# SESSION A4:

## [95] A large neighborhood
search for the vehicle routing problem with two-dimensional
loading constraints

Lei Wu, Mhand Hifi and Moudher Khalid Abdal-Hammed

In this paper we investigate the use of the large neighborhood search for solving the vehicle routing problem with two-dimensional loading constraints, an NP-hard combinatorial optimization problem. Such a problem may be viewed as the combination of two complementary well-known problems: the two-dimensional bin-packing problem and the capacitated vehicle routing problem. The proposed method is based on a framework of the large neighborhood search combined with several local search procedures and has been evaluated on Gendreau’s benchmark instances. The obtained results are compared to those reached by the best methods taken from the literature. Encouraging results have been obtained.

## [126] A Robust Optimization
Approach for the Vehicle Routing Problem with Uncertain
Travel Cost

Elyn Lizeth Solano Charris, Christian Prins and
Andréa Cynthia Santos

The Robust Vehicle Routing problem (RVRP) with discrete scenarios is studied here to handle uncertain travelling time, where a scenario represents a possible discretization of the possible travel time observed on each arc at a given traffic hour. The goal is to build a set of routes considering the minimization of the worst total cost over all scenarios. Heuristics and a Genetic Algorithm (GA) are proposed for the RVRP considering a bounded set of discrete scenarios and the asymmetric arc costs on the transportation network. Tests on small and medium size instances are presented to evaluate the performance of the proposed GA for the RVRP. On small-size instances, a maximum of 20 customers, 3 vehicles and 30 discrete scenarios are handled. For medium-size instances, 100 customers, 20 vehicles and 20 scenarios as maximum are tested. Computational results indicate the GA produces good solutions and retrive the majority of proven optima in a moderate computational time.

## [235] Genetic algorithm
to infer criteria weights for multicriteria Inventory
Classification

Hadhami Kaabi, Khaled Jabeur and Talel Ladhari

Multi Criteria Inventory Classification (MCIC) is a well known method to classify inventory items into three predefined and ordered categories A, B and C such as category A contains the most valuable inventory items and category C contains the least valuable ones. The aim of this classification is to keep related inventory costs under control. The process of MCIC consists in ranking items according to their weighted scores. The score of each item is the result of an aggregation function that combines the item evaluations on the different criteria and the criteria weights. In the literature, several methods propose different methodologies to determine the criteria weights (e.g. Linear Programming (LP), Artificial Intelligence (AI) and Multi Criteria Decision Making (MCDM)). This paper presents a method based on genetic algorithm to learn these weights. To estimate these criteria weights and to validate the usefulness of our proposed method, a benchmark data set of 47 items consumed in a Hospital Respiratory Therapy Unit (HRTU) is used.

## [136] An Exact Solution
Search for the Max-Min Multiple Knapsack Problem

Ferhan Al-Maliky, Mhand Hifi and Hedi Mhalla

In this paper, we propose to solve the max-min multiple knapsack problem by using an exact solution search. An instance of the problem is defined by a set of n items to be packed into m knapsacks as to maximize the minimum of the knapsacks' profits. The proposed method uses a series of interval searches, where each interval is bounded with a target value (considered as a lower bound) and an estimated upper bound. The target lower bound is computed by applying some aggressive fixation of some items to optimality whereas the upper bound is computed by using a surrogate relaxation. The performance of the proposed method is evaluated on a set of instances containing a variety of sizes. Computational results showed the superiority of the proposed method when comparing its provided results to those obtained by the Cplex solver and one of the best exact method available in the literature.