi.org/10.1287/ijoc.2016.0737 .

Many logistic problems arising in supply chain management, distribution and inventory management call for the integration of different components of the production/distribution system which have to be coordinated in such a way that a common objective, which can be the cost minimization or the revenue maximization, is optimized. Thus, in order to find the best management policy, one should be able to tackle the problem as a whole and to find an integrated policy that is aimed at optimizing the system behavior. However, known practices as well as the scientific literature have shown a major attitude in proposing strategies that are aimed at decomposing the system in parts and then proposing optimal policies for each single part. This clearly leads to a strategy that is far from being optimal for the global system. The aim of this work is to focus on the advantages that integrated policies can provide when used to handle production, inventory and distribution problems. We will present some cases that are mainly dealing with distribution problems and show the strategies proposed in the literature. We will also present a study on a distribution system where the inventory and the distribution costs have to be minimized.

Abstract In this article, we study the capacitated team orienteering problem where split deliveries are allowed. A set of potential customers is given, each associated with a demand and a profit. The set of customers to be served by a fleet of capacitated vehicles has to be identified in such a way that the profit collected is maximized, while satisfying constraints on the maximum time duration of each route and the vehicle capacity constraints. When split deliveries are allowed, each customer may be served by more than one vehicle. We show that the profit collected by allowing split deliveries may be as large as twice the profit collected under the constraint that each customer has to be served by one vehicle at most. We then present a branch‐and‐price exact algorithm and a hybrid heuristic. We show the effectiveness of the proposed approaches on benchmark instances and on a new set of instances that allow us to computationally evaluate the impact of split deliveries. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(1), 16–33 2014

Abstract In this article, we study a variant of the capacitated team orienteering problem, that is the problem where a fleet of vehicles, each with a constraint on the time available, is given to serve profitable customers with the objective of maximizing the collected profit. We study the variant where customers may be only partially served (incomplete service) and, if beneficial, also by more than one vehicle (split deliveries). We will analyze the maximum theoretical increase of the profit due to the incomplete service and to the split deliveries. We also computationally measure such increase on a set of instances, by means of an exact algorithm on small/medium size instances and of two heuristics on instances of larger size. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 135–145 2014

Abstract This article studies the double traveling salesman problem with two stacks. A number of requests have to be served where each request consists in the pickup and delivery of an item. All the pickup operations have to be performed before any delivery can take place. A single vehicle is available that starts from a depot, performs all the pickup operations and returns to the depot. Then, it performs all the delivery operations and returns to the depot. The items are loaded in two stacks, each served independently from the other with a last‐in‐first‐out policy. The objective is the minimization of the total cost of the pickup and delivery tours. We propose a branch‐and‐bound approach to solve the problem. The algorithm uses properties of the problem both to tighten the lower bounds and to avoid the exploration of redundant subtrees. Computational results performed on benchmark instances reveal that the algorithm outperforms the other exact approaches for this problem. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013

We consider an inventory routing problem in discrete time where a supplier has to serve a set of customers over a multiperiod horizon. A capacity constraint for the inventory is given for each customer, and the service cannot cause any stockout situation. Two different replenishment policies are considered: the order-up-to-level and the maximum-level policies. A single vehicle with a given capacity is available. The transportation cost is proportional to the distance traveled, whereas the inventory holding cost is proportional to the level of the inventory at the customers and at the supplier. The objective is the minimization of the sum of the inventory and transportation costs. We present a heuristic that combines a tabu search scheme with ad hoc designed mixed-integer programming models. The effectiveness of the heuristic is proved over a set of benchmark instances for which the optimal solution is known.

