This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstream partners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance. To solve this reverse supply chain design problem, an optimal cross-stage reverse logistics mathematical model was developed. In addition, we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms: the inertia weight method (PSOA_IWM),
Intense competition within the global market has prompted enterprise competition to change from a competition among companies to that among supply chains. In addition to reducing operating costs and improving competitiveness, effectively integrating the upstream and downstream suppliers and manufacturers of a supply chain can reflect market changes and meet consumer needs efficiently.
Previous studies on the design problems of supply networks include [
Cohen [
Based on literature review, reverse logistics includes management functions related to returned products, depot repair, rework, material reprocessing, material recycling, and disposal of waste and hazardous materials. These allow products to be returned upstream for processing in a reverse logistics system; thus, the circulation of an integral supply chain can be implemented. The reverse logistics flow of products is shown in Figure
The reverse logistics flow of the products (Gattorna [
Many scholars have defined reverse logistics briefly and clearly [
In addition, Savaskan et al. [
Reverse logistics is more complex than forward logistics, and this study aimed to develop a mathematical foundation for modeling a cross-stage reverse logistics plan that enables defective products with differing degrees of damage to be returned to upstream partners in the stages of a supply chain for maintenance, replacement, or restructuring. This cross-stage reverse logistics model can help save time, lessen unnecessary deliveries, and, more importantly, meet the conditions of reverse logistics operation more efficiently.
Recently, GAs have been regarded as a novel approach to solving complex, large-scale, and real-world optimization problems [
In addition, Dong et al. [
The remainder of this paper is structured as follows. Section
Reverse logistics activities include recycling, rework, replacement, and waste disposal; however, the reverse logistics activity of each function differs. Therefore, this study designed a forward and reverse cross-stage logistics system for maintaining, reassembling, and packaging recycled defective products. The structure is shown in Figure
The transportation model of reverse logistics.
When downstream partners generate defective products, the products can be returned directly to upstream supply chain partners for maintenance to restore product function and value, based on the degree of damage. Therefore, this study supposed that, when defective products are generated, they can be divided into N parts according to the average volume of defective products generated by a particular supplier. Downstream partners can then return defective products, based on the divided quantity, to upstream partners for maintenance. For example, when the first partner of the fourth stage generates defective products, the total defective amount is divided into three parts and then sent to the first, second, and third stage partners separately in the supply chain, thereby reducing general reverse logistics costs and transportation time.
For supply chain partner selection, this study considered productivity restrictions, transportation costs, manufacturing costs, transportation time, manufacturing quality, and other parameters. The
To satisfy the conditions of the actual production situation, this study used transportation losses and manufacturing losses to construct an unbalanced supply chain network. In considering the characteristics of all the suppliers addressed in this study, we developed a cross-stage reverse logistics course planning system for single-product and multiperiod programming.
We programmed the reverse logistics for recycled defective products, which were returned directly to the upstream supply chain partners for maintenance, reassembly, and repackaging through the cross-stage reverse logistics course programming based on the degree and nature of the damage. For selecting supply chain partners, this study considered the manufacturing characteristics (transportation costs, production costs, upper and lower limit of productivity, manufacturer’s defective product rate, transportation losses rate, and manufacturing quality) to construct the reverse logistics programming model. Based on these data, optimal manufacturing quality with minimal production cost, transportation cost, and transportation time can be determined.
In considering the different evaluation criteria, this study
The structure of this study.
The optimal mathematical model of cross-stage reverse logistics was developed as described in the following steps. The definitions of notations used in this model are listed as follows.
Notations for developing the optimal mathematical model:
Serial number of supplier
Production period
Stages of the supply chain network,
Total number of suppliers
Total production periods
Total stages of supply chain network
Customer requirement of supplier
Minimal starting up productivity of supplier
Maximal starting up productivity of supplier
Manufacturing cost of supplier
Product quality of supplier
Transportation cost from supplier
Transportation time from supplier
Average manufacturing cost of supplier
Average product quality of supplier
Average transportation cost from supplier
Average transportation time from supplier
Manufacturing cost of supplier
Product quality of supplier
Transportation cost from supplier
Transportation time from supplier
Manufacturing cost standard deviation of supplier
Transportation cost standard deviation of supplier
Product quality standard deviation of supplier
Transportation time standard deviation of supplier
Defective product rates of supplier
Transportation loss rate from supplier
Weights of manufacturing cost, transportation cost, transportation time, and product quality
Integer function for obtaining the integer value of the real number by eliminating its decimal.
