A comparison of three metaheuristics for the workover rig routing problem

The workover rig routing problem (WRRP) is a variant of the Vehicle Routing Problem with Time Windows (VRPTW) and arises in the operations of onshore oil fields. In this problem, a set of workover rigs located at different positions must service oil wells requesting maintenance as soon as possible. When a well requires maintenance, its production is reduced or stopped for safety reasons and some workover rig must service it within a given deadline. It is therefore important to service the wells in a timely fashion in order to minimize the production loss. Whereas for classical VRPTWs the objective is to minimize route length, in the WRRP the objective is to minimize the total lost production, equal to the sum of arrival times at the wells, multiplied by production loss rates. The WRRP generalizes the Delivery Man Problem with Time Windows by considering multiple open vehicle routes and multiple depots. This paper compares three metaheuristics for the WRRP: an iterated local search, a clustering search, and an Adaptive Large Neighborhood Search (ALNS). All approaches, in particular ALNS, have yielded good solutions for instances derived from a real-life setting.     

A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem

The heterogeneous fleet vehicle routing problem is investigated using some adaptations of the variable neighborhood search (VNS). The initial solution is obtained by Dijkstra’s algorithm based on a cost network constructed by the sweep algorithm and the 2-opt. Our VNS algorithm uses several neighborhoods which are adapted for this problem. In addition, a number of local search methods together with a diversification procedure are used. Two VNS variants, which differ in the order the diversification and Dijkstra’s algorithm are used, are implemented. Both variants appear to be competitive and produce new best results when tested on the data sets from the literature. We also constructed larger data sets for which benchmarking results are provided for future comparison.     

Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet

This paper discusses the two-dimensional loading capacitated vehicle routing problem (2L-CVRP) with heterogeneous fleet (2L-HFVRP). The 2L-CVRP can be found in many real-life situations related to the transportation of voluminous items where two-dimensional packing restrictions have to be considered, e.g.: transportation of heavy machinery, forklifts, professional cleaning equipment, etc. Here, we also consider a heterogeneous fleet of vehicles, comprising units of different capacities, sizes and fixed/variable costs. Despite the fact that heterogeneous fleets are quite ubiquitous in real-life scenarios, there is a lack of publications in the literature discussing the 2L-HFVRP. In particular, to the best of our knowledge no previous work discusses the non-oriented 2L-HFVRP, in which items are allowed to be rotated during the truck-loading process. After describing and motivating the problem, a literature review on related work is performed. Then, a multi-start algorithm based on biased randomization of routing and packing heuristics is proposed. A set of computational experiments contribute to illustrate the scope of our approach, as well as to show its efficiency.     

A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows

This paper presents a novel three-phase heuristic/algorithmic approach for the multi-depot routing problem with time windows and heterogeneous vehicles. It has been derived from embedding a heuristic-based clustering algorithm within a VRPTW optimization framework. To this purpose, a rigorous MILP mathematical model for the VRPTW problem is first introduced. Likewise other optimization approaches, the new formulation can efficiently solve case studies involving at most 25 nodes to optimality. To overcome this limitation, a preprocessing stage clustering nodes together is initially performed to yield a more compact cluster-based MILP problem formulation. In this way, a hierarchical hybrid procedure involving one heuristic and two algorithmic phases was developed. Phase I aims to identifying a set of cost-effective feasible clusters while Phase II assigns clusters to vehicles and sequences them on each tour by using the cluster-based MILP formulation. Ordering nodes within clusters and scheduling vehicle arrival times at customer locations for each tour through solving a small MILP model is finally performed at Phase III. Numerous benchmark problems featuring different sizes, clustered/random customer locations and time window distributions have been solved at acceptable CPU times.     

An interactive GRAMPS algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls

In this article, a visual interactive approach based on a new greedy randomised adaptive memory programming search (GRAMPS) algorithm is proposed to solve the heterogeneous fixed fleet vehicle routing problem (HFFVRP) and a new extension of the HFFVRP, which is called heterogeneous fixed fleet vehicle routing problem with backhauls (HFFVRPB). This problem involves two different sets of customers. Backhaul customers are pickup points and linehaul customers are delivery points that are to be serviced from a single depot by a heterogeneous fixed fleet of vehicles, each of which is restricted in the capacity it can carry, with different variable travelling costs.     

Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil

In this paper, we consider a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries that occurs in a major Brazilian retail group. A single depot attends 519 stores of the group distributed in 11 Brazilian states. To find good solutions to this problem, we propose heuristics as initial solutions and a scatter search (SS) approach. Next, the produced solutions are compared with the routes actually covered by the company. Our results show that the total distribution cost can be reduced significantly when such methods are used. Experimental testing with benchmark instances is used to assess the merit of our proposed procedure.     

