Maria Michalopoulou, Panayiotis Kolios, Tania Panayiotou, Georgios Ellinas
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Meal delivery services have undergone a tremendous evolution during the last decade and, according to market predictions, this trend will continue to grow in the following years. The service growth forecast in combination with the high complexity of the problem indicate the importance of achieving efficient solutions. This article presents a detailed description of the meal delivery problem (MDP) as well as the main research directions appearing in the existing literature. The characteristics that increase the complexity of the problem are highlighted, namely, the dynamic nature of the delivery tasks; the tight delivery time requirements; and the interdependencies among stakeholders, which are connected by nonexclusive relationships. Open challenges of the problem are analyzed, including the expected future shift toward autonomous deliveries as well as other general future directions.
The term meal delivery services refers to delivery services provided by third parties—called aggregators—via which customers order their favorite meals from a variety of restaurants through an aggregator’s online platform and have the meals delivered to their location within a specified time limit. In the scientific literature, MDPs appeared in the late 2010s, referring to a newly emerged class of dynamic delivery problems associated with these services.
The food delivery market underwent exponential growth in 2020–2021 during the COVID-19 pandemic. The digital acceleration driven by the pandemic impacted all sectors, including the ready-meal industry (Almeida et al., 2020). Restaurants were compelled to collaborate with delivery aggregators and invest significant effort and resources in the handling of delivery orders. Moreover, in an effort to increase growth, the concept of ghost kitchens has emerged. Actually, food delivery showed a potential for robust growth even before the pandemic. The proliferation of mobile devices and Internet connectivity encourage a lifestyle in which online ordering is an essential convenience (Weber and Chatzopoulos, 2019). In fact, some third-party delivery aggregators have started to expand their services to goods and products other than food, and this is more likely to further evolve in the future, motivating the need to develop efficient solutions for this family of problems.
The meal delivery ecosystem, depicted in Figure 1, involves four actors: aggregators, drivers, restaurants, and customers. Aggregators establish partnerships with restaurants and freelance drivers and act as a bridge among all entities in the sense that all interactions in the process go through the aggregator. All relationships in the problem are typically nonexclusive, meaning that a partnership does not exclude partnerships with competitors. In particular, restaurants and drivers can collaborate simultaneously with multiple aggregators. As drivers work as freelancers for an aggregator, they have the option to accept or reject every single delivery task they are offered. Another implication of this freelance relationship is that, although most aggregators suggest a route for each assigned delivery task, this is not binding.
Fig 1 The meal delivery ecosystem.
The flow of required actions for a single order is illustrated in Figure 2 and detailed here:
Fig 2 The complete flow of actions for a single order.
One of the distinguishing elements of the MDP is order bundling. The aggregator can merge multiple orders in a single delivery task, which is assigned to one driver if the timing as well as the pickup and drop-off locations of the orders can be efficiently and effectively combined.
The bundling of orders is beneficial for both aggregators and drivers. For aggregators, it keeps the cost lower, as adding orders in a single delivery route incurs an additional, not a multiplicative, cost per additional order. Moreover, it achieves more efficient utilization of the available drivers, which is especially important during peak hours. For drivers, it significantly increases their per-distance and per-time revenue. In reality, experienced drivers work simultaneously for two or even three aggregators and, when possible, perform their own bundling of orders received from different aggregators.
The task of bundling orders significantly increases the complexity of the problem, as there are several dynamic conditions and stochastic parameters that one could consider—for instance, the potential of orders to be bundled with future orders or the effect of cascading delays for other orders in the bundle given the probability that a restaurant delays preparing an order by a certain time.
Combining orders in one delivery task incurs delays in their delivery times but saves in terms of driver utilization and compensation. The objective is to strike a balance among these factors that should be dynamically adjustable according to the current circumstances. For example, if there are too many orders to serve at a certain time and the availability of drivers is limited, longer delivery times may be a better option than refusing to serve orders.
The MDP involves several stochastic elements that significantly increase its complexity. First, the customers’ orders are dynamic and stochastic. The flow of incoming orders changes with time, and each order becomes known the moment it is submitted by the customer. At a given time instant, the aggregator optimizes the assignment of orders and sends the delivery tasks to the available drivers based on the already submitted orders. However, a few moments later, new orders will be arriving, which certainly interrelate with the last order assignment in terms of timings because, due to the nature of the problem, orders need to be delivered within a very limited time span (less than an hour). To improve the delivery task assignment, past data can be used to create statistical models of the orders’ arrivals and predictions.