Transportation quantity from supplier
Defective products quantity from supplier
Notations for developing the update models for the position and velocity of each particle:
Learning factors
Constriction factor
Random numbers between 0 and 1
New position of particle
Original velocity of particle
New velocity of particle
The set maximal velocity
Inertia weight
Totaling of cognition parameter and social parameter, which must exceed 4.
Notations for performing hypotheses on the objective function value, convergence time, and completion time among four proposed approaches:
Convergence time of GA
Convergence time of PSOA_IWM
Convergence time of PSOA_VMM
Convergence time of PSOA_CFM
Completion time of GA
Completion time of PSOA_IWM
Completion time of PSOA_VMM
Completion time of PSOA_CFM
Objective function value of GA
Objective function value of PSOA_IWM
Objective function value of PSOA_VMM
Objective function value of PSOA_CFM.
Acquire the minimization of manufacturing costs, transportation costs, and transportation time, as well as the maximization of the manufacturing quality of the different suppliers, at various stages of forward and reverse logistics.
Manufacturing cost for forward logistics:
The detailed procedures of a GA-solving model are described as follows.
The encoding of this study was performed according to the cross-stage reverse logistics problem including forward and reverse transportation routes; therefore, one route is one encoding value. The scope is randomly generated based on the demands and (
Chromosome structure.
Substitute all the generated encoding values in the objective function equation (
This study adopted the roulette wheel selection proposed by Goldberg [
The crossover of this study involves using the single-point crossover method. Randomly select two chromosomes from the parent body for crossover, and generate one crossover point, then exchange the genes of the chromosome. The crossover course is shown in Figure
Crossover process.
The mutation of this study also adopts a single-point mutation method and treats the delivery route of one supplier as a “single-point” of value. The mutation method is shown in Figure
Mutation process.
The new filial generation was generated through the gene evolution of Steps
This study sets the iteration times as the termination condition for gene evolution.
The detailed procedures involved in PSO-solving models are described as follows.
Set the relative coefficients as particle population, velocity, weight, and iteration times; then all forward and reverse transportation routes are viewed as one particle based on the supply chain structure. The forward and reverse particle swarm encodings are shown in Figures
Particle swarm encoding for forward logistics.
Particle swarm encoding for reverse logistics.
The forward transportation volume produces the parental generation solution, adopting demand, transportation loss, manufacturer’s defective products, and (
All particles received by the initial solutions of objective function equation (
The target value of each particle generated in Step
Modify the
For the renewal portion of this study, the inertia weight method (PSOA_IWM) proposed by Eberhart and Shi [
(1) PSOA_IWM (Eberhart and Shi [
(2) PSOA_VMM (Eberhart and Kennedy [
When the particle velocity was too extreme, it could be guided to the normal velocity vector.
(3) PSOA_CFM (Clerc [
After the velocity and position of the particles are updated, they must be verified to determine whether they met (
Steps
This section presents an illustrative example involving a semiconductor supply chain network to demonstrate the effectiveness of the proposed approaches. A typical semiconductor supply chain network is shown in Figure
Typical supply chain network for semiconductor.
This case programmed one unbalanced supply chain network structure, including forward and reverse logistics, so that downstream suppliers or retailers can return defective products directly to upstream supply chain partners. The manufacturer can restore a broken product’s function, depending on the damage, so that the product’s purpose is recovered. This case addressed forward and reverse logistics partner selection and quantity delivery problems using a {3-4-5-6} network structure. It also programmed a three-period customer requirement list for a single product. This case supposed that the initial inventory of the first period was zero, transportation losses were considered waste and cannot be reproduced, and different reverse logistics for defective products of different damage levels were programmed. For example, when 10 defective products were generated by the first supplier of the fourth stage, this study assumes that 30% were returned to the third stage, 30% were returned to the second stage, and the rest were returned to the first stage. Therefore, the reverse logistics of this study would generate a cross-stage reverse delivery status.
