The environmental factors are receiving increasing attention in different life cycle stages of products. When a product reaches its End-Of-Life (EOL) stage, the management of its recovery process is affected by the environmental and also economical factors. Selecting efficient methods for the collection and recovery of EOL products has become an important issue. The European Union Directive 2000/53/EC extends the responsibility of the vehicle manufacturers to the postconsumer stage of the vehicle. In order to fulfill the requirements of this Directive and also efficient management of the whole recovery process, the conceptual framework of a reverse logistics network is presented. The distribution of new vehicles in an area and also collecting the End-of-Life Vehicles (ELVs) and their recovery are considered jointly. It is assumed that the new vehicles distributors are also responsible for collecting the ELVs. Then a mathematical model is developed which minimizes the costs of setting up the network and also the relevant transportation costs. Because of the complexity of the model, a solution methodology based on the genetic algorithm is designed which enables achieving good quality solutions in a reasonable algorithm run time.

Economical, social, and environmental dimensions are three main pillars of sustainable development. The environmental factors have been mainly taken into account in the developed countries, while in the developing countries the economical issues have been the main concern. However issues such as air and water pollution and increased public concern on these problems, resources scarcity, and international legislations have increased the importance of environmental topic in the developing countries.

The Environmental Conscious Manufacturing (ECM) and its related Design For Environment (DFE) guidelines are getting more and more attention. ECM involves producing products such that their overall negative environmental effects are minimized [

When a product reaches its End-Of-Life stage, it would usually have potential for polluting the environment. On the other hand, EOL products may have valuable parts, components, and materials which could be used again or returned to the production cycle. That is because the EOL products recovery is an important stage in products life cycle.

Vehicle is a complex product composed of thousands parts with different types of materials; so the ELV recovery is a complicated process. Based on the quality of the ELV's parts and also the economical considerations, different recovery and disposal options could be selected. These options include reuse, remanufacture, material recycling, incineration, and landfill. The last two options have more negative environmental effects.

As ELVs recovery is a very important issue, therefore the European Union has set up the Directive 2000/53/EC [

The vehicle manufacturers may need to set up an efficient recovery network in order to fulfill the Directive 2000/53/EC requirements. They may also outsource the take back and recovery activities and its management. For instance, in the UK, the producers have contract with the network of administrators. On behalf of the manufacturers they are responsible for the free take-back (from the beginning of 2007), depollution, dismantling, and forwarding the ELV's hulk to the treatment facilities for shredding [

The importance of management of the ELVs in the developing countries where the number of vehicles on the roads is increasing at an alarming rate is also becoming more apparent. The implementation of strict product-oriented legislation will sooner or later become of paramount interest in developing countries [

In this paper, a reverse logistics network for the management of the ELVs recovery process is designed. Based on a conceptual model, a mathematical model for minimizing the costs of collecting the ELVs and flow of materials between treatment facilities is developed. The distribution of new vehicles and collecting the ELVs are considered simultaneously in the model and performed in the same facilities. Advantages of building such integrated facilities might include cost savings and pollution reduction as results of sharing material handling equipment and infrastructure [

Research areas related to End-of-Life products and ELVs are extremely diverse. Some researches have concentrated on the Optimal Recovery Plan and Disassembly Sequence for EOL products. In such problems the objective is to determine to what extent the return products must be disassembled and which recovery and disposal options should be applied [

Technical-cost models of ELV processing operators were developed and the results obtained show that the recycling targets defined in the EU Directive for 2006 require the removal of an increased number of plastic parts from an ELV [

A demanufacturing optimization model has been applied to the ELV recovery process problem where different scenarios including current ELV recycling in the North America and implementing the EU Directive are discussed [

An expanding research area related to EoL products is designing reverse logistics networks and developing associated mathematical models. The traditional supply chain models have been extended to incorporate environmental factors and used products flow from customers to manufacturers or recyclers. Some researches have concentrated only on used products reverse flow while some other works have considered new products and used products flows simultaneously.

