Localisation and Circularity in Apple Supply Chains: An Algorithmic Exploration

This paper presents a weighted-sum mixed-integer linear programming model to optimize the UK apple supply chain by balancing economic and sustainability objectives—specifically price, quantity, freshness, and distance—to enhance localisation and circularity while reducing waste and emissions.

The Gist

Imagine the UK apple supply chain as a massive, chaotic potluck dinner happening every day. You have hundreds of farmers (the hosts) bringing baskets of apples, and hundreds of shops, juice makers, and restaurants (the guests) with empty plates waiting to be filled.

The problem? Apples are perishable. If they sit too long, they rot. If they travel too far, they get bruised and cost more to ship. And if the host brings 500 apples but the guest only wants 5, or if the host wants $2 a pound and the guest only has $1, the apples go to waste.

This paper by Baraa Alabdulwahab and Ruzanna Chitchyan is essentially a smart recipe book (an algorithm) designed to help the potluck run smoothly, save money, and ensure no apples are thrown away.

Here is the breakdown of their solution in simple terms:

1. The Core Problem: The "Wasteful Potluck"

In the real world, apples often get wasted because the matching process is messy.

• Too far: An apple from Scotland travels to London, burning fuel and getting old.
• Wrong price: A farmer wants a high price, but the buyer can't afford it, so the apple rots in the field.
• Wrong timing: A buyer needs fresh apples for tomorrow, but the only available ones are expiring next week (or vice versa).

The authors wanted to build a digital "matchmaker" that doesn't just look at price, but also cares about local sourcing (keeping food local) and freshness (using the oldest apples first).

2. The Solution: The "Weighted Scorecard"

The authors created a computer program that acts like a judge for every possible match between a farmer and a buyer.

Instead of just picking the cheapest deal, the program gives every potential trade a score based on four things:

1. Price: Do the buyer and seller agree on the cost?
2. Quantity: Does the basket size match the plate size? (No one wants to buy 500 apples if they only need 5).
3. Freshness: Is the apple fresh enough for the buyer's needs? (Prioritizing apples that are about to expire).
4. Distance: How far does the truck have to drive? (Shorter is better for the planet).

The Magic Knob:
The most important part of their system is that the "judge" has a knob (or weights) that can be turned.

• If you turn the knob toward "Save the Planet," the computer prioritizes short distances and fresh apples, even if it costs a bit more.
• If you turn the knob toward "Save Money," it prioritizes the best price, even if the truck has to drive further.
• If you turn it toward "Feed Everyone," it tries to fill as many plates as possible, even if the apples are split up into tiny portions.

3. The "Leftover" Strategy: The Second Chance

In a normal potluck, if you can't find a match for a basket of apples, you throw them away.
In this paper's system, nothing is thrown away immediately.

If an apple basket doesn't get matched in the first round, the system puts it in a "holding pen" and tries to match it again in the next round.

• If the apples are still fresh, they get another chance to find a home.
• If they are getting too old, the system suggests a Plan B: Maybe they can't be sold as fresh dessert apples, but they can be sent to a juice factory or animal feed. This is the "Circular Economy" part—using the apple for something rather than the trash.

4. What They Found (The Results)

The authors tested this system with real data from UK apple farmers and buyers. Here is what they discovered:

• There is no "Perfect" Setting: You can't just set the knob to "Best" and be done. If you prioritize distance (local food), you might end up with fewer apples sold because local buyers can't buy enough to clear the farmer's whole basket. If you prioritize quantity, you might have to ship apples very far.
• The Network Matters: The results depend heavily on where the farmers and buyers live. If everyone is clustered in one area (like Kent), "local" matching works great. If they are spread out, it's harder.
• "Good Enough" is Okay: The computer can't find the perfect mathematical solution for millions of apples in a split second. But it found "good enough" solutions very quickly. It's better to have a 95% match that happens instantly than a 100% match that takes too long.
• Transparency is Key: Because the system shows why a match failed (e.g., "Price was too low" or "Too far away"), farmers and buyers can fix their own problems. They can say, "Oh, I see I'm too expensive; I'll lower my price for the next round."

The Big Takeaway

This paper proves that we don't need magic to stop food waste; we need smart, flexible rules.

By using a simple computer algorithm that can be tuned to care about the environment, the economy, or fairness, we can turn a chaotic food market into a well-organized potluck where:

1. Apples stay fresher.
2. Trucks drive less.
3. Farmers get paid.
4. And almost nothing ends up in the trash.

It's about building a digital system that understands that an apple is not just a commodity; it's a resource that needs to be used wisely.

Technical Summary

Here is a detailed technical summary of the paper "Localisation and Circularity in Apple Supply Chains: An Algorithmic Exploration" by Baraa Alabdulwahab and Ruzanna Chitchyan.

1. Problem Statement

The paper addresses the critical challenge of allocating perishable food (specifically UK apples) within supply chains to balance economic viability with circular economy (CE) objectives.

• Core Issue: Perishable food supply chains suffer from significant waste due to time-sensitive quality decay, inefficient long-distance transport, and poor matching of supply to demand.
• Gap in Existing Solutions: While Multi-Objective Optimization (MOO) and Mixed-Integer Linear Programming (MILP) are common in supply chain design, existing models often:
  • Treat circularity implicitly (e.g., minimizing waste) rather than operationalizing it as a continuous process (e.g., recirculating unallocated goods).
  • Lack transparency in how economic vs. environmental priorities are weighted in operational, short-term decisions.
  • Focus on strategic planning rather than repeated, real-time operational allocation.
• Research Questions:
  • RQ1: How can an optimization framework allocate apples to demand while explicitly encoding CE objectives (localization, freshness) alongside economic performance?
  • RQ2: How do different priority settings (weights) influence allocation patterns, specifically regarding localization, supply utilization, and distributional fairness?