This study considered the productivity restrictions, manufacturing costs, delivery costs, manufacturing quality, and transportation time for all suppliers in selecting supply chain partners. This study also considered the manufacturer’s defective product rate and the transportation loss rate of suppliers to form a so-called “unbalanced” supply chain network. The details of all of the suppliers are shown in Figure
Data of transportation cost and defect rate.
Transportation line | 1.1–2.1 | 1.1–2.2 | 1.1–2.3 | 1.1–2.4 | 1.2–2.1 | 1.2–2.2 | 1.2–2.3 | 1.2–2.4 | 1.3–2.1 | 1.3–2.2 | 1.3–2.3 | 1.3–2.4 | 2.1–3.1 | 2.1–3.2 | 2.1–3.3 | 2.1–3.4 |
Transportation defect rate | 0.01 | 0.03 | 0.02 | 0.02 | 0.02 | 0.01 | 0.04 | 0.05 | 0.04 | 0.03 | 0.05 | 0.01 | 0.03 | 0.02 | 0.01 | 0.04 |
Transportation cost | 5 | 6 | 10 | 3 | 7 | 5 | 6 | 4 | 4 | 3 | 5 | 10 | 4 | 5 | 3 | 4 |
Transportation line | 2.1–3.5 | 2.2–3.1 | 2.2–3.2 | 2.2–3.3 | 2.2–3.4 | 2.2–3.5 | 2.3–3.1 | 2.3–3.2 | 2.3–3.3 | 2.3–3.4 | 2.3–3.5 | 2.4–3.1 | 2.4–3.2 | 2.4–3.3 | 2.4–3.4 | 2.4–3.5 |
Transportation defect rate | 0.02 | 0.02 | 0.03 | 0.04 | 0.02 | 0.05 | 0.03 | 0.04 | 0.02 | 0.03 | 0.01 | 0.03 | 0.04 | 0.02 | 0.01 | 0.02 |
Transportation cost | 5 | 4 | 5 | 6 | 2 | 2 | 5 | 8 | 5 | 4 | 6 | 5 | 6 | 5 | 4 | 5 |
Transportation line | 3.1–4.1 | 3.1–4.2 | 3.1–4.3 | 3.1–4.4 | 3.1–4.5 | 3.1–4.6 | 3.2–4.1 | 3.2–4.2 | 3.2–4.3 | 3.2–4.4 | 3.2–4.5 | 3.2–4.6 | 3.3–4.1 | 3.3–4.2 | 3.3–4.3 | 3.3–4.4 |
Transportation defect rate | 0.03 | 0.02 | 0.01 | 0.02 | 0.01 | 0.03 | 0.02 | 0.03 | 0.01 | 0.04 | 0.02 | 0.03 | 0.02 | 0.03 | 0.04 | 0.05 |
Transportation cost | 4 | 5 | 4 | 6 | 4 | 6 | 4 | 6 | 3 | 5 | 4 | 5 | 5 | 6 | 4 | 8 |
Transportation line | 3.3–4.5 | 3.3–4.6 | 3.4–4.1 | 3.4–4.2 | 3.4–4.3 | 3.4–4.4 | 3.4–4.5 | 3.4–4.6 | 3.5–4.1 | 3.5–4.2 | 3.5–4.3 | 3.5–4.4 | 3.5–4.5 | 3.5–4.6 | ||
Transportation defect rate | 0.02 | 0.01 | 0.02 | 0.03 | 0.05 | 0.04 | 0.02 | 0.03 | 0.03 | 0.02 | 0.03 | 0.04 | 0.05 | 0.03 | ||
Transportation cost | 6 | 5 | 4 | 4 | 6 | 5 | 5 | 6 | 2 | 5 | 6 | 5 | 4 | 2 |
{3-4-5-6} forward and reverse supply chain network.