A reactive variable neighborhood tabu search for the heterogeneous fleet vehicle routing problem with time windows

This paper presents a solution methodology for the heterogeneous fleet vehicle routing problem with time windows. The objective is to minimize the total distribution costs, or similarly to determine the optimal fleet size and mix that minimizes both the total distance travelled by vehicles and the fixed vehicle costs, such that all problem’s constraints are satisfied. The problem is solved using a two-phase solution framework based upon a hybridized Tabu Search, within a new Reactive Variable Neighborhood Search metaheuristic algorithm. Computational experiments on benchmark data sets yield high quality solutions, illustrating the effectiveness of the approach and its applicability to realistic routing problems. This work is supported by the General Secretariat for Research and Technology of the Hellenic Ministry of Development under contract GSRT NM-67.     

A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem

In real life situations most companies that deliver or collect goods own a heterogeneous fleet of vehicles. Their goal is to find a set of vehicle routes, each starting and ending at a depot, making the best possible use of the given vehicle fleet such that total cost is minimized. The specific problem can be formulated as the Heterogeneous Fixed Fleet Vehicle Routing Problem (HFFVRP), which is a variant of the classical Vehicle Routing Problem. This paper describes a variant of the threshold accepting heuristic for the HFFVRP. The proposed metaheuristic has a remarkably simple structure, it is lean and parsimonious and it produces high quality solutions over a set of published benchmark instances. Improvement over several of previous best solutions also demonstrates the capabilities of the method and is encouraging for further research.     

A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads

Four multi-objective meta-heuristic algorithms are presented to solve a multi-objective capacitated rural school bus routing problem with a heterogeneous fleet and mixed loads. Three objectives are considered: the total weighted traveling time of the students, the balance of routes among drivers, and the routing costs. The proposed methods were compared with one from the literature, and their performance assessed observing three multi-objective metrics: cardinality, coverage, and hyper-volume. All four devised methods outperformed the one from the literature. The algorithm with a path relinking procedure embedded during the crowding distance selection scheme had the best overall performance.     

Hybrid heuristics for a short sea inventory routing problem

We consider a short sea fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The inventory management has to be considered at the demand side only, and the consumption rates are given and assumed to be constant within the planning horizon. The objective is to determine distribution policies that minimize the routing and operating costs, while the inventory levels are maintained within their limits. We propose an arc-load flow formulation for the problem which is tightened with valid inequalities. In order to obtain good feasible solutions for planning horizons of several months, we compare different hybridization strategies. Computational results are reported for real small-size instances.     

Solving a finite horizon EPQ problem with backorders

This paper presents an alternative approach to solve a finite horizon production lot sizing model with backorders using Cauchy-Bunyakovsky-Schwarz Inequality. The optimal batch size is derived from a sequence number of batches. We prove that a constant batch size policy with one fill rate is better than the variable batch sizes with variable fill rates. Finally, a practical approach is proposed to find the optimal solutions for a discrete planning horizon and discrete batch sizes.     

A complementary tool to enhance the effectiveness of existing methods for heterogeneous fixed fleet vehicle routing problem

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of the standard vehicle routing problem (VRP), in which the vertices have to be served using a fixed number of vehicles that could be different in size and fixed or variable costs. In this article, we propose an integer linear programming-based heuristic approach in order to solve the HFFVRP that could be used as a complementary tool to improve the performance of the existing methods of solving this problem. Computational results show the effectiveness of the proposed method.     

Tabu search variants for the mix fleet vehicle routing problem

The Mix Fleet Vehicle Routing Problem (MFVRP) involves the design of a set of minimum cost routes, originating and terminating at a central depot, for a fleet of heterogeneous vehicles with various capacities, fixed costs and variable costs to service a set of customers with known demands. This paper develops new variants of a tabu search meta-heuristic for the MFVRP. These variants use a mix of different components, including reactive tabu search concepts; variable neighbourhoods, special data memory structures and hashing functions. The reactive concept is used in a new way to trigger the switch between simple moves for intensification and more complex ones for diversification of the search strategies. The special data structures are newly introduced to efficiently search the various neighbourhood spaces. The combination of data structures and strategic balance between intensification and diversification generates an efficient and robust implementation, which is very competitive with other algorithms in the literature on a set of benchmark instances for which some new best-known solutions are provided.     

