Research Express@NCKU - Articles Digest
Research Express@NCKU Volume 3 Issue 4 - February 15, 2008 [ http://research.ncku.edu.tw/re/articles/e/20080215/6.html ]
Fast Heuristics for Designing Integrated E- Waste Reverse Logistics Networks
I-Lin Wang * , Wen-Cheng Yang
Department of Industrial and Information Management, National Cheng Kung University, No.1 University Rd. Tainan 701, Taiwan
[email protected]
*IEEE Transactions on Electronics Packaging Manufacturing (IF=1.000), Vol.30, No.2, Apr. 2007, 147-154.
I ntroduction:
With the growing economy, the increasing amount of disposed goods can induce important environmental issues if they are not properly managed at product end of life. Reverse logistics, the activities to collect and process used products, has been extensively investigated recently to preserve as much of the residual value of used products in a way
friendly to the environment. For example, the environmental
regulations in Taiwan mandate the manufacturers and importers to take-back their products.
Manufacturers and importers contribute approximately 20 USD of disposition fees for each new electronic appliance and computer to a fund established by the Environmental Protection Administration (EPA) of Taiwan. The fund committee is responsible in evaluating the amount of disposition fee and certifying the take-back rate to establish an effective reverse logistics system.
Decisions made by the fund committee may have great affects on the entire reverse logistics system. In particular, changing the disposition fee for a specific category of recycled products may encourage (or discourage) reverse logistics companies to raise (or lower down) its take-back rate. Besides specifying the subsidy for recycling specific products, a government may enact regulations to limit or encourage the locations or configurations for specific recycling facilities. To evaluate the performance of a reverse logistics system in its planning stage, a government or a company may first formulate their problem as a mathematical programming problem, solve it, and then perform sensitivity analysis. The design of a reverse logistics system is usually treated as a mixed integer linear programming problem (MIP) which seeks the maximum total revenue or minimum total cost obtained by optimal facility locations and transportation assignments for processing and shipping the recycled products or materials in accordance with the operational capacities and the regulations. The sensitivity analysis for MIP may be conducted by iteratively solving MIPs of the same problem structure but with slightly different settings of coefficients.
Unfortunately, solving such an MIP in reasonable time is usually a hard task even using a state-of-the- art optimization software like CPLEX.
Developing a solution method that computes the optimal or near-optimal solutions in shorter time is not only useful for conducting the sensitivity analysis, but also beneficial in solving network design problem under uncertainty. In particular, during the supply chain design phase, the uncertainty in demands and prices should be considered to achieve better management over the planned time horizon. The
discounted cash flow analysis incorporated with the decision tree methodologies can be used for
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evaluating the network design decisions under uncertainty, in which each node in the decision tree corresponds to an MIP. As one solves an MIP at each node in the decision tree and works backwards from future period based on the Bellman’s principle, exponentially many MIPs have to be solved which could be a very time-consuming task. In practice, such a strategy analysis may not require all the MIPs to be solved to optimality, thus fast heuristics to compute for solutions in shorter time will definitely
decrease the computational efforts required for conducting the sensitivity analysis or designing the network under uncertainty.
Previous research in reverse logistics network design problem usually only considers universal facilities which can collect or process all kinds of recycled products. A more reasonable assumption in designing a reverse logistics network should also consider different configurations of facilities for different
categories of recycled products. Using different facility configurations to recycle different categories of recycled e-waste is a common practice in Taiwan’s e-waste recycling industry. In particular, given a candidate location qualified for building a facility that can collect or process exactly ρ of the entire γ categories of recycled products, the facility will have possible configurations to be built.
Furthermore, one may at most have 2
γoptions to build a facility that can collect or process up to γ categories of recycled products. Such flexibility in constructing different configurations of facilities is very important to achieve a better reverse supply chain management, although it will induce a large number of new variables and constraints.