This study used GA, PSOA_IWM, PSOA_CFM, and PSOA_VMM both to solve the problem of the optimal mathematical model of cross-stage reverse logistics constructed by this study and to determine the optimal parameter values. We used the experimental design to determine the optimal parameter values, and the parameters of the GA used in this study refer to the proposal of Eiben et al. [
Experimental design results of GA with different groups of parameters.
GA | ||||||
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Generation | Population | Mutation rate | Crossover rate | Convergence time (S) | Execution time (S) | Objective function value |
1000 | 10 | 0.02 | 0.6 | 45.65 | 65.22 | 585845.5 |
0.95 | 36.91 | 52.72 | 586401.9 | |||
0.05 | 0.6 | 58.88 | 84.12 | 582052.4 | ||
0.95 | 60.12 | 85.88 | 585355.2 | |||
20 | 0.02 | 0.6 | 99.07 | 141.53 | 585731.7 | |
0.95 | 58.49 | 83.57 | 579156.2 | |||
0.05 | 0.6 | 111.26 | 158.94 | 578879.4 | ||
0.95 | 94.15 | 134.51 | 578760.4 | |||
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2000 | 10 | 0.02 | 0.6 | 59.42 | 112.12 | 583037.4 |
0.95 | 51.87 | 97.88 | 587388.3 | |||
0.05 | 0.6 | 90.85 | 171.42 | 576988.8 | ||
0.95 | 89.87 | 169.58 | 580298.8 | |||
20 | 0.02 | 0.6 | 88.23 | 166.49 | 576920.3 | |
0.95 | 72.51 | 136.81 | 579347.1 | |||
0.05 | 0.6 | 155.42 | 293.72 | 575504.7 | ||
0.95 | 133.79 | 252.45 | 576902.9 |
For the PSO, this study used PSOA_IWM, PSOA_CFM, and PSOA_VMM to solve the problems. PSOA_IWM was suggested by Eberhart and Shi [
Experimental design results of PSOA_IWM with different groups of parameters.
PSOA_IWM | ||||||
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Generation | Particle | Velocity | Weight | Convergence time (S) | Execution time (S) | Objective function value |
1000 | 10 | 20 | 0.4 | 1.17 | 2.49 | 581660.2 |
0.9 | 1.26 | 2.69 | 585355.5 | |||
50 | 0.4 | 2.28 | 4.86 | 588147.3 | ||
0.9 | 2.94 | 5.62 | 593565.2 | |||
20 | 20 | 0.4 | 3.45 | 5.21 | 593858.8 | |
0.9 | 2.71 | 5.77 | 582468.5 | |||
50 | 0.4 | 5.76 | 10.12 | 581133.8 | ||
0.9 | 6.17 | 11.21 | 589921.1 | |||
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2000 | 10 | 20 | 0.4 | 2.96 | 4.89 | 612950.3 |
0.9 | 2.38 | 5.21 | 581756.6 | |||
50 | 0.4 | 4.69 | 9.24 | 584003.4 | ||
0.9 | 5.10 | 10.26 | 585192.6 | |||
20 | 20 | 0.4 | 4.73 | 9.31 | 591258.4 | |
0.9 | 5.02 | 10.06 | 580391.2 | |||
50 | 0.4 | 7.56 | 18.88 | 573972.1 | ||
0.9 | 11.94 | 22.34 | 580979.8 |
Experimental design results of PSOA_CFM with different groups of parameters.