The time needed for a restaurant to prepare an order is also nondeterministic, and this comes into play twice in the flow of the problem. At first, the aggregator has to provide potential customers with estimated delivery times before placing orders. This estimation entails a prediction of the time the restaurant will need to prepare an order and can be based on past data and on a general estimate given by the restaurant. After an order is submitted to the system by the customer, the corresponding restaurant accepts it and responds back to the aggregator with an estimated pickup time for that particular order—which, at the end, may deviate from the actual time. This deviation can be significant when a driver is assigned a combination of orders either as a bundle or back to back.
In most cases, the drivers are freelancers, and the partnership relationship between the aggregator and drivers is such that the aggregator offers a delivery task, but drivers can decide whether they want to handle it or reject it. Therefore, the problem also involves the stochastic binary decisions of the drivers with regard to the assignment of the delivery tasks and, subsequently, reassignment of the rejected tasks.
Finally, the travel time is also stochastic, depending on the route and the current traffic conditions. Nevertheless, this fact is not accounted for in real platforms or in research articles. Usually, the Euclidean distance is used for estimating the driver’s travel time. The fact that the vast majority of drivers ride two-wheelers negates the dependence on traffic; however, the route selected by the driver as well as accidents or other major road incidents are worthy of consideration.
The MDP belongs to the broad family of dynamic vehicle routing problems, and, specifically, it is closely related to the dynamic pickup and delivery problem (DPDP) and to the same-day delivery problem (SDDP). The DPDP deals with transporting goods from unique pickup locations to unique drop-off locations with requests arriving dynamically from geographically dispersed customers. When transportation refers to people instead of goods, DPDP is also known as the dial-a-ride problem. The SDDP, a variant of the DPDP, has only recently emerged, mainly due to the rising interest of online retailers in providing same-day delivery. Unlike the DPDP, in the SDDP, vehicles may return to the depot after performing delivery to pick up new products and continue serving new requests (i.e., all orders are picked up from the same location).
While the MDP, similarly to the SDDP and DPDP, is a dynamic, capacitated, stochastic problem with restricted customer time windows, it is also differentiated from these problems mainly due to the shorter time windows for delivery; the requirement that the load, once dispatched, has to be delivered; and the presence of independent drivers with flexible working schedules. As such, even though optimization methods for the MDP can, to some extent, share similar ideas with methods used for other related dynamic delivery problems (e.g., rolling horizon methods), the MDP is today considered to be the ultimate challenge in last-mile logistics.
The majority of works have addressed the MDP as an assignment problem, while others tried to solve it as a scheduling problem. In addition, there is a selection of scientific publications that investigate other incentives entailed in the problem.
The MDP is a multiobjective problem. A list of selected objectives found in the literature is given in Table 1. Apart from short delivery times, which are in favor of all actors involved in the problem, the importance of fuel/energy consumption has been stressed lately. Especially as the demand for deliveries of goods is increasing, the environmental footprint of such services becomes an even more important factor that must be considered in the formulated optimization problem.
Table 1. The meal delivery problem’s objectives addressed in the current literature.
From the aggregator’s point of view, given a set of orders to accommodate and a set of drivers, the purpose is to assign the orders to the drivers so that one or several parameters are optimized. With their extensive work, Reyes et al. (2018) laid the foundation of this research topic. They apply a rolling horizon matching-based algorithm that is executed periodically to determine the next pickup and delivery assignment for each driver so that orders are delivered without exceeding a given time limit.
Most works address the subproblem of order bundling, which plays a significant role, as it can significantly increase the performance with respect to the optimization objectives. In some studies, bundling and assignment are tackled together in a joint optimization formulation in the context of assigning every order to a driver and allowing multiple orders to be assigned to every driver. Alternatively, a two-step approach is employed. As a first step, all orders are bundled together to form delivery tasks, which are subsequently assigned to the available drivers. The former approach is, in theory, more flexible, yet the resulting optimization problem may easily become too complex to tackle. On the contrary, the latter approach is more tractable.
Multiobjective integer programming models and Markov decision processes are dominant in the literature for modeling the assignment task. As the problem is large and complex, it is rather impossible to solve with exact methods. Therefore, matching algorithms; heuristics; and machine learning methods, such as reinforcement learning and deep neural networks, have been utilized to attack the problem.