The multidimensional knapsack problem (MKP) is a well-known, strongly NP-hard problem and one of the most challenging problems in the class of the knapsack problems. In the last few years, it has been a favorite playground for metaheuristics, but very few contributions have appeared on exact methods. In this paper we introduce an exact approach based on the optimal solution of subproblems limited to a subset of variables. Each subproblem is faced through a recursive variable-fixing process that continues until the number of variables decreases below a given threshold (restricted core problem). The solution space of the restricted core problem is split into subspaces, each containing solutions of a given cardinality. Each subspace is then explored with a branch-and-bound algorithm. Pruning conditions are introduced to improve the efficiency of the branch-and-bound routine. In all the tested instances, the proposed method was shown to be, on average, more efficient than the recent branch-and-bound method proposed by Vimont et al. [Vimont, Y., S. Boussier, M. Vasquez. 2008. Reduced costs propagation in an efficient implicit enumeration for the 0-1 multidimensional knapsack problem. J. Combin. Optim. 15(2) 165–178] and CPLEX 10. We were able to improve the best-known solutions for some of the largest and most difficult instances of the OR-LIBRARY data set [Chu, P. C., J. E. Beasley. 1998. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics 4(1) 63–86].

Abstract This article studies the pickup and delivery traveling salesman problem with multiple stacks. The vehicle contains a number of (horizontal) stacks of finite capacity for loading items from the rear of the vehicle. Each stack must satisfy the last‐in‐first‐out constraint that states that any new item must be loaded on top of a stack and any unloaded item must be on top of its stack. A branch‐and‐cut algorithm is proposed for solving this problem. Computational results are reported on different types of randomly generated instances as well as on classical instances for some well‐known special cases of the problem. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012

Abstract In this article we present a branch‐and‐price‐and‐cut method for the solution of the split delivery vehicle routing problem (SDVRP). The SDVRP is the problem to serve customers with a fleet of capacitated vehicles at minimum traveling cost. With respect to the classical vehicle routing problem, where each customer is visited exactly once, in the SDVRP a customer may be visited any number of times. The exact method we propose is based on a decomposition of the problem where the possible routes, with the delivery quantities, are generated in the subproblem. The generated routes are also used to find a heuristic solution to the problem. We consider both the case where the fleet of vehicles is unlimited and the case where the fleet is limited to the minimum possible number of vehicles. We solve to optimality instances with larger size with respect to previous approaches, find new best solutions to several benchmark instances and reduce the optimality gap on most of the benchmark instances. © 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(4), 241–254 2011

Abstract In this article we present mathematical programming formulations and solution approaches for the optimal solution of the Double Travelling Salesman Problem with Multiple Stacks (DTSPMS). A set of orders is given, each one requiring transportation of one item from a customer in a pickup region to a customer in a delivery region. The vehicle available for the transportation in each region carries a container. The container is organized in rows of given length. Each row is handled independently from the others according to a Last In First Out stack policy. The DTSPMS problem consists of determining the pickup tour, the loading plan of the container and the delivery tour in such a way that the total length of the two tours is minimized. The formulations are based on different modeling ideas and each formulation gives rise to a specific solution approach. We present computational results on a set of benchmark instances that compare the different approaches and show that the most successful one is a decomposition approach applied to a new model. © 2010 Wiley Periodicals, Inc. NETWORKS, 2010

Abstract We study a dynamic multiperiod routing problem where, at the beginning of each time period, a set of orders arrive that have to be fulfilled either that time period or the next. Thus, in each time period there are customers that have to be served and customers whose service may be postponed. Once it has been decided which customers to serve, an optimal route is constructed and executed. The objective of the problem is to minimize the total distance traveled during the planning horizon. Deciding which customers to serve in a time period is done on the basis of incomplete information, analyzing simultaneously customers in two consecutive periods. No knowledge is available about customers requiring service in future time periods. We introduce simple algorithms, ones which naturally arise in practice, and analyze these algorithms by studying their competitive ratio. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 49(4), 308–317 2007

Abstract In this paper, we study the reoptimization problems which arise when a new node is added to an optimal solution of a traveling salesman problem (TSP) instance or when a node is removed. We show that both reoptimization problems are NP‐hard. Moreover, we show that, while the cheapest insertion heuristic has a tight worst‐case ratio equal to 2 when applied to a TSP instance, it guarantees, in linear time, a tight worst‐case ratio equal to 3/2 when used to add the new node and that also the simplest heuristic to remove a node from the optimal tour guarantees a tight ratio equal to 3/2 in constant time. © 2003 Wiley Periodicals, Inc.