This study aims to improve the efficiency of disassembly planning in remanufacturing environment. Even though disassembly processes are considered as the reverse of the corresponding assembly processes, under some technological and management constraints the feasible and efficient disassembly planning can be achieved by only welldesigned algorithms. In this paper, we propose a heuristic for disassembly planning with the existence of disassembled part/subassembly demands. A mathematical model is formulated for solving this problem to determine the sequence and quantity of disassembly operations to minimize the disassembly costs under sequencedependent setup and capacity constraints. The disassembly costs consist of the setup cost, part inventory holding cost, disassembly processing cost, and purchasing cost that resulted from unsatisfied demand. A simple but efficient heuristic algorithm is proposed to improve the quality of solution and computational efficiency. The main idea of heuristic is to divide the planning horizon into the smaller planning windows and improve the computational efficiency without much loss of solution quality. Performances of the heuristic are investigated through the computational experiments.
In a recent decade, most of environmentconscious industries have recognized the importance of remanufacturing where endoflife products are collected and some useful parts are used again to remanufacture new parts. Remanufacturing may save resources on earth and production costs of company. As shown in Figure
Conceptual framework of remanufacturing [
In this paper, we deal with disassembly processes and especially focus on disassembly planning. Because disassembly is a preprocess of refurbishing or recycling, efficiency of it affects the whole remanufacturing system. In sustainable and environmentconscious industry, as the number of returned products increases, disassembly process becomes more significant and its related decisionmaking is getting complicated for most companies.
As though disassembly planning problem in remanufacturing system looks like just the reverse of the conventional assembly planning problem, it is quite different in the purpose of retrieving necessary parts with the choice of efficient disassembly operations, which requires some different and unique approaches. Also, it deals with not only necessary parts but also unnecessary parts that are disposed or used later in future purpose. With all these reasons, disassembly planning problems is generally considered to be more complicated than assembly planning.
Previous researches on disassembly planning can be classified into three categories: full disassembly of a product with efficient sequence, disassembly to maximize the value of disposal parts, and disassembly to retrieve specific parts with minimum costs. The first category research aims to generate efficient or even optimal sequence of disassembly operations to disassemble a whole product. Most researches try to minimize disassembling costs because the costs are dependent on the selection of disassembly sequence. As one of the corner stone researches, Homem de Mello and Sanderson [
The second category of research focuses on maximizing the value of disassembled parts, which is very practical issue in remanufacturing system. The problem is to maximize total profit incurred by disassembly process by comparing the costs of disassembly to the value of all disassembled parts. Gupta and Taleb [
For development of heuristic in this paper, we consider the rolling horizon planning technique which was firstly proposed by Modigliani and Hohn [
The previous researches show that disassembly planning is more than just the reverse of assembly planning but should consider the recovery of useful parts/materials, impact of disposal on environment, and total costs as well. In this study, we are concerned about disassembly planning with efficiency and applicability in real remanufacturing environment. In order to do that, we make disassembly planning allow timeconstrained operations, sequencedependent setup, disassembled part demand, and multiple planning periods, and finally we propose an efficient heuristic to solve this NPhard problem. This paper is organized as follows: We first develop a mathematical model of disassembly planning in Section
Disassembly planning in this study has the objective to minimize total disassembly costs of meeting part demands at each period. We recognize that this problem has the same property of the capacitated lotsizing problem. Moreover, disassembly planning in remanufacturing has the demands of subassemblies at each period, not only the end parts in BOM (BillofMaterial) structure. Also, since most workshops with disassembly process belong to small or mediumsize company which produces so many different types of products, we assume jobshop production environment rather than mass production line. This means that setup time and the related costs need to be included in the model. For the purpose of modeling, we assume the following production environment.
The demands of parts/subassemblies are known at each period.
The unfulfilled demand through disassembly is fulfilled by purchase from vendor. The purchase cost is considered as penalty cost.
All setup and workload can be transformed to time units.
There exists a working available time at each production period.
Setup can be carried over the next period, that is, the same operation can be carried over the next production period.
Transition matrix:
Disassembly transform matrix of ballpen with 15 subassemblies.
1  2  3  4  5  6  7  8  9  10  11  12  13  