Proposed Mathematical Model:
Let I, S, P, and R be the set of collecting points, storage sites, recycle plants, and final treatment sites, respectively. An e-waste reverse logistics network is illustrated in Figure 1, where a node represents a site in the node set N=I∪S∪P∪R and an arc belongs to the arc set
. In particular, products for recycling are collected in a node in I, then they are either shipped to a node in S and then to a node in P, or directly to a node in P. Products will be
recycled in a node in P (e.g. some disassembling or sorting processes) to obtain sorted materials which are then to be shipped to nodes in R for final treatment or landfill. This paper investigates a decision- making problem that decides the nodes in S∪P, their associated facility configurations to be built, as well as the optimal assignment of arc flows such that the overall profits is maximized. In particular, the profit is calculated by the subsidies earned from the recycling processes and the revenues earned from sorted materials sold in the final treatment sites minus the transportation costs along all arcs, fixed costs for opening new storage sites and recycle plants, operational costs of all facilities, and costs to process all the useless materials. The constraints cover flow balance relationships (i.e., flow entering a node plus its supply/demand equals to flow leaving it), facility capacities including both the minimum and maximum designed capacities, and the dependency relationships between the arc flows and decisions of building each candidate facility. By considering the flexibility of facility configurations, our proposed model becomes more complicated than conventional mathematical programming models that are already NP- hard.
Proposed Solution Methods:
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we give four procedures: (1) Random Selection (RS), (2) Heuristic Concentration (HC), (3) modified Heuristic Expansion (MHE), and (4) modified CC (MCC) to solve our problem. Our first algorithm contains three procedures. In particular, RS iteratively solves smaller min-cost flow subproblems with randomly selected candidate sites, where each subproblem seeks the best transportation assignments between the selected candidate sites that minimize the total facility and transportation costs. Since each subproblem corresponds to an easier linear programming (LP) problem, we run this procedure for b times (e.g. b=100 ), and rank the sites ever appeared in the optimal solutions for these smaller LP subproblems. Intuitively, a candidate site that appears more often in the optimal solution sets of RS may tend to appear in the optimal solution of the original problem. HC then selects sites appeared more often in the solution sets of RS, solves a small MIP to determine the optimal candidate sites among those selected candidate sites, and then updates the optimal solution obtained in the procedure. To prevent possible bias caused by the small MIP solved in HC, procedure MHE further expands the scale of candidate sites based on HC’s solution set, and then iteratively adds new candidate sites to the small MIP and solves the MIP of larger size until no further improvement in the objective function is occurred.
Our MHE requires much fewer iterations and shorter time than its original version HE. Even better, our computational results show our method (RS+HC+MHE) can obtain a solution of similar quality in shorter time than previous method (RS+HC+HE).
In addition to the RS and HC, we also propose another procedure named MCC which considers the unit capacity cost induced by the fixed and operational cost and all the transportation costs for each facility.
In particular, MCC calculates the ratio of the total fixed and operational and transportation cost to the capacity for each facility, and then selects the facilities with smaller unit capacity cost and all the transportation costs as a starting point to apply the MHE procedure.
Results and Conclusions:
Our proposed algorithms (RS+HC+MHE and MCC+MHE) can successfully compute a solution of good quality in shorter time, compared with previous heuristics and the exact optimal solution methodologies.
Our computational experiments validate the effectiveness and efficiency of our proposed algorithms, and also suggest the advantage of understanding the problem nature in designing simple and good
heuristics. The solution quality obtained by our methods is also very good, which makes our methods especially suitable for solving difficult reverse logistics network design problems.
We have given a new mixed integer linear programming model that considers both the location and configuration for a new facility to maximize the overall utilization and revenue for designing an e-waste reverse logistics network. Our mathematical model is based on the common practice of the e-waste recycling industry in Taiwan where different facility configurations are used to recycle different categories of recycled e-waste. Although only two categories of recycled products are considered in our model, our mathematical modeling techniques can be further generalized to the cases of more categories with slight modifications. This consideration of facility configuration is not only practical but also very important in the network design phase since more flexibility can be obtained to achieve a better reverse supply chain management.
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