Christelle Gueret

A review of dynamic vehicle routing problems

A number of technological advances have led to a renewed interest in dynamic vehicle routing problems. This survey classifies routing problems from the perspective of information quality and evolution. After presenting a general description of dynamic routing, we introduce the notion of degree of dynamism, and present a comprehensive review of applications and solution methods for dynamic vehicle routing problems.

A new lower bound for the open‐shop problem

In this paper, we present a new lower bound for the open‐shop problem.In shop problems,a classical lower bound LB is the maximum of job durations and machineloads. Contrary tothe flow‐shop and job‐shop problems, the open‐shop lacks tighter bounds.For the generalopen‐shop problem OS, we propose an improved bound defined as theoptimal makespan ofa relaxed open‐shop problem OSk. In OSk, the tasks of any job may be simultaneous, except for a selected job k. We prove the NP-hardness of OSk.However, for a fixed processingroute of k, OSk boils down to subset‐sumproblems which can quickly be solved via dynamicprogramming. From this property, we define a branch‐and‐bound method for solvingOSkwhich explores the possible processing routes of k. The resultingoptimal makespan givesthe desired bound for the initial problem OS. We evaluate the method ondifficult instancescreated by a special random generator, in which all job durations and all machine loads areequal to a given constant. Our new lower bound is at least as good as LBand improves ittypically by 4%, which is remarkable for a shop problem known for its rather small gapsbetween LB and the optimal makespan. Moreover, the computational timeson a PC arequite small on average. As a by‐product of the study, we determined and propose to theresearch community a set of very hard open‐shop instances, for which the new boundimproves LB by up to 30%.

Classical and new heuristics for the open-shop problem: A computational evaluation

We study the problem of constructing minimum makespan schedules for the Open-Shop problem. This paper presents two new heuristics: the first one is a list scheduling algorithm with two priorities. The second is based on the construction of matchings in a bipartite graph. We develop several versions of these two heuristics. A computational evaluation shows that around 90% of randomly generated instances are solvable optimally, whereas classical (list scheduling) heuristics achieve less than 20% on average. Therefore, our algorithms make most Open-Shop instances easy to solve in practice, and this raises the problem of generating hard instances. We extend the evaluation to two kinds of such instances: the results are not so good, but remain better than classical heuristics.

Using intelligent backtracking to improve branch-and-bound methods: An application to Open-Shop problems

Abstract Only two branch-and-bound methods have been published so far for the Open-Shop problem. The best one has been proposed by Brucker et al. But some square problems from size 7 remain still unsolved with it. We present an improving technique for branch-and-bound methods applied to Brucker et al.s algorithm for Open-Shop problems. Our technique is based on intelligent backtracking. An adaptation of a generic explanation system we have initially developed in the constraint programming scheme is used to develop that technique. We tested our approach on Open-Shop problems from the literature (benchmarks of Taillard). The search is definitely improved: on some square problems of size 10, the number of backtracks is reduced by more than 90% and we even solved an open problem of that size.

An event-driven optimization framework for dynamic vehicle routing

The real-time operation of a fleet of vehicles introduces challenging optimization problems. In this work, we propose an event-driven framework that anticipates unknown changes arising in the context of dynamic vehicle routing. The framework is intrinsically parallelized to take advantage of modern multi-core and multi-threaded computing architectures. It is also designed to be easily embeddable in decision support systems that cope with a wide range of contexts and side constraints. We illustrate the flexibility of the framework by showing how it can be adapted to tackle the dynamic vehicle routing problem with stochastic demands.

Complexity of flowshop scheduling problems with a new blocking constraint

This article deals with makespan minimization in the flowshop scheduling problem under the condition of no intermediate storage between machines. A new blocking constraint met in several industrial problems is introduced, and several complexity results are presented from two to five machines. Some problems with four machines in which the new and the classical blocking constraints are mixed, are polynomial. Problems with only the new blocking constraint are polynomial for up to three machines. Although the complexity of the problem with four machines is left open, several cases are shown to be polynomial. Finally the problem with five machines is NP-hard.

Joint-optimization of inventory policies on a multi-product multi-echelon pharmaceutical system with batching and ordering constraints

This paper presents a methodology to find near-optimal joint inventory control policies for the real case of a one-warehouse, n-retailer distribution system of infusion solutions at a University Medical Center in France. We consider stochastic demand, batching and order-up-to level policies as well as aspects particular to the healthcare setting such as emergency deliveries, required service level rates and a new constraint on the ordering policy that fits best the hospital’s interests instead of abstract ordering costs. The system is modeled as a Markov chain with an objective to minimize the stock-on-hand value for the overall system. We provide the analytical structure of the model to show that the optimal reorder point of the policy at both echelons is easily derived from a simple probability calculation. We also show that the optimal policy at the care units is to set the order-up-to level one unit higher than the reorder point. We further demonstrate that optimizing the care units in isolation is optimal for the joint multi-echelon, n-retailer problem. A heuristic algorithm is presented to find the near-optimal order-up-to level of the policy of each product at the central pharmacy; all other policy parameters are guaranteed optimal via the structure provided by the model. Comparison of our methodology versus that currently in place at the hospital showed a reduction of approximately 45% in the stock-on-hand value while still respecting the service level requirements.

A Memetic Algorithm for a Pick-Up and Delivery Problem by Helicopter

This paper presents a memetic algorithm for a pick-up and delivery problem. The specific application studied here is the personnel transportation within a set of oil platforms by one helicopter that may have to undertake several routes in sequence. Different versions of the algorithm are presented and tested on randomly generated instances as well as on real instances provided by a petroleum company. The results show that the solutions obtained are 8% better than construction and improvement solutions on randomly generated instances.

Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.

An Optimal Constraint Programming Approach to the Open-Shop Problem

This paper presents an optimal constraint programming approach for the open-shop scheduling problem, which integrates recent constraint propagation and branching techniques with new upper bound heuristics. Randomized restart policies combined with nogood recording allow us to search diversification and learning from restarts. This approach is compared with the best-known metaheuristics and exact algorithms, and it shows better results on a wide range of benchmark instances.