ABCDEF  −1  −1  
ABCDE  1  −1  −1  
ABCDF  1  −1  −1  
ABCD  1  −1  −1  
ABF  −1  1  
BCD  1  −1  1  
AB  1  −1  1  
AE  −1  1  
CD  1  −1  1  1  
A  1  1  
B  1  1  
C  1  
D  1  
E  1  1  1  
F  1  1  1 
Disassembly AND/OR diagram of ballpen [
With the above assumptions, the nomenclature shown at the end of the paper is needed for our model.
The objective function is represented as the sum of all relevant costs such as operation processing cost, inventory holding cost, setup cost, and purchasing cost. Then the model for disassembly planning is formulated as follows.
Model (
Constraints (
In order to develop a heuristic for the problem presented in the previous section, we first examined the computation time for finding the optimal solution. Computational experiments were done using OPL Studio 6.0 by ILOG on the Pentium 4 2.8 Ghz WinXP platform. We generated 21 types of problems by changing the size of demand (three types) and the length of planning horizon (seven types). Demand sizes are determined by the proportion of production capacity, that is, the order quantity of 10%, 20%, and 30% of production capacity, and the planning horizons are in the range of 4 to 10 planning periods, that is, total 6 types of planning horizon. For each type of problem, ten problems are generated using random number generator and total 210 problems were finally tested. Figure
Computation time (sec) according to the length of planning horizon and demand quantity.
The investigation indicates that the computation time for solving the mathematical model increases in highly nonlinear fashion as the length of planning horizon increases, but there seems to be no strong relationship with demand pattern. Based on the experiments, in order to overcome the problem with the long planning horizon in real production environment, we consider decomposing the original problem into the smaller size of subproblems with shorter planning horizon and then aggregating them back to get the final solution. Figure
Generation of subproblems using rolling horizon technique.
This procedure is known to be rolling horizon planning technique which was firstly proposed by Modigliani and Hohn [
Based on the concept described before, our heuristic consists of three steps: (1) adjusting setup cost, (2) solving subproblems, and (3) aggregation of solutions. Figure
Procedure of heuristic.
Setup costs for each subproblem are adjusted as follows.
Set a fixed planning horizon of subproblem, such as
Inventory holding cost of subassembly (
New inventory cost (
Then, new setup cost (
Case 1: If
Case 2: If
Case 3: If
Using adjusted setup cost, each subproblem with planning horizon
Then the model (
Set iteration,
The demand quantity for the
Solve the problem
The inventory at the first period of
Set
Aggregation of subproblem solutions is simple. All the solutions are represented as the cost parameters of the original problem, but decision variables are replaced with the aggregated solution of subproblems as follows:
The heuristic is programmed with pseudocode as shown in Pseudocode
For
For
}
Solving
}
}
Solving
}
In the pseudocode,
In this section, the efficiency of our heuristic is investigated through computational experiments with the ballpen example in Figure
Unit holding cost
Subassembly  ABCDEF  ABCDE  ABCDF  ABCD  ABF  BCD  AB  AE  CD  A  B  C  D  E  F 


0  9  8  6  6  8  5  6  5  4  4  2  1  1  1 
Operation  1  2  3  4  5  6  7  8  9  10  11  12  13 


50  40  30  20  10  50  40  30  20  10  50  40  30 
Unit processing cost of operations

1  2  3  4  5  6  7  8  9  10  11  12  13 

A  5  4  3  2  1  5  4  3  2  1  5  4  3 
B  20  16  12  8  4  20  16  12  8  4  20  16  12 
Unit purchase cost of subassemblies

ABCDEF  ABCDE  ABCDF  ABCD  ABF  BCD  AB  AE  CD  A  B  C  D  E  F 

A  0  58  56  52  46  44  42  40  38  34  32  30  28  26  24 
B  0  174  168  156  138  132  126  120  114  102  96  90  84  78  72 
Production rate
Operation  1  2  3  4  5  6  7  8  9  10  11  12  13  