2. Methodology

The authors propose a Weighted-Sum Mixed-Integer Linear Programming (WS-MILP) framework designed for repeated, short-term operational allocation.

A. Mathematical Formulation

Instead of a Pareto-based approach (which yields a set of non-dominated solutions), the authors use a Scalarized Weighted-Sum approach to produce a single, implementable solution per run.

• Objective Function: Maximize the total weighted score of allocated flows:
  $$\text{Maximize } \sum_{i,j} x_{ij} \cdot \text{score}(offer_i, order_j)$$
  Where $x_{ij}$ is the quantity allocated from offer $i$ to order $j$.
• Scoring Components: The score for each potential pair is a linear combination of four normalized criteria ($[0, 100]$):
  1. Price Alignment ($f_{price}$): Similarity between buyer and seller price expectations.
  2. Quantity Alignment ($f_{quantity}$): Compatibility between offered and requested volumes.
  3. Freshness Alignment ($f_{freshness}$): Adherence to First-Expired-First-Out (FEFO) principles; minimizing the gap between offer expiry and order requirement.
  4. Geographic Distance ($f_{distance}$): Minimizing transport distance (proxy for emissions), modeled via an exponential decay function.
• Weights ($w_k$): Adjustable parameters ($\sum w_k = 1$) that allow operators to shift priorities dynamically (e.g., prioritizing "Distance First" for localization).

B. Implementation Architecture

The framework is implemented in Java using the ojAlgo optimization library. The process follows a four-stage pipeline:

1. Feasible Flow Construction: Filters offer-order pairs based on hard constraints (product type, time windows, logistics, price bounds). Infeasible pairs are recorded with diagnostic reasons.
2. Weighted-Sum Scoring: Calculates the scalar score for all feasible pairs based on the current weight vector.
3. MILP Optimization: Solves the allocation problem. To ensure scalability, it employs Candidate Pruning (Top-K scoring) and LP-Screening (discarding arcs with negligible relaxed flow).
4. Residual Circulation: Unallocated supply is not discarded. Non-expired leftovers are carried forward to the next iteration. Expired goods are flagged for downgrading (e.g., from fresh fruit to processing/juice).

C. Evaluation Setup

• Dataset: Derived from the synthetic ENG-Apple dataset (2302 offers, 262 orders). The evaluation focused on edible apples (932 offers, 118 orders) to manage computational complexity.
• Strategies Tested: Seven weight configurations were evaluated, including "Equal Weights" (baseline), "Price First," "Quantity First," "Expiry First," "Distance First," and two "Extreme" variants.
• Protocol: Iterative allocation runs until no feasible matches remain or a cap (5 iterations) is reached.

3. Key Contributions

1. Operationalizing Circularity: The framework moves beyond theoretical waste minimization to a practical mechanism for residual circulation, where unallocated supply is systematically re-introduced into subsequent trading cycles.
2. Transparent Priority Control: By using explicit, adjustable weights, the system allows platform operators and policymakers to visualize and control the trade-offs between economic goals (price/quantity) and sustainability goals (localization/freshness).
3. Diagnostic Feedback Loop: The system generates diagnostic data explaining why trades failed (e.g., price mismatch, expiry gap), enabling stakeholders to adjust inputs or relax constraints dynamically.
4. "Good-Enough" Allocation Philosophy: The paper argues that in large-scale operational contexts, exhaustive optimization is often infeasible. Instead, the system prioritizes bounded, interpretable solutions that maximize resource circulation within computational limits.

4. Key Results

The evaluation revealed that allocation outcomes are heavily dependent on both the weight settings and the structural characteristics of the supply network (e.g., geographic concentration).

• Supply Utilization: All strategies achieved high utilization rates (~95.5% – 96.7%), demonstrating the effectiveness of the iterative residual circulation mechanism.
• Strategy-Specific Outcomes:
  • Price First: Improved seller revenue but did not significantly improve localization or freshness.
  • Quantity First: Maximized the number of fully met orders but led to higher transport distances and left more supply unused (concentration bias).
  • Expiry First: Successfully tightened the "expiry gap" (FEFO behavior) without significantly compromising throughput, though it required sourcing from more distant locations.
  • Distance First: Achieved the strongest localization (reducing mean transport distance from ~865km to ~670km) and highest supply-side utilization. However, this resulted in thinner fulfillment per buyer (fewer fully met orders) and lower buyer-side prices.
• Trade-offs: No single strategy was optimal across all metrics. For instance, prioritizing distance improved localization but reduced order fulfillment rates.
• Leftover Supply: Approximately 3–5% of supply remained unallocated, primarily due to non-overlapping price ranges. The framework successfully identified these as diagnostic failures rather than unavoidable waste.

5. Significance and Implications

• For Digital Platforms: The study suggests that digital trading platforms for perishables should be designed around configurable, transparent allocation mechanisms rather than static "black box" optimizers. They must explicitly expose incompatibilities to allow for human-in-the-loop adjustments.
• For Circular Economy: The research demonstrates that circularity in food supply chains is not just about technology but about process design. The ability to carry forward unallocated goods and re-route expired products is critical for reducing waste.
• Context Dependence: The results highlight that optimization outcomes are inextricably linked to the underlying network structure (e.g., geographic clustering of UK apple production). Therefore, a "one-size-fits-all" static optimization model is insufficient; systems must be adaptable to local network characteristics.
• Future Directions: The paper advocates for "bounded optimization" that accepts "good-enough" solutions to ensure computational tractability while maintaining high resource circulation, shifting the focus from perfect optimality to systemic resilience and waste reduction.