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Optimizing Shanghai's Household Waste Recycling Collection Program by Decision-Making based on Mathematical Modeling

This paper optimizes Shanghai's household waste recycling collection program by applying the Analytical Hierarchy Process (AHP) to evaluate and select the best alternatives based on a comprehensive multi-criteria framework that balances economic, environmental, and logistical factors.

Original authors: Jiaxuan Chen, Ling Zhou Shen, Jinchen Liu

Published 2026-02-02

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Jiaxuan Chen, Ling Zhou Shen, Jinchen Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the mayor of a busy city like Shanghai, and you have a giant, overflowing trash can. You can't clean up everything at once because your garbage trucks have limited space, your budget is tight, and your workers have limited time. You need to decide: Which types of trash should we pick up and recycle first?

This paper is like a sophisticated "decision-making recipe" created by three high school students to solve that exact problem. They didn't just guess; they built a mathematical model to score different types of trash and see which ones give the city the most "bang for its buck."

Here is how they did it, broken down into simple steps:

1. The Two Scales: Benefits vs. Costs

The students realized that recycling isn't just about saving money. It's a balancing act between two giant scales:

The Benefit Scale (The Good Stuff): How much does recycling help? This includes saving money, saving energy, protecting nature, and saving land that would otherwise be filled with trash.
The Cost Scale (The Bad Stuff): How hard is it to recycle? This includes the cost of machines, the electricity used, the time workers spend sorting it, and the pollution created during the recycling process itself.

2. The "Taste Test" (The AHP Method)

To figure out which factor is more important (e.g., is saving money more important than saving energy?), they used a method called Analytical Hierarchy Process (AHP).

Think of this like a taste test. Imagine you are a food critic trying to decide what makes a perfect sandwich. You can't just say "bread is best." You have to compare them:

"Is the bread slightly more important than the cheese?"
"Is the cheese much more important than the lettuce?"

The students asked their science teachers to do this "taste test" for recycling. They compared every factor against every other factor. A computer then took all these opinions, averaged them out, and turned them into a weighting system. This told the model exactly how much "points" each factor should get.

3. The Specific Case: Glass Bottles

First, they tested their recipe on just one item: Glass bottles.

They gathered real data: How much is glass worth? How much energy does it take to make new glass? How long does a glass bottle sit in a landfill before it rots? (Spoiler: It takes 4,000 years!)
They plugged these numbers into their model.
The Result: They got a "Benefit Score" and a "Cost Score" for glass.

4. Expanding the Menu: The General Model

Once they proved the recipe worked for glass, they expanded it to include six types of trash:

Glass (bottles/jars)
Aluminum (cans/foil)
Rigid Plastic
Paper (newspapers/magazines)
Cardboard
Steel Cans

They collected data for all of these. For example, they found out that paper rots very quickly (good for landfills, but bad for recycling urgency?), while plastic takes centuries to break down. They also checked how much pollution is created when burning plastic versus burying it.

5. The Final Scorecard

To get the final answer, they did a simple math trick:
Final Score = (Total Benefits) minus (Total Costs)

If the score is positive, recycling that item is a "win." If it's negative, the costs outweigh the benefits.

Here is what their scoreboard looked like:

Paper: The big winner! It had the highest positive score. It's cheap to recycle, saves a lot of trees, and the process isn't too expensive.
Cardboard & Plastic: Also good winners, with positive scores.
Aluminum: A small winner.
Glass & Steel: These actually had negative scores. Why? Because while recycling them is good for the planet, the process is so expensive and energy-heavy (especially for glass) that, according to their specific math, it costs more than the city gains in the short term.

The Conclusion

The students concluded that if Shanghai wants to optimize its recycling program right now, it should prioritize Paper, Cardboard, and Plastic. They should perhaps rethink how they handle Glass and Steel, as the current system might be too costly for the immediate return.

In short: They built a mathematical "scorecard" that weighs the pros and cons of recycling different trash items, helping city leaders make smarter, data-driven decisions on what to pick up first.

