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Editorial
ODYSSEUS 2012 was the fifth edition of the International
Workshop on Freight Transportation and Logistics
that took place in Mykonos, Greece, between May 21 and
May 25, 2012. The overarching aim of the Workshop was
to provide a high-level forum for scientific exchange and
cooperation with respect to the theory, practice, and application
of mathematical models and optimization methodologies
in the field of freight transportation and logistics. To disseminate
some of the scientific contributions presented at
ODYSSEUS 2012, we publish a special issue of Networks
with a focus on Vehicle Routing. This issue contains six high
quality papers
A Benders decomposition-based framework for solving quay crane scheduling problems
In this paper, we study the Quay Crane Scheduling Problem (QCSP) in container terminals. We describe a new mathematical formulation for the QCSP and by addressing the structure of workload assignments we develop an easier way to handle non-crossing constraints. The proposed mathematical formulation is used in an exact solution framework based on logic-based Benders decomposition. The proposed approach decomposes the problem into a workload-assignment master problem and operation-sequence slave subproblems. Logic-based cuts are proposed to ensure the convergence of the approach. Computational results show the effectiveness of the proposed solution approach
An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation
Scheduling heterogeneous delivery tasks on a mixed logistics platform
Large e-commerce retailers usually establish their own logistics systems. Such systems make use of their own dedicated fleets but will also use a crowdsourced delivery mode by hiring occasional fleets. These mixed logistics systems with both dedicated and occasional fleets serve both retailers’ internal delivery tasks and external tasks requested by local businesses. This paper studies the problem of scheduling heterogeneous (internal and external) delivery tasks on a mixed logistics platform with multiple depots and two types of vehicles (dedicated and occasional). A delivery task is executed by either a dedicated vehicle or an occasional vehicle. The dedicated vehicles depart from and return to the platform's depots; the occasional vehicles depart from their original location and pick up goods from depots or external pickup locations, fulfill the delivery tasks, and finish their route at the final delivery location. We propose mixed integer programming models and column generation-based solution methods to solve the problem. A computational study is conducted based on a series of randomly generated instances and real-world instances involving 15 depots, 120 internal customers, 15 external delivery tasks, and 38 dedicated and occasional vehicles. The results obtained demonstrate the efficiency of the column generation-based solution methods. Moreover, the effectiveness of the proposed models is validated by a significant cost saving in comparison to intuitive decision rules. A sensitivity analysis is also conducted to derive a number of managerial implications
An exact algorithm for the unidirectional quay crane scheduling problem with vessel stability
This paper addresses the quay crane scheduling problem (QCSP) with vessel stability constraints. Vessel stability is essential to improve quay crane operations in container terminals, but it significantly com- plicates the basic QCSP and the corresponding solutions methods. We describe a novel mathematical formulation for the unidirectional QCSP with vessel stability, and we propose an exact algorithm based on logic-based Benders decomposition to solve the problem efficiently. The problem is decomposed into two subproblems, e.g., a task-assignment master problem without vessel stability constraints, and a time- allocation problem, aimed at determining the operation time of each task under the premise of the vessel stability requirements. The proposed algorithm is tested on benchmark instances derived from the litera- ture, and the effectiveness of the proposed model and solution approach is demonstrated
Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs
In the well-known vehicle routing problem (VRP), a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. An important variant of the VRP arises when a mixed fleet of vehicles, characterized by different capacities and costs, is available for distribution activities. The problem is known as fleet size and mix VRP with fixed costs FSMF and has several practical applications. In this article, we present a new mixed integer programming formulation for FSMF based on a two-commodity network flow approach. New valid inequalities are proposed to strengthen the linear programming relaxation of the mathematical formulation. The effectiveness of the proposed cuts is extensively tested on benchmark instance
Customer Clustering and Sales Area Design
A common problem in local distribution arises when a company, or an agency in the case of city logistics,
has to plan recurrent delivery and collection activities over a certain, typically urban territory. Goods are
available at one or more warehouses and have to be transported to customers located in the territory,
where reverse logistics operations could also be needed. All customers are registered in the customer
anagraphic of the company ERP and have issued recurrent orders, to be serviced within the planning
period. Visits at the customers must be made on different days, according to feasible, well-spread day
combinations. Moreover, attempted sales could be tried by the vehicle driver along his route. The overall
objective is the minimization of the transportation costs, as resulting from the sum of travel costs of all
routes of the company vehicles during the planning period
A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy
The production routing problem (PRP) arises in the applications of integrated
supply chain which jointly optimize the production, inventory, distribution, and routing
decisions. The literature on this problem is quite rare due to its complexity. In this paper,
we consider the multivehicle PRP (MVPRP) with order-up-to-level inventory replenishment
policy, where every time a customer is visited, the quantity delivered is such that the
maximum inventory level is reached. We propose an exact Benders’ decomposition approach
to solve the MVPRP, which decomposes the problem as a master problem and a
slave problem. The master problem decides whether to produce the product, the quantity
to be produced, and the customers to be replenished for every period of the planning
horizon. The resulting slave problem decomposes into a capacitated vehicle routing
problem for each period of the planning horizon where each problem is solved using an
exact algorithm based on the set partitioning model, and the identified feasibility and
optimality cuts are added to the master problem to guide the solution process. Valid inequalities
and initial optimality cuts are used to strengthen the linear programming relaxation
of the master formulation. The exact method is tested on MVPRP instances and on
instances of the multivehicle vendor-managed inventory routing problem, a special case of
the MVPRP, and the good performance of the proposed approach is demonstrated
Routing Optimization with Generalized Consistency Requirements
The consistent vehicle routing problem (ConVRP) aims to design synchronized routes on multiple days to serve a group of customers while minimizing the total travel cost. It stipulates that customers should be visited at roughly the same time (time consistency) by several familiar drivers (driver consistency). This paper generalizes the ConVRP for any level of driver consistency and additionally addresses route consistency, which means that each driver can traverse at most a certain proportion of different arcs of routes on planning days, which guarantees route familiarity. To solve this problem, we develop two set partitioning-based formulations, one based on routes and the other based on schedules. We investigate valid lower bounds on the linear relaxations of both of the formulations that are used to derive a subset of columns (routes and schedules); within the subset are columns of an optimal solution for each formulation. We then solve the reduced problem of either one of the formulations to achieve an optimal solution. Numerical results show that our exact method can effectively solve most of the medium-sized ConVRP instances in the literature and can also solve some newly generated instances involving up to 50 customers. Our exact solutions explore some managerial findings with respect to the adoption of consistency measures in practice. First, maintaining reasonably high levels of consistency requirements does not necessarily always lead to a substantial increase in cost. Second, a high level of time consistency can potentially be guaranteed by adopting a high level of driver consistency. Third, maintaining high levels of time consistency and driver consistency may lead to lower levels of route consistency
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