The fleet size and mix problem for capacitated arc routing

There have been several attempts to solve the capacitated arc routing problem with m vehicles starting their tours from a central node. The objective has been to minimize the total distance travelled. In the problem treated here we also have the fixed costs of the vehicles included in the objective function. A set of vehicle capacities with their respective costs are used. Thus the objective function becomes a combination of fixed and variable costs. The solution procedure consists of four phases. In the first phase, a Chinese or rural postman problem is solved depending on whether all or some of the arcs in the network demand service with the objective of minimizing the total distance travelled. It results in a tour called the giant tour. In the second phase, the giant tour is partitioned into single vehicle subtours feasible with respect to the constraints. A new network is constructed with the node set corresponding to the arcs of the giant tour and with the arc set consisting of the subtours of the giant tour. The arc costs include both the fixed and variable costs of the subtours. The third phase consists of solving the shortest path problem on this new network to result in the least cost set of subtours represented on the new network. In the last phase a postprocessor is applied to the solution to improve it. The procedure is repeated for different giant tours to improve the final solution. The problem is extended to the case where there can be upper bounds on the number of vehicles with given capacities using a branch and bound method. Extension to directed networks is given. Some computational results are reported.     

A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

The two-dimensional loading heterogeneous fleet vehicle routing problem (2L-HFVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles. These vehicles have different capacities, fixed and variable operating costs, length and width in dimension, and two-dimensional loading constraints. The objective of this problem is to minimize transportation cost of designed routes, according to which vehicles are used, to satisfy the customer demand. In this study, we proposed a simulated annealing with heuristic local search (SA_HLS) to solve the problem and the search was then extended with a collection of packing heuristics to solve the loading constraints in 2L-HFVRP. To speed up the search process, a data structure was used to record the information related to loading feasibility. The effectiveness of SA_HLS was tested on benchmark instances derived from the two-dimensional loading vehicle routing problem (2L-CVRP). In addition, the performance of SA_HLS was also compared with three other 2L-CVRP models and four HFVRP methods found in the literature.     

The Wiener disorder problem with finite horizon

The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of ‘disorder’ when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is finite. The method of proof is based on reducing the initial problem to a parabolic free-boundary problem where the continuation region is determined by a continuous curved boundary. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundary can be characterized as a unique solution of the nonlinear integral equation.     

Efficient and effective heuristics for the coordinated capacitated lot-size problem

Coordinating procurement decisions for a family of products that share a constrained resource, such as an ocean shipping container, is an important managerial problem. However due to the problem’s difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. This paper proposes two heuristics, for the capacitated, coordinated dynamic demand lot-size problem with deterministic but time-varying demand. In addition to inventory holding costs, the problem assumes a joint setup cost each time any member of the product family is replenished and an individual item setup cost for each item type replenished. The objective is to meet all customer demand without backorders at minimum total cost. We propose a six-phase heuristic (SPH) and a simulated annealing meta-heuristic (SAM). The SPH begins by assuming that each customer demand is met by a unique replenishment and then it seeks to iteratively maximize the net savings associated with order consolidation. Using SPH to find a starting solution, the SAM orchestrates escaping local solutions and exploring other areas of the solution state space that are randomly generated in an annealing search process. The results of extensive computational experiments document the effectiveness and efficiency of the heuristics. Over a wide range of problem parameter values, the SPH and SAM find solutions with an average optimality gap of 1.53% and 0.47% in an average time of 0.023 CPU seconds and 0.32 CPU seconds, respectively. The heuristics are strong candidates for application as stand alone solvers or as an upper bounding procedure within an optimization based algorithm. The procedures are currently being tested as a solver in the procurement software suite of a nationally recognized procurement software provider.     

Scatter search for the fleet size and mix vehicle routing problem with time windows

This work proposes a scatter search (SS) approach to solve the fleet size and mix vehicle routing problem with time windows (FSMVRPTW). In the FSMVRPTW the customers need to be serviced in their time windows at minimal costs by a heterogeneous fleet. Computational results on 168 benchmark problems are reported. Computational testing revealed that our algorithm presented better results compared to other methods published in the literature.     

A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers

The purpose of this article is to propose a perturbation metaheuristic for the vehicle routing problem with private fleet and common carrier (VRPPC). This problem consists of serving all customers in such a way that (1) each customer is served exactly once either by a private fleet vehicle or by a common carrier vehicle, (2) all routes associated with the private fleet start and end at the depot, (3) each private fleet vehicle performs only one route, (4) the total demand of any route does not exceed the capacity of the vehicle assigned to it, and (5) the total cost is minimized. This article describes a new metaheuristic for the VRPPC, which uses a perturbation procedure in the construction and improvement phases and also performs exchanges between the sets of customers served by the private fleet and the common carrier. Extensive computational results show the superiority of the proposed metaheuristic over previous methods.