PSOA_CFM | ||||||
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Generation | Particle | Velocity |
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Convergence time (S) | Execution time (S) | Objective function value |
1000 | 10 | 20 | 2.05, 2.05 | 2.77 | 3.76 | 596860.2 |
2.8, 1.3 | 1.84 | 3.92 | 580909.7 | |||
50 | 2.05, 2.05 | 4.85 | 8.18 | 591679.5 | ||
2.8, 1.3 | 4.14 | 7.95 | 575782.2 | |||
20 | 20 | 2.05, 2.05 | 3.37 | 5.05 | 604557 | |
2.8, 1.3 | 4.43 | 7.29 | 588076.4 | |||
50 | 2.05, 2.05 | 9.01 | 19.16 | 598957.1 | ||
2.8, 1.3 | 8.54 | 15.41 | 583530.4 | |||
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2000 | 10 | 20 | 2.05, 2.05 | 6.45 | 9.08 | 579670.6 |
2.8, 1.3 | 6.20 | 8.68 | 574969.5 | |||
50 | 2.05, 2.05 | 11.53 | 19.22 | 601022.2 | ||
2.8, 1.3 | 9.86 | 16.44 | 583479.2 | |||
20 | 20 | 2.05, 2.05 | 8.34 | 15.57 | 594554.6 | |
2.8, 1.3 | 9.91 | 16.53 | 579629.1 | |||
50 | 2.05, 2.05 | 22.64 | 37.74 | 605729.6 | ||
2.8, 1.3 | 18.84 | 31.40 | 574033.9 |
Experimental design results of PSOA_VMM with different groups of parameters.
PSOA_VMM | |||||
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Generation | Particle | Velocity | Convergence time (S) | Execution time (S) | Objective function value |
1000 | 10 | 20 | 1.97 | 2.95 | 620767.6 |
50 | 3.89 | 5.81 | 626354.4 | ||
20 | 20 | 3.91 | 5.83 | 621080.6 | |
50 | 8.74 | 13.04 | 616409.3 | ||
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2000 | 10 | 20 | 3.53 | 5.21 | 617751.6 |
50 | 7.27 | 12.12 | 614025.9 | ||
20 | 20 | 7.13 | 10.05 | 614276.1 | |
50 | 14.45 | 24.09 | 609603.7 |
For the hardware configuration of this experiment, the CPU was P4-3.0 GHz and the RAM DDR was 512 MB. This study used ANOVA and Scheffé to verify system operation times and convergence times and to select the indices for the GA and the three renovation methods. The Scheffé method was first promoted by Scheffé [
ANOVA verification of objective function.
Algorithm | Total | Average | Variance |
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GA | 17244286.9 | 574809.5 | 32263393.4 |
PSOA_IWM | 17206940.5 | 573564.6 | 25588275.7 |
PSOA_VMM | 18113738.4 | 603791.2 | 106679602.3 |
PSOA_CFM | 17252708.0 | 575090.2 | 157150309.7 |
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Hypothesis: |
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ANOVA verification of completion time.
Algorithm | Total | Average | Variance |
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GA | 9207.5 | 306.9 | 3999.0 |
PSOA_IWM | 567.3 | 18.9 | 8.3 |
PSOA_VMM | 608.7 | 20.2 | 12.5 |
PSOA_CFM | 661.2 | 22.0 | 15.5 |
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Hypothesis: |
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ANOVA verification of convergence time.
Algorithm | Total | Average | Variance |
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GA | 4662.6 | 155.4 | 96.7 |
PSO_IWM | 226.9 | 7.5 | 3.2 |
PSO_VMM | 433.2 | 14.4 | 10.1 |
PSO_CFM | 567.2 | 18.9 | 12.0 |
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Hypothesis: |
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Tables
Table
Multiple comparison on objective function.
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(−, +) | ||
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(−, −) | (−, −) | |
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(+, −) | (−, +) | (+, +) |
Multiple comparison on execution time.
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(+, +) | ||
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(+, +) | (−, +) | |
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(+, +) | (−, +) | (−, +) |
Multiple comparison on convergence time.
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(+, +) | ||
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(+, +) | (−, −) | |
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(+, +) | (−, −) | (−, −) |
For validating the solving capabilities of the proposed approaches in cross-stage reverse logistics problems, more large-scope network structures {6-6-6-6}, {6-6-6-6-6}, {3-10-10-60}, {6-8-8-10-30}, and {8-10-20-20-60} were demonstrated. The analysis results also show that PSOA_IWM has better capabilities for the proposed problems, as shown in Table
Analysis results on different network structures.
