Rodolfo Dondo

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.

The multi-echelon vehicle routing problem with cross docking in supply chain management

Multi-echelon distribution networks are quite common in supply chain and logistics. Deliveries of multiple items from factories to customers are managed by routing and consolidating shipments in warehouses carrying on long-term inventories. On the other hand, cross-docking is a logistics technique that differs from warehousing because products are no longer stored at intermediate depots. Instead, cross-dock facilities consolidate incoming shipments based on customer demands and immediately deliver them to their destinations. Hybrid strategies combining direct shipping, warehousing and cross-docking are usually applied in real-world distribution systems. This work deals with the operational management of hybrid multi-echelon multi-item distribution networks. The goal of the N-echelon vehicle routing problem with cross-docking in supply chain management (the VRPCD-SCM problem) consists of satisfying customer demands at minimum total transportation cost. A monolithic optimization framework for the VRPCD-SCM based on a mixed-integer linear mathematical formulation is presented. Computational results for several problem instances are reported.

A hybrid local improvement algorithm for large-scale multi-depot vehicle routing problems with time windows

One of the major research topics in the supply chain management field is the multi-depot vehicle routing problem with time windows (m-VRPTW). It aims to designing a set of minimum-cost routes for a vehicle fleet servicing many customers with known demands and predefined time windows. This paper presents an m-VRPTW local search improvement algorithm that explores a large neighborhood of the current solution to discover a cheaper set of feasible routes. The neighborhood structure comprises all solutions that can be generated by iteratively performing node exchanges among nearby trips followed by a node reordering on every route. Manageable mixed-integer linear programming (MILP) formulations for both algorithmic steps were developed. To further reduce the problem size, a spatial decomposition scheme has also been applied. A significant number of large-scale benchmark problems, some of them including up to 200 customers, multiple depots and different vehicle-types, were solved in quite reasonable CPU times.

A sweep-heuristic based formulation for the vehicle routing problem with cross-docking

Abstract Cross-docking is a warehousing strategy in logistics used by process industries making products with high proportions of distribution costs. It is described as the process of moving goods from suppliers to customers through a cross-dock terminal without a long-term storage in this facility. The vehicle routing problem with cross-docking (VRPCD) consists of fulfilling a set of transportation requests using a fleet of homogeneous vehicles to sequentially accomplish the pickup and delivery tasks. Between those operations, there is a consolidation process of incoming shipments at the cross-dock. This work introduces a monolithic formulation for the VRPCD that determines pickup/delivery routes and schedules simultaneously with the truck scheduling at the terminal. To derive a more efficient formulation, a constraint set mimicking the widely known sweep algorithm was incorporated into the rigorous model. The resulting model based on the sweep heuristic can find near-optimal solutions to large problems at very acceptable CPU times.

Optimal management of logistic activities in multi-site environments

The new emerging area of Enterprise Wide Optimization (EWO) has focused the attention in effectively solving the combined production/distribution scheduling problem. The importance of logistic activities performed in multi-site environments comes from the relative magnitude of the associated transportation costs and the good chance of getting large savings on such expenses. This paper first develops an exact MILP mathematical formulation for the multiple vehicle time-window-constrained pickup and delivery (MVPDPTW) problem. The approach is able to account for many-to-many transportation requests, pure pickup and delivery tasks, heterogeneous vehicles and multiple depots. Optimal solutions for a variety of benchmark problems with cluster/random distributions of pickup and delivery locations and limited sizes in terms of customer requests and vehicles have been discovered. However, the computational cost exponentially grows with the number of requests. For large-scale m-PDPTW problems, a local search improvement algorithm steadily providing a better solution through two evolutionary steps is also presented. A neighborhood structure around the starting solution is generated by first allowing multiple request exchanges among nearby trips and then permitting the reordering of nodes on every individual route. If a better set of routes is found, both steps are repeated until no improved solution is discovered. Compact MILP mathematical formulations for both sub-problems have been developed and solved through an efficient branch-and-bound algorithm. A significant number of large-scale m-PDPTW benchmark problems, some of them including up to 100 transportation requests, were successfully solved in reasonable CPU times.

