Claudia Archetti

A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem

We consider a distribution problem in which a product has to be shipped from a supplier to several retailers over a given time horizon. Each retailer defines a maximum inventory level. The supplier monitors the inventory of each retailer and determines its replenishment policy, guaranteeing that no stockout occurs at the retailer (vendor-managed inventory policy). Every time a retailer is visited, the quantity delivered by the supplier is such that the maximum inventory level is reached (deterministic order-up-to level policy). Shipments from the supplier to the retailers are performed by a vehicle of given capacity. The problem is to determine for each discrete time instant the quantity to ship to each retailer and the vehicle route. We present a mixed-integer linear programming model and derive new additional valid inequalities used to strengthen the linear relaxation of the model. We implement a branch-and-cut algorithm to solve the model optimally. We then compare the optimal solution of the problem with the optimal solution of two problems obtained by relaxing in different ways the deterministic order-up-to level policy. Computational results are presented on a set of randomly generated problem instances.

Metaheuristics for the team orienteering problem

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.

An Optimization-Based Heuristic for the Split Delivery Vehicle Routing Problem

The split delivery vehicle routing problem is concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost. Contrary to what is assumed in the classical vehicle routing problem, a customer can be served by more than one vehicle, if convenient. We present a solution approach that integrates heuristic search with optimization by using an integer program to explore promising parts of the search space identified by a tabu search heuristic. Computational results show that the method improves the solution of the tabu search in all but one instance of a large test set.

Ants can solve the team orienteering problem

The team orienteering problem (TOP) involves finding a set of paths from the starting point to the ending point such that the total collected reward received from visiting a subset of locations is maximized and the length of each path is restricted by a pre-specified limit. In this paper, an ant colony optimization (ACO) approach is proposed for the team orienteering problem. Four methods, i.e., the sequential, deterministic-concurrent and random-concurrent and simultaneous methods, are proposed to construct candidate solutions in the framework of ACO. We compare these methods according to the results obtained on well-known problems from the literature. Finally, we compare the algorithm with several existing algorithms. The results show that our algorithm is promising.

Worst-Case Analysis for Split Delivery Vehicle Routing Problems

In the vehicle routing problem (VRP) the objective is to construct a minimum cost set of routes serving all customers where the demand of each customer is less than or equal to the vehicle capacity and where each customer is visited once. In the split delivery vehicle routing problem (SDVRP) the restriction that each customer is visited once is removed. We show that the cost savings that can be realized by allowing split deliveries is at most 50. We also study the variant of the VRP in which the demand of a customer may be larger than the vehicle capacity, but where each customer has to be visited a minimum number of times. We show that the cost savings that can be realized by allowing more than the minimum number of required visits is again at most 50. Furthermore, we analyze the performance of simple heuristics that handle customers with demands larger than the vehicle capacity by employing full load out-and-back trips to these customers until the demands become less than or equal to the vehicle capacity. Finally, we investigate situations in which demands are discrete and vehicle capacities are small.

A Hybrid Heuristic for an Inventory Routing Problem

We consider an inventory routing problem in discrete time where a supplier has to serve a set of customers over a multiperiod horizon. A capacity constraint for the inventory is given for each customer, and the service cannot cause any stockout situation. Two different replenishment policies are considered: the order-up-to-level and the maximum-level policies. A single vehicle with a given capacity is available. The transportation cost is proportional to the distance traveled, whereas the inventory holding cost is proportional to the level of the inventory at the customers and at the supplier. The objective is the minimization of the sum of the inventory and transportation costs. We present a heuristic that combines a tabu search scheme with ad hoc designed mixed-integer programming models. The effectiveness of the heuristic is proved over a set of benchmark instances for which the optimal solution is known.

Vehicle routing problems with split deliveries

This paper is a survey on the vehicle routing problems with split deliveries, a class of routing problems where each customer may be served by more than one vehicle. Starting from the most classical routing problems, we introduce the split delivery vehicle routing problem (SDVRP). We review a formulation, the main properties and exact and heuristic solution approaches for the SDVRP. Then, we present a general overview of several variants of the SDVRP and of the literature available.

The capacitated team orienteering and profitable tour problems

In this paper, we study the capacitated team orienteering and profitable tour problems (CTOP and CPTP). The interest in these problems comes from recent developments in the use of the Internet for a better matching of demand and offer of transportation services. We propose exact and heuristic procedures for the CTOP and the CPTP. The computational results show that the heuristic procedures often find the optimal solution and in general cause very limited errors.

Reoptimizing the traveling salesman problem

In this paper, we study the reoptimization problems which arise when a new node is added to an optimal solution of a traveling salesman problem (TSP) instance or when a node is removed. We show that both reoptimization problems are NP-hard. Moreover, we show that, while the cheapest insertion heuristic has a tight worst-case ratio equal to 2 when applied to a TSP instance, it guarantees, in linear time, a tight worst-case ratio equal to 3/2 when used to add the new node and that also the simplest heuristic to remove a node from the optimal tour guarantees a tight ratio equal to 3/2 in constant time.

The Split Delivery Vehicle Routing Problem: A Survey

In the classical Vehicle Routing Problem (VRP) a fleet of capacitated vehicles is available to serve a set of customers with known demand. Each customer is required to be visited by exactly one vehicle and the objective is to minimize the total distance traveled. In the Split Delivery Vehicle Routing Problem (SDVRP) the restriction that each customer has to be visited exactly once is removed, i.e., split deliveries are allowed. In this chapter we present a survey of the state-of-the-art on the SDVRP.