Strategic network design for the ELVs collection problem in Mexico has been studied [

A facility location model for the reverse logistics systems, in which both direct and reverse flows have to be considered simultaneously, is presented [

A conceptual model for simultaneous location-allocation of facilities for a cost effective and efficient reverse logistics network is developed [

A facility location-allocation model for the carpet materials has been developed [

A model for reverse supply chain which considers the collection, recycling, and processing of electronic waste has been developed [

A stochastic programming approach has been implemented for sand recycling treatment facility location problem [

Due to inherent high complexity of the reverse logistics problems, especially when the forward flows are considered simultaneously, different solution methodologies based on the search algorithms, such as genetic algorithm (GA), have been used in solving these problems. A mathematical model of a remanufacturing system by considering a three-stage logistics network has been presented [

A nonlinear mixed integer programming model and a genetic algorithm that can solve the reverse logistics problem involving both initial collection points and centralized return centers were presented [

A mixed integer nonlinear programming model for the design of a dynamic integrated distribution network to account for the integrated aspect of optimizing the forward and return network simultaneously is given [

A facility-location model in a reverse logistics context has been combined with queueing relationships, which enables to account for some dynamic aspects like lead time and inventory positions [

In this paper, the problem of designing a reverse logistics network for ELVs recovery has been addressed; furthermore, the forward distribution of new cars is also considered. The distribution-collection center entity is then introduced, which its benefit is discussed in Section

In [

The “Manufacturer Network” Building Blocks.

In [

In this paper it is assumed that the new vehicle distributors are also responsible for collecting the ELVs. These new entities are called distribution-collection centers. The main purpose for considering this assumption is reducing the total cost of the system setup, since there will be no need to establish extra facilities for collecting the ELVs. Based on this assumption, the whole problem network should be optimized as an integrated system and the transportation of the new vehicles and the ELVs will be considered collectively in the model.

The following assumptions have been considered in developing the mathematical model.

The whole problem area is divided into I sections, called demand points. For each of these points, the demand for new vehicle and also the number of ELVs are estimated. All the estimated demands for new vehicles should be materialized and also all the estimated ELVs should be collected and recovered by the network. The developed model could be applied to a geographical area where a manufacturer wants to establish its distribution centers and also collect and recover all its manufactured vehicles that have reached to their end-of-life stage.

The potential locations for setting up the distribution-collection centers are assumed to be

For each distribution-collection center, the capacities for stocking new vehicles and ELVs may be different and also the costs of setting up these capacities may vary.

In order to set up each facility, a fixed cost and a variable cost, which is related to its capacity, have been assumed.

It is assumed that reused and remanufactured parts are sold at the dismantling sites. Note that the remanufacturing process is not performed by dismantlers and the disassembled parts and components are sold without any refurbishment. Hence the transportation of the remanufactured parts to the Part Suppliers is not considered. Based on this assumption, the Part Suppliers are not taken into account in the developed model.

After dismantling, the removed fluids, tyres, and nonresalable plastics are sent to the recyclers. Reused/remanufactured parts and resalable plastic parts are sold at the dismantlers' sites, while the hulk is sent to the shredder. Note that removed hazardous materials are neglected because of their low weight, which is less than 0.1 percent of the vehicle total weight [

The optimal percentages of the above mentioned streams, based on year 2006 requirements (i.e., 85% of ELV weight recovery with maximum of 5% energy reclamation) are given in Table

Optimal recovery policy for year 2006.

Material stream | The ELVs with resale parts | The ELVs without resale parts |
---|---|---|

Fluids | 1.8% | 1.8% |

Tyres | — | 2.5% |

Nonresalable plastics parts | 0.3% | 2% |

Reused and remanufactured parts | 59.3% | — |

Hulk | 38.6% | 93.7% |

The simplified designed reverse logistics network which is the base of the developed mathematical model is shown in Figure

The Simplified Network.