The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system

Abstract Cross-docking is a logistics technique applied by many industrial firms to get substantial savings in two warehousing costly functions like storage and order picking. Incoming shipments are unloaded from inbound trucks on a cross-dock terminal with minimal storage space and directly transferred to outbound vehicles that carry them to their destinations. The major decisions at the operational level are the vehicle routing and scheduling, the dock door assignment and the truck scheduling at the cross-dock. Because such decisions are interdependent, all of them are simultaneously considered in the so-called vehicle routing problem with cross-docking (VRPCD). Previous contributions on VRPCD assume that pickup and delivery tasks are accomplished by a homogeneous vehicle fleet, and they mostly ignore the internal transportation of goods through the cross-dock. This work introduces a new rigorous mixed-integer linear programming (MILP) formulation for the VRPCD problem to determine the routing and scheduling of a mixed vehicle fleet, the dock door assignment, the truck docking sequence and the travel time required to move the goods to the assigned stack door all at once. To improve the computational efficiency of the branch-and-cut search, an approximate sweep-based model is developed by also considering a set of constraints mimicking the sweep algorithm for allocating nodes to vehicles. Numerous heterogeneous VRPCD examples involving up to 50 transportation requests and a heterogeneous fleet of 10 vehicles with three different capacities were successfully solved using the proposed approaches in acceptable CPU times.

A monolithic approach to vehicle routing and operations scheduling of a cross-dock system with multiple dock doors

Abstract Cross-docking is a logistic strategy for moving goods from suppliers to customers via a cross-dock terminal with no permanent storage. The operational planning of a cross-dock facility involves different issues such as vehicle routing, dock door assignment and truck scheduling. The vehicle routing problem seeks the optimal routes for a homogeneous fleet of vehicles that sequentially collects goods at pickup points and delivers them to their destinations. The truck scheduling problem deals with the timing of unloading and reloading operations at the cross-dock. This work introduces a mixed-integer linear programming formulation for the scheduling of single cross-dock systems that, in addition to selecting the pickup/delivery routes, simultaneously decides on the dock door assignment and the truck scheduling at the cross-dock. The proposed monolithic formulation is able to provide near-optimal solutions to medium-size problems involving up to 70 transportation orders, 16 vehicles and 7 strip/stack dock doors at acceptable CPU times.

A branch-and-price approach to evaluate the role of cross-docking operations in consolidated supply chains

Abstract Supply-chain management and optimization aims at reducing costs and inventories. One way to increase the supply-chain efficiency is to use cross-docking for consolidating shipments from different suppliers. Cross-docking is a warehousing strategy used in logistics that consists on moving goods from suppliers to customers through a cross-dock facility. The employment of this strategy must be carefully evaluated because sometimes transportation requests can be better directly moved from source-sites to destination. A realistic problem studying the convenience of direct delivery, avoiding some cross-docking transfers, is here discussed. An efficient methodology for finding (near)optimal solutions is also described. The methodology is based on the use of column generation embedded into an incomplete branch-and-price tree. The approach provides (near)optimal solutions by solving the column generation sub-problems without necessarily considering all unexplored nodes in the search-tree. Finally, we show computational results on numerous test problems and on four configurations of the addressed case study.

A reactive MILP approach to the multidepot heterogeneous fleet vehicle routing problem with time windows

The time-window-constrained vehicle routing problem (VRPTW) is a well-known combinatorial problem. Its goal is to discover the best set of routes for a vehicle fleet in order to service a given number of customers at minimum cost. Vehicle capacity, maximum service time and time-window constraints must be satisfied. Most proposed VRPTW optimizing approaches intend to discover the best or a near-optimal solution at once. Improvement methods are old strategies that apply heuristics to insert customers into tours and/or rearrange nodes to obtain better routes. They are performed until no further improvement is achieved. Little research has been focused on model-based reactive approaches seeking a better solution by exploring a small solution space around the current solution. This work presents a new model-based improvement methodology for the multi-depot heterogeneous-fleet VRPTW problem to enhance an initial solution through solving a series of MILP mathematical problems that allow exchanges of nodes among tours and node reordering on every route. By restricting the range of improvement options, the problem size can be bounded and a limited number of binary variables is required for real-world problems. The improvement formulation is based on a continuous time-domain representation that handles assignment and sequencing decisions through different sets of binary variables and uses the notion of a generalized predecessor instead of a direct predecessor. Several types of VRPTW problems have been efficiently solved.

A MILP-based column generation strategy for managing large-scale maritime distribution problems

Abstract This paper presents a novel column generation algorithm for managing the logistics activities performed by a fleet of multi-parcel chemical tankers. In our procedure, for providing elementary routes, the conventional dynamic programming routes-generator is replaced by an efficient continuous-time MILP-slave problem. The performance of the decomposition method is evaluated by solving several examples dealing with the operations of a shipping company operating in the Asia Pacific Region. Computational results show that the proposed approach outperforms a pure exact optimization model and an alternative heuristic solution method reported in the literature.