V 

50  25  100  25  75  50  25  20  25  10  50  100  25 
V 

0.15  0.05  0.10  0.20  0.15  0.05  0.15  0.05  0.01  0.05  0.10  0.15  0.15 
W 

40  25  25  40  60  70  45  40  100  90  55  70  65 
W 

0.20  0.15  0.10  0.20  0.10  0.20  0.05  0.20  0.15  0.15  0.20  0.05  0.05 
All experiments were implemented using OPL Studio 6.0 by ILOG on the Pentium 4 2.8 Ghz WinXP platform. For efficiency of experiments, we limited the run time at 5,400 seconds and over the limit the best value was taken. We considered three different planning horizons of 10, 15, and 20 periods. Demand data were generated according to the ordering probability of 10, 20, and 30%. For each ordering probability, two sets of data were generated. Therefore, 18 experiments (=6 types of demand * 3 planning horizons) were performed for each cost structure (AV, AW, BV, and BW). The results are shown in Table
Performance results of heuristic.
Cost structure  Number of optimal solution  Avgerage computation time (sec)  Deviation from OPL solution  

OPL  Heuristic 



Average optimal  Average total 


Optimal  All  Optimal  All  
A, V  7  1183.9  Over 6983.1  57.8  156.6  0.96%  3.32%  0.74%  2.45% 
A, W  6  675.1  Over 7223.9  107.5  252.8  3.00%  2.09%  3.04%  1.73% 
B, V  7  916.5  Over 23246.9  95.2  376.7  2.30%  4.39%  1.44%  3.25% 
B, W  10  20653  Over 27045  185.9  820.7  1.14%  1.97%  0.87%  1.43% 
From the results, we observe that the proposed heuristic finds a solution with very short computation time and the quality of solution is also quite good with less than 5% deviation from the optimal solution. We also find many cases where as the planning horizons increase the accuracy of solution is deteriorated. In order to improve it, one method is to make the subproblems with the longer planning horizon (
Average objective function costs by OPL and heuristic.
MIP  





 
A, V  5658.4  6842.5  6645.8  4451.1  23597.8 
A, W  5450.5  6214.0  7387.1  4702.6  23754.2 
B, V  32158.1  6915.5  13451.7  6877.4  59402.7 
B, W  34654.5  5677.2  13542.4  6150.3  60024.4 







 
A, V  7726.2  4102.4  6699.3  5120.8  23648.7 
A, W  9451.2  4412.3  5673.1  4672.4  24208.9 
B, V  34248.6  5052.0  17536.1  4765.6  61602.4 
B, W  35975.2  5735.0  14196.5  5471.9  61378.5 







 
A, V  6314.5  6712.9  6513.1  4731.3  24271.8 
A, W  5578.0  6325.3  7392.2  4825.8  24121.3 
B, V  32574.5  6937.8  14782.9  6925.6  61220.9 
B, W  35112.1  5752.3  13945.9  6184.2  60994.5 
In summary of experiments, our heuristic is quite good enough to be used in real disassembly planning system because of the high quality of solution and efficient computation time.
Disassembly planning determines the sequence and schedule of disassembly operations to meet demand of disassembled subassemblies in remanufacturing environment. Unlike assembly planning, it is much more complicated due to reverse sequence generation and demand of inprocess subassemblies. However, most previous researches have certain limits in applying to multiperiods disassembly planning with demand.
In this study, we formulated disassembly planning problem over multiperiods planning horizon with demands of subassemblies. Since the problem is known to be NPhard, it requires tremendous computational time for reasonable size of problems in real production environments. For practical solution methods, we developed a heuristic based on rolling horizon planning technique which is useful in decomposing the large size problem and solving the subproblems efficiently. The heuristics has been investigated through computational experiments on a set of data reflecting various disassembly planning environments. The results show that our heuristic can be a good alternative method applicable to real production system in terms of computational efficiency and the quality of solution.
Remanufacturing system is still open area to be investigated and improved, especially for identifying many practical issues regarding sustainable environment. We need to continuously find those issues and provide good methods. Specifically, the concept behind the proposed heuristic in this study can be applied to many planning problems found in remanufacturing system in order to improve the planning efficiency.
Subassembly
Disassembly operation
The length of planning horizon,
Order quantity of subassembly
Processing cost of operation
Unit holding cost of subassembly
Setup cost of operation
Unit purchase cost of subassembly
Production rate of operation
−1 if subassembly
1 if subassembly
The number of subassembly
Setup time for operation
Available work time at period
Processing time of operation
1 if operation
1 if there is a setup for operation
Inventory of subassembly
The number of purchased subassembly
1 if operation
1 if operation
1 if there is no operation to be performed in period
1 if there is more than one operation to be performed in period
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MEST) (no. 20090085893).