Online food delivery and supply chain management by optimization of innovative models

2.1 Customer experience and key service dimensions

The quality of food delivery services has been widely analyzed in terms of customer experience, emphasizing the multidimensional nature of user satisfaction. Previous studies identify four main determinants: application quality, perceived price value, delivery time, and overall service quality. The quality of the application influences user satisfaction by shaping the accessibility and intuitiveness of the ordering process. Features such as simplified interfaces, customizable options, and real-time order tracking contribute to improved usability and customer retention [6], [7], [8]. Similarly, diversified payment systems and responsive communication tools—such as direct contact with riders or restaurants—enhance trust and perceived reliability [9].

The perceived price value extends beyond cost, encompassing intangible elements such as social reputation, sustainability, and ethical consumption [10], 11]. Promotions and membership programs can influence purchase frequency, but long-term loyalty ultimately depends on perceived consistency and transparency [12].

Among the four factors, delivery time has consistently emerged as the most influential determinant of customer satisfaction [13], 14]. The ability to ensure timely, accurate deliveries directly affects consumer trust, particularly in dense urban environments where expectations for punctuality are high. Therefore, optimizing delivery time not only improves operational performance but also represents a key driver of customer experience and platform reputation.

While these dimensions provide valuable insight into user perception, they do not directly address the operational and algorithmic mechanisms that produce such outcomes. The following section focuses on the technical foundations and optimization models that enable the achievement of these service objectives.

2.2 Optimization models and simulations approach in food delivery logistics

Recent advances in data analytics and machine learning have led to a new generation of delivery optimization models, aimed at improving both routing and order assignment efficiency. The problem of delivery time optimization is often conceptualized as a variant of the estimated time of arrival (ETA) problem [15], 16], which seeks to predict or minimize travel times between multiple locations under uncertain and dynamic conditions.

In the field of food delivery, ETA optimization is particularly challenging due to its dependence on real-time variables—such as traffic, restaurant preparation delays, and rider availability—that evolve continuously within the system. Studies by Liu et al. [17], Hildebrandt and Ulmer [18], and Gao et al. [19] integrate predictive analytics with order assignment logic, combining supervised learning and simulation to optimize dispatch decisions. Similarly, Salari et al. [20] propose a data-driven framework that determines optimal promised delivery times through decision tree-based models, bridging the gap between customer expectations and operational feasibility.

Beyond ETA prediction, researchers have also explored route optimization and vehicle routing problems (VRP) [21], 22]. Foundational algorithms such as Dijkstra’s shortest-path method [23] remain crucial to these models [24], providing computational efficiency and theoretical rigor for distance minimization in complex urban networks.

A more recent research stream focuses on multi-order (or batch) delivery optimization, which aims to group temporally and spatially compatible orders to improve fleet utilization. Multi-drop models have been shown to significantly reduce total travel distance and idle time, especially during peak hours [25], 26]. Among these, priority-based optimization frameworks [27] offer an additional refinement by dynamically sequencing orders according to urgency and preparation readiness, further improving overall service efficiency. However, such systems also introduce challenges related to route complexity and fairness among customers with different delivery priorities.

Another emerging area involves heterogeneous fleet models, which consider differences in vehicle speed, accessibility, and environmental impact [28]. These models highlight the operational advantages of assigning riders with different vehicles − such as bicycles and scooters—based on travel distance, delivery density, and urban topology. Despite their potential, few studies have integrated this aspect into full-scale simulations of urban delivery systems.

2.3 Research gap and contribution

Although substantial progress has been made in ETA estimation, route optimization, and order assignment, the integration of these components into a unified, realistic simulation framework remains limited. Most existing approaches either focus on single-order scenarios or assume homogeneous rider fleets, overlooking the heterogeneity and real-time adaptability required in modern delivery ecosystems.

This study addresses this gap by developing a three-level simulation model that combines:

1. vehicle-based rider assignment,

2. multi-order (batch) delivery management, and

3. shortest-path route optimization.

By merging these dimensions, the proposed framework bridges the gap between theoretical optimization models and practical logistics operations, offering a more comprehensive representation of urban food delivery dynamics. The next section details the methodological approach used to implement and compare the three proposed delivery models.

