Heuristics for a green orienteering problem

We address a routing problem where a vehicle with limited time, loading capacity and battery autonomy can optionally serve a set of customers, each providing a profit. Such a problem is of particular relevance both because of its practical implications in sustainable transportation and its use as a sub-problem in Green Vehicle Routing column generation algorithms. We propose a dynamic programming approach to obtain both primal and dual bounds to the value of the optimal solutions, a fast greedy heuristics and a very large scale neighbourhood search procedure

Inventory rebalancing in bike-sharing systems

We address an optimization problem arising in rebalancing operations of inventory levels in bike-sharing systems. Such systems are public services where bikes are available for shared use on a short term basis. To ensure the availability of bikes in each station and avoid disservices, the bike inventory level of each station must met a forecast value. This is achieved through the use of a fleet of vehicles moving bikes between stations. Our problem can be classified as a Split Pickup and Split Delivery Vehicle Routing Problem. We propose a formulation in which routes are decomposed in smaller structures and we exploit properties on the structure of the optimal solutions, to design an exact algorithm based on branch-and-price

A single machine on-time-in-full scheduling problem

A relevant feature in many production contexts is flexibility. This becomes a key issue, for instance, in the case of third-party cosmetics manufacturing [1]. There, the core business is the production of high quality, fully custom orders in limited batches. Competition is pushing companies to aggressive commercial policies, involving tight delivery dates. At the same time, the custom nature of the orders makes it impossible to keep materials in stock; lead times are always uncertain, often making release dates tight as well, and ultimately yielding unexpected peaks of production loads

Dynamic cloudlet assignment problem: A column generation approach

Major interest in network optimization is currently given to the integration of clusters of virtualization servers, also referred to as 'cloudlets', into mobile access networks for improved performance and reliability. Mobile access points (APs) are assigned (i.e., route their packets) to one or more cloudlets, with a cost in terms of latency for the users they provide connections to. Assignment of APs to cloudlet can be changed over time, with a cloudlet synchronization cost. We tackle the problem of the optimal assignment of APs to cloudlets over time, proposing dedicated mathematical models and column generation algorithms

Mathematical Programming bounds for Large-Scale Unit Commitment Problems in Medium-Term Energy System Simulations

We consider a large-scale unit commitment problem arising in medium-term simulation of energy networks, stemming from a joint project between the University of Milan and a major energy research centre in Italy. Optimal plans must be computed for a set of thermal and hydroelectric power plants, located in one or more countries, over a time horizon spanning from a few months to one year, with a hour-by-hour resolution. We propose a mixed-integer linear programming model for the problem. Since the complexity of this unit commitment problem and the size of real-world instances make it impractical to directly optimise this model using general purpose solvers, we devise ad-hoc heuristics and relaxations to obtain approximated solutions and quality estimations. We exploit an incremental approach: at first, a linear relaxation of an aggregated model is solved. Then, the model is disaggregated and the full linear relaxation is computed. Finally, a tighter linear relaxation of an extended formulation is obtained using column generation. At each stage, metaheuristics are run to obtain good integer solutions. Experimental tests on real-world data reveal that accurate results can be obtained by our framework in affordable time, making it suitable for efficient scenario simulations

Mathematical Programming Algorithms for Spatial Cloaking

We consider a combinatorial optimization problem for spatial information cloaking. The problem requires computing one or several disjoint arborescences on a graph from a predetermined root or subset of candidate roots, so that the number of vertices in the arborescences is minimized but a given threshold on the overall weight associated with the vertices in each arborescence is reached. For a single arborescence case, we solve the problem to optimality by designing a branch-and-cut exact algorithm. Then we adapt this algorithm for the purpose of pricing out columns in an exact branch-and-price algorithm for the multiarborescence version. We also propose a branch-and-price-based heuristic algorithm, where branching and pricing, respectively, act as diversification and intensification mechanisms. The heuristic consistently finds optimal or near optimal solutions within a computing time, which can be three to four orders of magnitude smaller than that required for exact optimization. From an application point of view, our computational results are useful to calibrate the values of relevant parameters, determining the obfuscation level that is achieved

The multiple vehicle balancing problem

This paper deals with the multiple vehicle balancing problem (MVBP). Given a fleet of vehicles of limited capacity, a set of vertices with initial and target inventory levels and a distribution network, the MVBP requires to design a set of routes along with pickup and delivery operations such that inventory is redistributed among the vertices without exceeding capacities, and routing costs are minimized. The MVBP is NP\u2010hard, generalizing several problems in transportation, and arising in bike\u2010sharing systems. Using theoretical properties of the problem, we propose an integer linear programming formulation and introduce strengthening valid inequalities. Lower bounds are computed by column generation embedding an ad\u2010hoc pricing algorithm, while upper bounds are obtained by a memetic algorithm that separate routing from pickup and delivery operations. We combine these bounding routines in both exact and matheuristic algorithms, obtaining proven optimal solutions for MVBP instances with up to 25 stations

Column Generation for the Split Delivery VRP

In this paper we tackle a variation of the Vehicle Routing Problem (VRP) in which each customer can be served by more than one vehicle, each serving a fraction of its demand. This problem is known as the Split Delivery VRP (SDVRP). Due to the potential savings that can be achieved in this way, the SDVRP recently received great attention in the combinatorial optimization community. We propose a new extended formulation for the problem. We exploit its properties to derive an effective column generation scheme. Our method is compared to the previous ones in the literature from both a theoretical and a computational point of view. In particular, our formulation involves a polynomial number of constraints and flow variables, can be optimized by solving well understood resource constrained shortest path problems and yields a bound which is not dominated by any previous one in the literature

Column generation for a real world vehicle routing problem

We present an optimization algorithm we developed for a software provider of planning tools for distribution logistics companies. The algorithm computes a daily plan for a heterogeneous fleet of vehicles, that can depart from different depots and must visit a set of customers for delivery operations. Besides multiple capacities and time windows associated with depots and customers, the problem also considers incompatibility constraints between goods, depots, vehicles and customers, maximum route length and durations, upper limits on the number of consecutive driving hours and compulsory drivers' rest periods, the possibility to skip some customers and to use express courier services instead of the given fleet to fulfill some orders, the option of splitting up the orders, the possible existence of pick-up operations to be performed by empty vehicles traveling back to their depots and the possibility of ``open" routes that do not terminate at depots. Moreover, the cost of each vehicle route is computed through a system of fares, depending on the locations visited by the vehicle, the distance traveled, the vehicle load and the number of stops along the route. We developed a column generation algorithm, where the pricing problem is a particular resource constrained elementary shortest path problem, solved through a bounded bi-directional dynamic programming algorithm. We describe how to encode the cost function and the complicating constraints by an appropriate use of resources and we present computational results on real instances obtained from the software company