The model decision variables and parameters have been defined in the appendix. The objective function is given in (

The first term in (

The fifth term in (

The last two terms in (

In order to build the mathematical model, the following constraints have been considered.

All the ELVs should be collected from demand points:

Any purchase demands for the new vehicles should be satisfied. The customers may buy their vehicles from any of the distribution-collection centers:

The cost of setting up each distribution-collection center should not exceed its determined available budget:

ELV capacity of each distribution-collection center is calculated as follows (used for model simplification):

Dismantler's capacity is calculated as follows (used for model simplification):

Distribution-collection centers' capacity constraints. two maximum capacities related to the new vehicles and ELVs are considered for each of the distribution-collection centers. These capacities are dependent on each location available resources:

Dismantlers' capacity constraints: a maximum capacity for setting up each dismantling site is considered:

Materials flow constraints: transportation of all collected ELVs from distribution-collection centers to dismantlers and transportation of hulks from dismantlers to the shredders:

Decision variables sign restrictions:

With the knowledge that the proposed mathematical model is a general variant of the location-allocation model and hence an NP-hard problem [

Genetic algorithms (GAs) are powerful and broadly applicable stochastic search and optimization techniques based on principles of evolution theory. In the past few years, genetic algorithms have received considerable attention for solving difficult combinatorial optimization problems [

The proper representation of a solution plays a key role in the development of a genetic algorithm. In the proposed coding scheme, each gene corresponds to one of available locations. A solution is partially represented by an array of size

The adopted representation helps to decide where the required facilities should be located. The intractability of this reverse logistics network design problem comes directly from the discrete nature of the locations related variable. Once the locations are fixed, the remaining problem of deciding the quantity variables becomes tractable since this squeezed problem is simply a continuous linear program. When this linear program is solved optimally the objective value of the corresponding solution is determined. It is considered that this value corresponds to the fitness of the relevant chromosome.

The generated solutions should satisfy all the model constraints. To ensure the feasibility of the generated solutions, it is necessary to verify if the solutions can satisfy constraints (

The initial population is generated randomly through using a Bernoulli process [

A simple genetic algorithm that yields good results in many practical problems is composed of three operators, namely, reproduction, crossover, and mutation [

The crossover operator takes two chromosomes and swaps a part of their genetic information to produce new chromosomes. The easiest and the most classical method for crossover is to choose a random cut-point and generate the offspring by combining the segment of one parent to the left of the cut-point with the segment of the other parent to the right of the cut-point. At the crossover stage, the one-cut crossover is employed twice, one for the parental parts between genes 1 through

Illustration of the crossover operator.

Mutation produces spontaneous random changes in various chromosomes. This genetic operation serves the crucial role of replacing the genes lost from population during the selection process so that they can be tried in a new context, or providing the genes that were not present in the initial population. In the implementation the simplest method is used, in which some genes are selected by a small probability and their content is changed. Adopting the elitist strategy, two best chromosomes are excluded from the crossover procedure and they are directly copied to the next generation. Moreover, the best chromosome is excluded from the mutation procedure. The detailed procedure to generate the next generation is as follows.

Copy two best chromosomes to the next generation.

Select two chromosomes by the roulette wheel method. If a random number from

For every gene in the chromosomes generated at Step

In order to measure the effectiveness of the proposed mathematical model and the adapted GA methodology for real word applications, a number of test problem instances are generated. Table

Constant parameters and their values.

Parameter | Value | Parameter | Value |
---|---|---|---|

50000 | 0.018 | ||

100000 | 0 | ||

100 | 0.003 | ||

50 | 0.018 | ||

11 | 0.025 | ||

10 | 0.02 | ||

0.5 | 0.386 | ||

300 | 0.937 |

The proposed GA methodology was implemented through a computer program written in MATLAB 7.04 and executed on a laptop computer with 2 GHz of CPU speed and 2048 MB RAM. The mathematical model is also implemented in LINGO 9.0 and executed on the same computer. The preliminary computations showed that the choice of 0.5, 0.05, 10, and 100 would be suitable for

The GA approach was executed 10 times on each of the four problems and the best, worst, and average results are reported here. For each problem, the time taken to conclude the search is also reported. Results are summarized in Table

Computational results.