3.1 Experimental setting and empirical dataset

The proposed simulation replicates an urban food delivery ecosystem during peak operating hours (18:00–20:00), using empirical data collected from a real delivery platform operating in a medium-sized European city. The dataset collected by survey includes historical records of completed deliveries, providing detailed information on order creation times, restaurant and customer coordinates, preparation durations, and actual delivery timestamps. Each observation o _i is defined by the tuple t i ord , t i ready , p i , d i , v i , r i , where t i ord and t i ready denote the order placement and ready times respectively, p _i and d _i represent pickup and drop-off coordinates, v _i is the vehicle type used (bicycle or scooter), and r _i the assigned rider. The empirical dataset covers a three-week period and contains approximately 3,000 deliveries, which are used both to parameterize and validate the simulation model. The follow figure depicts the conceptual architecture (Figure 1).

Figure 1:

Simulation-based optimization framework.

Descriptive statistics from the dataset inform the main parameters of the simulation:

1. 65 % of deliveries were completed by bicycle, 35 % by scooter;

2. Average restaurant-to-customer distance: 2.7 ± 1.2 km;

3. Average preparation time: 11.8 ± 4.5 min;

4. Mean delivery time: 21.3 ± 5.7 min.

Rider speeds and service areas are calibrated from GPS traces, yielding empirical velocity distributions: v_bike ∈ [9.16] km/h and v_scooter ∈ [18.32] km/h. These empirical profiles ensure that the model’s variability reflects observed operational conditions.

Spatial routing occurs on a reconstructed street graph G = (V, E), extracted from “OpenStreetMap” data (Figure 2). Edge weights w _e correspond to empirically estimated travel times derived from the dataset’s historical routes, aggregated by road category and vehicle type. Route computation follows Dijkstra’s algorithm for single-order deliveries and a simplified traveling salesman problem (TSP) heuristic (nearest-neighbor + 2-opt) for multi-stop scenarios.

Figure 2:

Customers’ orders area.

The vehicle assignment follows an empirically validated rule (equation (1)):

where D_bikecorresponds to the 80th percentile of bicycle trip distances observed in the empirical dataset (approximately 3.0 km).

3.2 Single-order delivery model (baseline)

In the first configuration (Model 1), each rider is assigned exactly one order per trip. The system simulates the operational paradigm of most existing delivery platforms, where batching is not permitted and routing is optimized only for the shortest path between the pickup and drop-off points. For every order that becomes available ( t ≥ t i ready ), the model evaluates both vehicle types and selects the one with the lowest expected travel time, based on empirical averages from the dataset. The chosen order is assigned to the nearest idle rider of that type, determined by equation (2):

The resulting route r^*→p _i →d _i is computed using Dijkstra’s algorithm. Riders remain unavailable until the order is completed, preventing new assignments mid-trip. This model forms the baseline scenario for efficiency comparisons.

3.3 Multiple-order delivery model (greedy batching)

The second configuration (Model 2) introduces the possibility of multi-order delivery through a greedy batching mechanism. Orders are grouped when their pickup and delivery coordinates, as well as preparation times, satisfy empirical compatibility thresholds derived from the observed data:

1. Temporal proximity: ∣ t i ready − t j ready ∣ ≤ Δ t , where Δtequals the 75th percentile of preparation-time differences (≈5 min);

2. Pickup proximity: dist(p _i ,p _j ) ≤ R _p , with R _p  = 400 m;

3. Drop-off proximity: dist(d _i ,d _j ) ≤ R _d , with R _d  = 700 m.

Batches are built greedily from the pool of available orders until the capacity k = 2 is reached. The route structure includes all pickups ordered by readiness time and all drop-offs sequenced by nearest neighbor. Riders may accept additional compatible orders before their first delivery, reflecting the partial dynamism observed in actual platforms.

This model approximates real-world practice, improving resource utilization while accepting limited inefficiency from non-optimal routing. It represents an intermediate configuration between operational realism and optimization.

3.4 Optimized multiple-order delivery model

The third configuration (Model 3) extends the previous one by introducing full pre-planning and routing optimization. All orders in a batch are pre-assigned before departure, and no additional tasks are accepted once the trip begins.

At discrete decision intervals (every 60 s), the system analyzes the active order pool and constructs candidate batches through spatial clustering, using empirical radii R _p and R _d as derived from paragraph 3.3. For each batch B, feasible pickup and drop-off sequences (π _p , π _d ) are generated and their total travel time estimated by following equation (3):

The optimal batch minimizes T_total(B) jointly over rider, vehicle, and sequence configurations (equation (4)):

This optimized multiple-delivery model aims to capture the performance of an algorithmically advanced platform capable of planning entire delivery rounds ex ante, balancing travel efficiency with service reliability.

3.5 Learning and routing components

Empirical records from historical deliveries are used to train a k-nearest neighbors (k-NN) regressor that predicts travel times for each segment e and vehicle v (equation (5)):

where N K e , v represents the Kmost similar past observations by distance, traffic condition, and time of day.

