Integrating Social Sustainability into Supply Chain Design: Optimization of a Capacitated Two-Echelon Location-Routing Problem
Abstract
:1. Introduction
2. Literature Review
2.1. Supply Chain Management
2.2. Traditional and Modern Supply Chain Management
- Processes of SCM
- Planning:
- Sourcing:
- Production:
- Delivery:
- Return:
Management Strategies
- Lean Management:
- 2.
- Total Quality Management:
- Quality of Technology:
- Quality of Humans:
- Quality of Economy:
- Quality of Processes:
2.3. Challenges of SCM
2.4. Sustainable Supply Chain Management
2.5. Social Pillar of Sustainability
Challenges Facing the Social Pillar
- Undermining of the Social Pillar
2.6. Problem Definition and Applications
2.6.1. Problem Type
2.6.2. Number of Echelons
2.6.3. Number of Objectives
2.6.4. Type of Input
2.6.5. Solution Methods and Applications
2.7. Literature Findings and Gap
3. Methodology
3.1. Research Flow
3.1.1. Problem Definition
3.1.2. Problem Description
3.1.3. Model Construction
3.1.4. Model Testing
3.1.5. Experimentation and Validation
4. Case Study
4.1. Research Flow Application
4.1.1. Problem Description: Normal Case
4.1.2. Model Construction: Normal Case
Definition of Model Assumptions
- Assumptions that are used by other authors in the literature:
- Each vehicle can, at most, be at one location at any time.
- The vehicles must start and end at the facility location.
- Each of the two vehicles is assigned to one type of destination (one for suppliers and the other for distribution centers).
- Temporary visits are made to the facility in case the vehicle assigned is fully capacitated for suppliers or empty in case of distribution centers.
- The capacity of both vehicles is equal.
- The cost of leasing/renting both vehicles is equal.
- The number of suppliers required is equal to the number of distribution centers needed.
- Assumptions that are specific to this research article:
- The break time duration for each driver.
- The break rate, in USD, per break.
- The compensation fee for proximity to a transportation hub.
- Number of employees in facility.
Definition of Model Input
- The following information is provided in the model:
- The locations of each possible facility for purchasing, the suppliers, and distribution centers for contracting are given.
- The capacity of each vehicle is given.
- The capacity of each supplier and distribution center is given.
- The distances between each location and the other are given in Euclidean distances.
- The cost of each facility location, each supplier, and distribution center available for contracting are given.
- The cost of fuel liter per kilometer is given.
- The cost of carbon emissions per kilometer is given.
- The leasing/renting cost for each vehicle is given.
- The tank capacity of both vehicles is given.
Creation of Mathematical Notation
Definition of Model Constraints
- No vehicle can be at multiple locations at the same time:
- The trucks should start and finish at the same point:
- A total of three or four suppliers are required (in case of both versions of the model):
- A total of three or four distribution centers are required (in case of both versions of the model):
- The capacity of both vehicles at any time cannot exceed the value of 30:
Definition of Model Objective
4.1.3. Problem Description: Uncertain Case
4.1.4. Model Construction: Uncertain Case
Definition of Model Assumptions
- Temporary visits are made to the main facility and secondary facilities in case the vehicle assigned is fully capacitated for suppliers or empty in case of distribution centers;
- The tank capacity of the new vehicles is the same as the old ones;
- The number of employees in the main facility is equal to the number of employees in the secondary facility;
- The compensation fee given to the employees in the main facility is the same as the one given to the employees in the secondary facility.
Definition of Model Input
- The locations of the secondary facilities to select from are given;
- The purchasing value for each facility is given;
- The fixed cost inflicted as penalties for abandoning the old vehicles’ leases is given;
- The new leasing/renting value of the new vehicles is given.