Network | GA | PSOA_IWM | PSOA_CFM | PSOA_VMM | |
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Objective function | 3-4-5-6 | 574809.5a/1b | 573564.6/1 | 575096.2/1 | 603791.2/2 |
6-6-6-6 | 644482.1/2 | 642426.8/1 | 650475.1/3 | 725523.7/4 | |
3-10-10-60 | 972412.2/2 | 954457.3/1 | 980211.5/3 | 1022415.6/4 | |
6-6-6-6-6 | 760460.1/2 | 758655.5/1 | 761552.1/3 | 823544.4/4 | |
6-8-8-10-30 | 1201225.3/2 | 1153252.1/1 | 1242273.4/3 | 1345758.7/4 | |
8-10-20-20-60 | 1685442.3/2 | 1637241.6/1 | 1711412.5/3 | 1811279.4/4 | |
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Execution time | 3-4-5-6 | 306.9/2 | 18.9/1 | 22.0/1 | 20.2/1 |
6-6-6-6 | 326.4/2 | 41.8/1 | 42.4/1 | 39.0/1 | |
3-10-10-60 | 621.4/4 | 74.5/3 | 65.8/2 | 61.3/1 | |
6-6-6-6-6 | 533.1/3 | 61.0/2 | 51.3/1 | 48.4/1 | |
6-8-8-10-30 | 782.6/4 | 112.5/3 | 92.1/2 | 85.2/1 | |
8-10-20-20-60 | 997.8/4 | 187.4/3 | 138.5/2 | 102.7/1 | |
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Convergence time | 3-4-5-6 | 155.4/4 | 7.5/1 | 18.9/3 | 14.4/2 |
6-6-6-6 | 196.6/2 | 18.6/1 | 22.7/1 | 22.6/1 | |
3-10-10-60 | 415.3/3 | 28.7/1 | 30.2/2 | 31.2/2 | |
6-6-6-6-6 | 302.9/3 | 23.6/1 | 26.5/2 | 27.2/2 | |
6-8-8-10-30 | 557.4/3 | 35.2/1 | 40.7/2 | 42.5/2 | |
8-10-20-20-60 | 632.5/4 | 39.8/1 | 44.2/2 | 48.6/3 |
Tables
The first period transportation plan by PSOA_IWM.
From | To | Stage 1 | Stage 2 | Stage 3 | Stage 4 | ||||||||||||||
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1.1 | 1.2 | 1.3 | 2.1 | 2.2 | 2.3 | 2.4 | 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 | ||
Stage 1 | 1.1 | 0 | 0 | 0 | 34 | ||||||||||||||
1.2 | 5 | 646 | 17 | 0 | |||||||||||||||
1.3 | 1615 | 154 | 6 | 15 | |||||||||||||||
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Stage 2 | 2.1 | 379 | 392 | 190 | 237 | 327 | |||||||||||||
2.2 | 38 | 0 | 8 | 261 | 459 | ||||||||||||||
2.3 | 0 | 10 | 10 | 0 | 2 | ||||||||||||||
2.4 | 0 | 0 | 48 | 0 | 0 | ||||||||||||||
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Stage 3 | 3.1 | 6 | 28 | 194 | 163 | 1 | 5 | ||||||||||||
3.2 | 0 | 9 | 114 | 13 | 146 | 100 | |||||||||||||
3.3 | 0 | 0 | 0 | 27 | 168 | 56 | |||||||||||||
3.4 | 126 | 61 | 1 | 154 | 0 | 137 | |||||||||||||
3.5 | 291 | 366 | 0 | 8 | 0 | 72 | |||||||||||||
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Demand | 400 | 450 | 300 | 350 | 300 | 350 |
The second period transportation plan by PSOA_IWM.