For route computation, Dijkstra’s algorithm is applied to single-order paths, while a TSP heuristic combining nearest-neighbor initialization and 2-opt refinement is used for multi-stop optimization. These techniques ensure computational tractability while maintaining alignment with real routing data.

3.6 Evaluation metrics and validation protocol

Model performance is evaluated using both empirical validation and simulation-based comparison.

Customer-oriented metrics include:

1. Mean delivery time T_deliv;

2. Mean waiting time after preparation T_wait;

3. On-time delivery rate for thresholds τ ∈ {25, 35} min.

Operational metrics include:

1. Orders per trip (OPT);

2. Distance per order (km/order);

3. Idle time ratio (waiting/active time);

4. Vehicle utilization rate (bikes vs scooters);

5. Batch share (% of orders delivered in batches).

All results from the simulated models are compared against the empirical benchmarks extracted from the dataset, enabling quantitative validation of each configuration.

The multiple-order model is expected to outperform the single-order baseline, while the optimized multiple-order model should further reduce delivery times and distances, demonstrating its validity and practical potential when aligned with real-world delivery data.

To ensure the reliability and external validity of the proposed simulation framework, a two-step validation process is adopted. The first phase consists of parameter calibration using empirical data, while the second focuses on model validation through quantitative comparison between simulated outcomes and observed real-world performance.

Empirical data described in paragraph 3.1 (dataset description) are used to calibrate the model’s key parameters:

1. Mean and variance of restaurant preparation times;

2. Average rider speeds and their distribution by vehicle type;

3. Typical pickup–delivery distances and time-window thresholds (Δt, R _p , R _d );

4. Historical order density over time (orders/hour).

Calibration minimizes the mean absolute percentage error (MAPE) between simulated and observed trip durations for the single-order baseline, depicted in equation (6).

The model is considered sufficiently calibrated when MAPE ≤10 %, indicating that simulated delivery times approximate the empirical distributions within acceptable bounds.

The second phase evaluates the predictive consistency of the simulation by comparing model outputs with held-out empirical data. Three key aspects are assessed:

1. Temporal validation: comparison of average delivery time trends (15 min intervals) between empirical and simulated datasets using Pearson [29] correlation r and Root Mean Square Error (RMSE), visible in equation (7).

2. Spatial validation: comparison of mean delivery distances across city zones to verify consistency of routing patterns.

3. Operational validation: evaluation of vehicle usage and batching rates against observed values, using chi-square goodness-of-fit tests.

Model reliability is confirmed when correlation r > 0.85 and RMSE ≤3 min for delivery times. The validation process is repeated independently for bicycles and scooters to ensure that both fleet components are realistically reproduced.

Finally, the simulated performance of the three models—single-order, multiple-order, and optimized multiple-order—is benchmarked against the empirical baseline extracted from the dataset. Statistical tests—Wilcoxon signed-rank for paired measures, analysis of variance (ANOVA) for aggregated metrics)—determine whether observed improvements are significant at a 95 % confidence level [28], 30].

This validation setup provides a robust methodological link between empirical observations and simulated optimization results, ensuring that the model’s conclusions are grounded in real operational data.

4.1 Model assumptions and limitations

The proposed simulation relies on several simplifying assumptions that enable analytical tractability but may limit generalization. First, the model assumes that all restaurants and customers are static points on a fixed street network, neglecting short-term variations in accessibility or temporary closures. Rider behavior is modeled deterministically within each delivery phase—pickup, travel, and drop-off—without accounting for micro-level variability such as waiting at traffic lights or searching for parking.

The fleet is considered fully available during the simulation window, and rider cancellations or off-platform activities are not simulated. Similarly, restaurant preparation times are treated as exogenous and independent across orders, although in practice they may depend on kitchen workload and staffing levels. The model does not incorporate stochastic traffic congestion or weather disruptions, which could affect real-world travel speeds.

Another limitation concerns the optimization scope. The optimized multiple-order model assumes perfect information about order readiness and travel conditions at the time of assignment, which may not always be achievable in operational settings. While empirical calibration mitigates some of these biases, real-time uncertainty remains a challenge for future extensions.

Despite these simplifications, the model reproduces aggregate performance patterns observed in empirical data with high fidelity. Therefore, the assumptions primarily affect the precision of individual predictions rather than the validity of the overall comparative results. Future research could address these limitations by integrating stochastic travel models, real-time rider behavior, and adaptive reallocation mechanisms after batch completion.