An integrated approach for collection network design,capacity planning and vehicle routing in reverse logistics

This study considers network design, capacity planning and vehicle routing for collection systems in reverse logistics. The network design and capacity planning problems are to determine the static locations and capacities of collection points as well as the dynamic allocations of demand points to the opened collection points over a planning horizon, and the vehicle routing problem is to determine the number and routes of vehicles in such a way that each collection point must be visited exactly once by one vehicle starting and terminating at the depot while satisfying the return demands at collection points and the vehicle capacity. The objective is to minimize the sum of fixed costs to open collection points and to acquire vehicles as well as variable costs to transport returns at demand points to the opened collection points and travel the opened collection points by vehicles. Unlike the location-routing problems, the integrated problem considered in this study has several features: multi-period dynamic model, capacity planning for collection points, maximum allowable collection distances, etc. To solve the integrated problem, two types of tabu search algorithms, hierarchical and integrated ones, are suggested, and their test results are reported. In particular, the efficiency of the integrated approach is shown by comparing the two algorithm types.     

A memetic algorithm for the multiperiod vehicle routing problem with profit

In this paper, we extend upon current research in the vehicle routing problem whereby labour regulations affect planning horizons, and therefore, profitability. We call this extension the multiperiod vehicle routing problem with profit (mVRPP). The goal is to determine routes for a set of vehicles that maximizes profitability from visited locations, based on the conditions that vehicles can only travel during stipulated working hours within each period in a given planning horizon and that the vehicles are only required to return to the depot at the end of the last period. We propose an effective memetic algorithm with a giant-tour representation to solve the mVRPP. To efficiently evaluate a chromosome, we develop a greedy procedure to partition a given giant-tour into individual routes, and prove that the resultant partition is optimal. We evaluate the effectiveness of our memetic algorithm with extensive experiments based on a set of modified benchmark instances. The results indicate that our approach generates high-quality solutions that are reasonably close to the best known solutions or proven optima, and significantly better than the solutions obtained using heuristics employed by professional schedulers.     

Column generation for vehicle routing problems with multiple synchronization constraints

Synchronization of workers and vehicles plays a major role in many industries such as logistics, healthcare or airport ground handling. In this paper, we focus on operational ground handling planning and model it as an archetype of vehicle routing problems with multiple synchronization constraints, coined as “abstract vehicle routing problem with worker and vehicle synchronization” (AVRPWVS). The AVRPWVS deals with routing workers to ground handling jobs such as unloading baggage or refuelling an aircraft, while meeting each job’s time window. Moreover, each job can be performed by a variable number of workers. As airports span vast distances and due to security regulations, workers use vehicles to travel between locations. Furthermore, each vehicle, moved by a driver, can carry several workers. We propose two mathematical multi-commodity flow formulations based on time-space networks to efficiently model five synchronization types including movement and load synchronization. Moreover, we develop a branch-and-price heuristic that employs both conventional variable branching and a novel variable fixing strategy. We demonstrate that the procedure achieves results close to the optimal solution in short time when compared to the two integer models.     

A new mixed integer linear model for a rich vehicle routing problem with docking constraints

In this paper we address a rich vehicle routing problem that arises in real-life applications. Among other aspects we consider time windows, simultaneous delivery and pick-up at customer locations and multiple use of vehicles. To guarantee a coordinated material flow at the depot, we include the timed allocation of vehicles to loading bays at which the loading and unloading activities can occur. The resulting vehicle routing problem is formulated as a two-index vehicle-flow model which integrates the routing under real-life conditions and the assignment of vehicles to loading bays at the depot. We use CPLEX 11.0 to solve medium-sized instances that are derived from the extended Solomon test set. The selective implementation of preprocessing techniques and cutting planes improves the solver performance significantly.     