Technical Summary: Optimizing Shanghai's Household Waste Recycling Collection Program by Decision-Making based on Mathematical Modeling

Problem Statement
The paper addresses the challenge of optimizing household waste recycling collection programs in Shanghai, a densely populated city with limited resources. The core problem is to make a data-driven decision among various recyclable waste alternatives to achieve sustainable development. The authors aim to quantify the benefits and costs of recycling different types of waste—not only in monetary terms but also regarding environmental impact and land resource conservation—to determine which waste types should be prioritized for collection.

Methodology
The study employs the Analytical Hierarchy Process (AHP), a classical multi-criteria decision-making model, utilizing the eigenvector method for weight calculation. The methodology proceeds through the following stages:

Model Construction and Assumptions:
- The authors establish six key assumptions to simplify the model, including constant landfill depth, market stability, artificial waste selection, equal non-organic cleanliness, the exclusion of paper burning, and shared resource/market conditions across China.
- A hierarchical structure is built to decompose the complex evaluation into sub-steps.
Case Study: Glass Recycling (Specific Model):
- The authors first develop specific models for glass recycling (bottles and jars) to validate the approach.
- Benefit Model: Criteria include reuse benefits (price, demand, resource limitedness, energy saved, recycling rate), avoidance of environmental damage (CO2-eq emissions from treatment and production), and avoidance of landfill costs (monetary cost, land space, decomposition duration).
- Cost Model: Criteria include economic costs (selection time, equipment cost, electricity) and environmental costs (CO2-eq and acidic gas emissions during recycling).
- Weight Determination: Pairwise comparison matrices are constructed using a 1-9 scale based on questionnaires distributed to school science teachers. The geometric mean of responses is used to form the matrix. Consistency is verified using the Consistency Ratio (CR), ensuring CR < 0.1. Normalized principal eigenvectors are calculated to derive criterion weights.
Generalization to Multiple Materials:
- The model is extended to evaluate six waste types: glass, aluminum, rigid plastic, paper, cardboard, and steel cans.
- The hierarchical structure is updated to include an "Alternatives" level and a new criterion for Acidic & Toxic Gas Emissions (At) during regular waste treatment (burning/landfilling), which is relevant for plastics but not glass.
- Data Collection: Quantitative data for all criteria (e.g., material prices, energy consumption, carbon emissions, density, decomposition time) are gathered from official statistics, market reports, and literature.
- Normalization: A min-max normalization algorithm is applied to the raw data to create a comparable scoring matrix, as the original units vary significantly.
Final Scoring and Decision:
- Benefit Scores (BS) and Cost Scores (CS) are calculated for each waste type by summing the products of normalized criterion scores and their respective AHP-derived weights.
- The Final Score (FS) is determined by the difference: $FS = BS - CS$.
- The authors also consider interdependencies (transportation space and contamination) but conclude that these are sufficiently captured by existing variables (specifically the space variable $L$ and selection time cost $S$ ), requiring no further model extension.

Key Results
The application of the model yields the following Final Scores (FS) for the six waste types, where a higher score indicates a more beneficial recycling priority:

Paper: 0.2040 (Highest Priority)
Rigid Plastic: 0.0946
Cardboard: 0.1176
Aluminum: 0.0753
Steel Cans: -0.0464
Glass: -0.1383 (Lowest Priority)

Based on these scores, the model recommends prioritizing the recycling of Paper, Cardboard, and Rigid Plastic over Glass, Aluminum, and Steel Cans in the context of Shanghai's current data and constraints.

Significance and Claims
The paper claims to demonstrate a rigorous integration of mathematical modeling with sustainability development. Its primary contributions include:

Quantification of Sustainability: Providing a structured method to convert subjective and diverse factors (economic, environmental, spatial) into a single quantified decision metric.
Applicability of AHP: Showcasing the utility of the Analytical Hierarchy Process in handling complex, multi-criteria environmental decision-making problems.
Scalability: The model is designed to be adaptable for optimizing waste recycling programs in other cities, not just Shanghai.
Logical Framework: The authors assert that their work offers a logical decision-making framework for accelerating environmental protection processes in urban waste management systems.

The authors acknowledge limitations, specifically noting that the dynamic interdependency between the quantities of different waste types and the optimization of the system as a whole is not fully modeled as a set of simultaneous differential equations, suggesting this as a potential area for future refinement.