Creation of Mathematical Notation
Definition of Model Constraints
- No vehicle can be at multiple locations at the same time:
- The trucks should start and finish at the same point:
- A total of four or five suppliers are required (in case of both versions of the model):
- A total of four or five distribution centers are required (in case of both versions of the model):
- The capacity of both vehicles at any time cannot exceed the value of 40:
Definition of Model Objective
4.2. Selection of Algorithm
4.2.1. Initial Population Generation
- Normal Case: Initial Population;
- Uncertain Case: Initial Population.
4.2.2. Parents Selection
- Tournament Selection
- 2.
- Stochastic Universal Sampling (SUS) Selection
- 3.
- Elitism Selection
4.2.3. Crossover Agent Selection
- One-Point Crossover
- 2.
- Two-Point Crossover
- 3.
- Uniform Crossover.
4.2.4. Mutation Agent Selection
4.2.5. Algorithm Execution
- Normal Case
- 2.
- Uncertain Case.
4.2.6. Termination Criteria
4.2.7. Model Testing Steps
- Verification
- The chromosome is divided into two sections: the first half is for the first echelon and the second half is for the second echelon. This is performed by checking the numbering assigned for each bit, since the suppliers and distribution centers have different numberings.
- No duplication of bits; this means that the numbering of the bits that are assigned to the facilities are different from the other bits.
- The size of the chromosome is the same after crossover and mutation. This ensures that the length of the chromosome is the same after any step.
- The capacity constraint is respected; this is performed by manually calculating the capacities of the bits to make sure that they uphold the capacity constraint.
- 2.
- Validation
5. Experimentation
5.1. Normal Case
5.1.1. Parameters Setting and Calibration
5.1.2. Experimental Runs
5.2. Uncertain Case
5.2.1. Parameters Setting and Calibration: First Experiment
- Experimental Runs: First Experiment:
- Performance Metrics: First Experiment:
5.2.2. Parameters Setting and Calibration: Second Experiment
- Experimental Runs: Second Experiment:
- Performance Metrics: Second Experiment:
5.2.3. Parameters Setting and Calibration: Third Experiment
- Experimental Runs: Third Experiment:
- Performance Metrics: Third Experiment:
6. Results and Discussion
6.1. Normal Case Results
6.2. Uncertain Case Results
6.2.1. First Experimental Phase
6.2.2. Second Experimental Phase
6.2.3. Third Experimental Phase
6.3. Variable Selection Outlook
6.4. General Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
SDGs | Sustainability Development Goals |
TBL | Triple bottom line |
LRP | Location-routing problem |
VRP | Vehicle-routing problem |
B2B | Business-to-business |
B2C | Business-to-customer |
CLRP | Capacitated LRP |
2E-CLRP | Two-echelon capacitated LRP |
GA | Genetic algorithm |
SCM | Supply chain management |
TQM | Total quality management |
WBCSD | World Business Council for Sustainable Development |
WACOSS | Western Australian Council of Social Services |
OECD | Organization for Economic Cooperation and Development |
SSCs | Sustainable supply chains |
SBD | Sustainable business development |
SMEs | Small to medium enterprises |
B&C | Branch and cut algorithm |
RMSE | Root mean square error |
SUS | Stochastic universal sampling hybrid with elitism |
SUS W | Stochastic universal sampling |
TOURN | Tournament hybrid with elitism |
TOURN W | Tournament selection |
PS | Population size |
NOG | Number of generations |
NOE | Number of elites |
CO | Crossover percentage |
M | Mutation percentage |
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Mathematical Notation | Explanation |
---|---|
T | Time interval |
D | Distances traveled |
L | Location of facility |
S | Social aspects |
NS | Number of stops |
PS | Proximity factor |
NE | Number of employees in main facility |
SS | Suppliers location |
