Multi-directional local search for a sustainable supply chain network design model
Résumé
1. The problem considered
The increasing importance of environmental issues has prompted decisionmakers
to incorporate environmental factors into supply chain network
design (SCND) models. We propose a bi-objective SCND model to minimize
two conflicting objectives: the total cost and the environmental impact
expressed by CO2 emissions.
The logistics network consists of four layers: suppliers, plants, distribution
centers (DCs) and customers. The model considers several possible
transportations modes in the network, each transportation mode having
a lower and upper capacity limitation. Moreover, we consider different
candidate technology levels at the plants and DCs. Each technology represents
a type of service with associated fixed and variable costs and CO2
emissions. A higher-level technology may reduce carbon emissions, but is
likely to require more investment cost.
The model considers CO2 emissions caused by all industrial and logistics
operations as well as transportation. The main issues to be addressed
in the sustainable SCND model includes determining the number, location,
and technology level at plants and DCs, suitable transportation mode, and
product flows between facilities.
2. Solution method
We solve the corresponding bi-objective mixed integer linear programming
model with the multi-directional local search (MDLS) framework.
The efficiency of this recent framework has been proved on the multiobjective
knapsack, set packing and orienteering problems, but to the best
of our knowledge, this is the first attempt to solve a facility location problem
with it. The MDLS is based on the principle of separately using independent
single-objective local searches to iteratively improve the Pareto set
approximation. The motivation for using this framework is the capability
of using already implemented single objective optimization components.
In our case, we use a large neighborhood search algorithm as single objective
method. Our algorithm can be decomposed in the three following
steps:
Phase 1: look for an initial Pareto set approximation. The initial
phase of the single objective LNS is executed separately for each objective.
The output is an initial Pareto set approximation.
Phase 2: Intensification around the Pareto set approximation. The
Pareto set approximation is improved by exploring the neighborhood
of all the solutions in this set with a Multi-directional local search.
Phase 3: optimization of product flows. After stabilizing the location
and transportation mode decisions for all Pareto set approximation
solutions in phase 2, we determine the optimal product flows by applying
the Simplex algorithm to all solutions in the set.
3. Computational results
We assess the performance of our approach through a comparison with
the well-known "-constraint method. In particular, we analyze the Pareto
fronts given by both solutions on a set of 60 generated instances and show
that the efficiency of our approach improves when the instance size grows.