LINGO 9.0 | GA | ||||||
---|---|---|---|---|---|---|---|

Problems | Optimal | Time | Best | Worst | Average | Time | Gap |

objective | (sec) | (sec) | (%) | ||||

Problem 1 | 6545186 | 12 | 6630500 | 7178300 | 6988110 | 39.7 | 6.8 |

Problem 2 | 15574450 | 2400 | 16398000 | 16812000 | 16591100 | 147.9 | 6.5 |

Problem 3 | 26775590 | 8880 | 27416000 | 28774000 | 28232000 | 452.7 | 5.4 |

Problem 4 | 26618180 | 82800 | 27635000 | 30675000 | 28803800 | 1263.3 | 8.2 |

From Table

The management of the ELVs recovery process and setting up the required infrastructure is receiving increasing attention in developing countries. In this paper, a conceptual model including the production of new vehicles and recovery of used ones is designed. New entities called distribution-collection centers are assumed which are responsible for distributing new vehicles and also collecting the ELVs. The supervision of the whole network is conducted by the vehicle manufacturer. A mathematical model for minimizing the costs of setting up such network and the flow of materials between different facilities is then developed.

The proposed model can help manufacturers to efficiently fulfill the environmental legislations requirements. The model will also enable them to better manage the new vehicles and ELVs transportation routes by sharing the resources. By creating this network, valuable information such as recovery methods and Design For Disassembly advices would be exchanged between different network entities. In an upper tier, the government or the environmental organizations may be involved in designing the recovery network and its different aspects, for example, the monetary transactions.

The high complexity of the model does not permit for developing polynomial time exact algorithms; so a search methodology based on the genetic algorithm is adapted. After selecting a suitable representation of a solution and determining the genetic algorithm operators, a number of test problems were randomly generated and solved. The quality of the generated solutions and the algorithm run time were compared with the results of the LINGO 9.0 software. For large-scale problems in which there is little hope to solve the problem optimally, using the proposed genetic algorithm is a suitable method for finding good quality solutions in reasonable run time.

A number of extensions may be possible to further tightening the gaps reported by the GA. Devising suitable chromosomal representations, which handle concurrent location and allocation decisions, would be an interesting direction. Introducing a low -cost local neighborhood search for improvement of the candidate solutions is also another way of enhancing the GA methodology. Finally, employing other search methods such as tabu search, simulated annealing algorithm, and doing a comparison study would be suitable methods.

Demand points;

Distribution-collection centers;

Dismantling sites;

Shredders;

Recyclers;

Vehicle type;

ELV type;

The fixed cost of opening a distribution-collection center

The variable cost (per weight unit) of opening a distribution-collection center related to vehicle type

The fixed cost of opening a dismantling site

The variable cost (per weight unit) of opening a dismantling site

Distance between

Distance between

Distance between

Distance between

Distance between

Distance between manufacturer and

Transportation cost of a weight unit of vehicle type

Amount of ELVs in demand point

Amount of demand for new vehicle in demand point

Maximum potential capacity of distribution-collection center

Maximum potential capacity of dismantling site

The available budget for setting up distribution-collection center

Percentage of ELVs type

Percentage of fluids from the vehicle weight, for ELVs type

Percentage of tyres from the vehicle weight, for ELVs type

Percentage of removed non-resalable plastic parts from the vehicle weight, for ELVs type

Percentage of disassembled parts for reuse or remanufacture from the vehicle weight, for ELVs type

Percentage of the ELVs type

A binary variable which is equal to 1 if distribution-collection center

A binary variable which is equal to 1 if dismantling site

Amount of ELVs transported from

Amount of ELVs transported from

Amount of ELVs transported from

Amount of ELVs transported from

Amount of new vehicles transported from manufacturer to

Capacity of distribution-collection center

Capacity of dismantling site