Column generation based heuristic for tactical planning in multi-period vehicle routing

The periodic vehicle routing problem (PVRP) consists in establishing a planning of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. The tactical planning model considered here restricts its attention to scheduling visits and assigning them to vehicles while leaving sequencing decisions for an underlying operational model. The objective is twofold: to optimize regional compactness of the routes in a desire to specialize routes to restricted geographical area and to balance the workload evenly between vehicles. Approximate solutions are constructed using a truncated column generation procedure followed by a rounding heuristic. This mathematical programming based procedure can deal with problems with 50–80 customers over five working days which is the range of size of most PVRP instances treated in the literature with meta-heuristics. The paper highlights the importance of alternative optimization criteria not accounted for in standard operational models and provides insights on the implementation of a column generation based rounding heuristic.     

A goal programming approach to vehicle routing problems with soft time windows

The classical vehicle routing problem involves designing a set of routes for a fleet of vehicles based at one central depot that is required to serve a number of geographically dispersed customers, while minimizing the total travel distance or the total distribution cost. Each route originates and terminates at the central depot and customers demands are known. In many practical distribution problems, besides a hard time window associated with each customer, defining a time interval in which the customer should be served, managers establish multiple objectives to be considered, like avoiding underutilization of labor and vehicle capacity, while meeting the preferences of customers regarding the time of the day in which they would like to be served (soft time windows). This work investigates the use of goal programming to model these problems. To solve the model, an enumeration-followed-by-optimization approach is proposed which first computes feasible routes and then selects the set of best ones. Computational results show that this approach is adequate for medium-sized delivery problems.     

Multi-objective metaheuristics for a location-routing problem with multiple use of vehicles on real data and simulated data

We address an integrated logistic system where decisions on location of depot, vehicle routing and assignment of routes to vehicles are considered simultaneously. Total cost and workload balance are common criteria influencing decision-making. Literature on location-routing problems addressed the location and vehicle routing decisions with a common assumption of assigning one route to one vehicle. However, the cost of acquiring vehicles (and crew) is often more significant than the routing cost. This notion of assigning several routes to a vehicle during the routing procedure is explored in our integrated model. We apply metaheuristics of tabu search and simulated annealing on real data and simulated data, to compare their performances under two versions: simultaneous or sequential routes assignment to vehicles. A new statistical procedure is proposed to compare two algorithms on the strength of their multi-objective solutions. Results show that the simultaneous versions have advantage over the sequential versions in problems where routes are capacity-constrained, but not in the time dimension. The simultaneous versions are also more effective in generating non-dominated solutions than the sequential versions.     

Open vehicle routing problem with driver nodes and time deadlines

In this paper, we consider a variant of the open vehicle routing problem in which vehicles depart from the depot, visit a set of customers, and end their routes at special nodes called driver nodes. A driver node can be the home of the driver or a parking lot where the vehicle will stay overnight. The resulting problem is referred to as the open vehicle routing problem with driver nodes (OVRP-d). We consider three classes of OVRP-d: with no time constraints, with a maximum route duration, and with both a maximum route duration as well as time deadlines for visiting customers. For the solution of these problems, which are not addressed previously in the literature, we develop a new tabu search heuristic. Computational results on randomly generated instances indicate that the new heuristic exhibits a good performance both in terms of the solution quality and computation time.     

Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm

In this paper, we consider the open vehicle routeing problem (OVRP), in which routes are not sequences of locations starting and ending at the depot but open paths. The problem is of particular importance for planning fleets of hired vehicles, a common practice in the distribution and service industry. In such cases, the travelling cost is a function of the vehicle open paths. To solve the problem, we employ a single-parameter metaheuristic method that exploits a list of threshold values to guide intelligently an advanced local search. Computational results on a set of benchmark problems show that the proposed method consistently outperforms previous approaches for the OVRP. A real-world example demonstrates the applicability of the method in practice, demonstrating that the approach can be used to solve actual problems of routing large vehicle fleets.     

A heuristic method for the open vehicle routing problem

The open vehicle routing problem (OVRP) differs from the classic vehicle routing problem (VRP) because the vehicles either are not required to return to the depot, or they have to return by revisiting the customers assigned to them in the reverse order. Therefore, the vehicle routes are not closed paths but open ones. A heuristic method for solving this new problem, based on a minimum spanning tree with penalties procedure, is presented. Computational results are provided.