DC | Distribution center location |
TS | Transportation hub |
K | Vehicle no. 1 |
M | Vehicle no. 2 |
TC | Vehicle tank capacity |
LDC | Distance between facility location and distribution center |
LSS | Distance between facility location and supplier |
LTS | Distance between facility location and transportation hub |
SSS | Distance between one supplier and another |
DCC | Distance between one distribution center and another |
CL | Cost of purchasing a facility location |
CSS | Cost of contracting a supplier |
CDC | Cost of contracting a distribution center |
CCE | Cost of carbon emissions per kilometer |
Cost of vehicle M rental/leasing | |
Cost of vehicle K rental/leasing | |
Compensation fee for employee’s proximity to transportation hub | |
Price of liter per kilometer | |
Break time for driver | |
Break rate per USD | |
Variable is equal to 1 if vehicle M or K is located at the facility at time interval t and 0 otherwise | |
Variable is equal to 1 if vehicle K is located at the distribution center at time interval t and 0 otherwise | |
Variable is equal to 1 if vehicle M is located at the supplier at time interval t and 0 otherwise | |
Vehicle capacity during circulation between suppliers | |
Vehicle capacity during circulation between distribution centers |
Mathematical Notation | Explanation |
---|---|
LS | Location of secondary facility |
LLS | Distance between main facility and secondary facility |
LSDC | Distance between secondary facility and distribution center |
LSSS | Distance between secondary facility and supplier |
CLS | Cost of purchasing secondary facility |
LSTS | Distance between secondary facility and transportation hub |
New Cost of vehicle M rental/leasing | |
New Cost of vehicle K rental/leasing | |
Penalty for abandoning vehicle K rental/leasing | |
Penalty for abandoning vehicle M rental/leasing | |
Variable is equal to 1 if vehicle M or K is located at the secondary facility at time interval t and 0 otherwise. |
Constant Variables | Constant Values |
---|---|
Number of parents | 5 |
Mutation probability | 0.05 |
Number of elites (hybrid) | 1 |
Trial Number | Combination of Variables |
---|---|
Trial 1 | One-point–90–10% |
Trial 2 | Two-point–90–10% |
Trial 3 | Uniform–90–10% |
Trial 4 | One-point–80–20% |
Trial 5 | Two-point–80–20% |
Trial 6 | Uniform–80–20% |
Trial 7 | One-point–70–30% |
Trial 8 | Two-point–70–30% |
Trial 9 | Uniform–70–30% |
Population Size/Number of Generations | |
---|---|
300 at 300% | 600 at 125% |
9663.771 $ | 9719.086 $ |
600 at 300% | 1000 at 125% |
9412.102 $ | 9583.444 $ |
1000 at 300% | 3000 at 125% |
9381.037 $ | 9495.474 $ |
Population Size/Number of Generations | |
---|---|
300 at 300% | 600 at 125% |
9530.91 $ | 9768.953 $ |
600 at 300% | 1000 at 125% |
9405.056 $ | 9602.299 $ |
1000 at 300% | 3000 at 125% |
9340.663 $ | 9281.44 $ |
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Share and Cite
Nafea, M.; Shihata, L.A.; Mashaly, M. Integrating Social Sustainability into Supply Chain Design: Optimization of a Capacitated Two-Echelon Location-Routing Problem. Technologies 2025, 13, 149. https://doi.org/10.3390/technologies13040149
Nafea M, Shihata LA, Mashaly M. Integrating Social Sustainability into Supply Chain Design: Optimization of a Capacitated Two-Echelon Location-Routing Problem. Technologies. 2025; 13(4):149. https://doi.org/10.3390/technologies13040149
Chicago/Turabian StyleNafea, Mohamed, Lamia A. Shihata, and Maggie Mashaly. 2025. "Integrating Social Sustainability into Supply Chain Design: Optimization of a Capacitated Two-Echelon Location-Routing Problem" Technologies 13, no. 4: 149. https://doi.org/10.3390/technologies13040149
APA StyleNafea, M., Shihata, L. A., & Mashaly, M. (2025). Integrating Social Sustainability into Supply Chain Design: Optimization of a Capacitated Two-Echelon Location-Routing Problem. Technologies, 13(4), 149. https://doi.org/10.3390/technologies13040149