From | To | Stage 1 | Stage 2 | Stage 3 | Stage 4 | ||||||||||||||
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1.1 | 1.2 | 1.3 | 2.1 | 2.2 | 2.3 | 2.4 | 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 | ||
Stage 1 | 1.1 | 29 | 142 | 72 | 158 | ||||||||||||||
1.2 | 120 | 43 | 150 | 24 | |||||||||||||||
1.3 | 576 | 845 | 194 | 128 | |||||||||||||||
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Stage 2 | 2.1 |
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177 | 115 | 148 | 90 | 164 | ||||||||||
2.2 |
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189 | 139 | 51 | 183 | 421 | |||||||||||
2.3 |
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104 | 78 | 130 | 74 | 12 | |||||||||||
2.4 |
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136 | 30 | 15 | 91 | 37 | |||||||||||
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Stage 3 | 3.1 |
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67 | 95 | 130 | 69 | 126 | 95 | |||||
3.2 |
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41 | 54 | 111 | 106 | 27 | 5 | ||||||
3.3 |
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3.4 |
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3.5 |
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162 | 165 | 131 | 24 | 92 | 25 | ||||||
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Stage 4 | 4.1 |
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Demand | 300 | 350 | 450 | 400 | 430 | 250 |
Bold data are the reverse transportation volumes.
The third period transportation plan by PSOA_IWM.
From | To | Stage 1 | Stage 2 | Stage 3 | Stage 4 | ||||||||||||||
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1.1 | 1.2 | 1.3 | 2.1 | 2.2 | 2.3 | 2.4 | 3.1 | 3.2 | 3.3 | 3.4 | 3.5 | 4.1 | 4.2 | 4.3 | 4.4 | 4.5 | 4.6 | ||
Stage 1 | 1.1 | 227 | 24 | 48 | 73 | ||||||||||||||
1.2 | 17 | 47 | 0 | 65 | |||||||||||||||
1.3 | 900 | 738 | 84 | 37 | |||||||||||||||
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Stage 2 | 2.1 |
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133 | 156 | 180 | 239 | 383 | ||||||||||
2.2 |
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172 | 121 | 144 | 234 | 96 | |||||||||||
2.3 |
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45 | 0 | 66 | 27 | 0 | |||||||||||
2.4 |
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3 | 0 | 73 | 33 | 71 | |||||||||||
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Stage 3 | 3.1 |
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0 | 4 | 129 | 11 | 134 | 64 | |||||
3.2 |
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4 | 3 | 100 | 53 | 57 | 49 | ||||||
3.3 |
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0 | 81 | 75 | 50 | 139 | 107 | ||||||
3.4 |
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80 | 50 | 49 | 174 | 36 | 125 | ||||||
3.5 |
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180 | 172 | 64 | 27 | 0 | 77 | ||||||
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Stage 4 | 4.1 |
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4.5 |
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Demand | 250 | 300 | 400 | 300 | 350 | 400 |
Bold data are the reverse transportation volumes.
Enterprises should react to market changes to meet consumer demands in a timely manner to maintain and enhance competitive advantages in this rapidly changing market. The cross-stage reverse logistics course described in this study could help downstream partners return defective products to the upstream partners directly for maintaining and recovering product function, which in turn could reduce transportation costs and time. With this paper, we have accomplished three tasks. (1) We presented a mathematical model for partner selection and production-distribution planning in multistage supply chain networks with cross-stage reverse logistics. Based on our research, a mathematical model for solving multistage supply chain design problems considering the cross-stage reverse logistics has yet to be presented. However, cross-stage reverse logistics should meet the practical logistics operation conditions; therefore, (2) we applied a GA and three PSO algorithms to efficiently solve the mathematical model of cross-stage reverse logistics problems. In this paper, we emphasized the suitability of adopting a GA and three PSOs to find the solution to the mathematical model; hence, (3) we compared four proposed algorithms to find which one works best with the proposed problem. The comprehensive results show that PSOA_IWM has the qualities and capabilities for dealing with a multistage supply chain design problem with cross-stage reverse logistics. Further research should be conducted to employ other heuristic algorithms such as ant colony and simulated annealing for solving this problem. Consideration should also be given to extending this developed approach to encompass more complex problems such as problems involving resource constraints, transportation, and economic batches.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank Mr. K. Hsiao for supporting writing of programs and the National Science Council of Taiwan for their partial financial support (Grants no. NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006). The authors would also like to acknowledge the editors and anonymous reviewers for their helpful comments and suggestions, which greatly improved the presentation of this paper.