As discussed, the several stochastic elements that are involved remarkably increase the complexity of the problem. The more stochastic parameters one considers, the more difficult it is to reach a provably optimal solution. Most of the existing studies assume one or two stochastic or dynamic parameters, with the order of arrivals being the one that is most widely considered. A deterministic version of the problem can also provide solutions that, despite the unrealistic assumptions, constitute benchmarks that can be used for comparison purposes (Yildez and Savelsbergh, 2019).
A few works solve the MDP as a scheduling problem in which the task is to tackle, on behalf of the aggregator, the delivery of all incoming orders as timely as possible. Alternatively, scheduling aims to select and serve the largest number of orders so that a maximum delivery time limit for each order is not exceeded.
Cosmi et al. (2019) formulated the MDP problem in the context of classical scheduling theory, solving it by means of a dynamic programming algorithm. Considering a single restaurant, a single driver, and a specified set of delivery requests, the addressed problem was to find a subset of orders to be delivered within the acceptable time limits. The problem was reduced to the throughput maximization single machine scheduling problem with release times and bounded slacks, and it was shown that it can be solved by a dynamic programming algorithm in polynomial time. A few subsequent works were published based on similar problem formulations. A variety of integer linear programming (ILP) models as well as a combinatorial branch-and-bound algorithm have been employed in the literature for these problems, with the latter found to outperform ILP solutions in terms of speed and the ability to handle larger datasets.
There are a number of approaches that do not strictly follow the definitions and concepts of classical scheduling theory, but they can be classified as scheduling problems because they are optimizing scheduling objectives, e.g., maximizing the number of delivered orders in a specified interval. However, they are very similar to assignment problems in the sense that their output decisions include the matching of delivery tasks with drivers. In fact, there are problem formulations that could fall under both categories, i.e., of scheduling and assignment problems.
Also, as timing is central in scheduling, the task of bundling orders has to consider routing or, at least, specify an order for pickups and drop-offs of the orders in each created bundle.
Scheduling is one of the problem’s crucial elements; however, the MDP entails several additional aspects. Therefore, the disadvantage of pure scheduling approaches is that they cannot tackle the problem in its full complexity. Ideally, the solution of an MDP should address assignment and scheduling together while also considering stochasticity. However, a real MDP handles a large number of orders and drivers in a rather short-term time frame. This fact renders the task assignment element more dominant.
Various complementary elements can be addressed in the context of the MDP. Optimizing order bundling is complex enough to stand as a problem on its own. For example, a neural network method has been proposed to build a proactive and more efficient bundling policy that accounts for the potential of each order to be bundled with future unknown orders, considering the fact that order arrivals are dynamic and stochastic (Li et al., 2021).
The ability of an aggregator to respond to incoming orders is also considered. The required number of drivers to respond to a certain order demand, for example, is investigated. From the opposite perspective, the current coverage area for each restaurant is proposed as a measure to regulate the order demand, given that a certain number of drivers are currently in service. Also, the schedule of the drivers’ shifts is optimized so that the aggregator’s capacity is maximized. Finally, a multistage bonus allocation scheme for drivers is used to reduce the number of orders that are not accepted by any driver, thereby increasing the response of the aggregator to the incoming orders.
Time estimations are also important in the MDP, such as the order arrival times that are provided to the customer before placing an order. In a very interesting article by Hildebrandt and Ulmer (2022), the authors analyze, by means of Markov decision processes and learning methods, the impact of these time estimations on future restaurant selections by the customers. Similarly, Paul et al. (2020) empirically analyze how early delivery is positively correlated with the number of times the customer will again place an order.
The concept of introducing intermediate transfer stations—owned and operated by aggregators—to be able to handle long-distance orders is also proposed by Li et al. (2022).
Finally, the MDP in conjunction with fairness concerns has been recently examined, especially with respect to the income inequality that the drivers experience. Gupta et al. (2022) attempted to achieve fair income distribution among drivers while ensuring timely meal delivery. Toward a fair MDP, disciplines used to solve the generic fair resource allocation problem (e.g., game theory, welfare economics, and multiagent reinforcement learning) can be additionally leveraged.
In reality, aggregators suggest a route for each delivery task, but the driver is, in most cases, not obligated to follow it. In accordance with this, in the majority of the aforementioned literature routing is not considered as part of the optimization problem. The distance between locations is usually taken as a straight line (Euclidean distance) for travel time estimation. However, as previously mentioned, in some cases, the state of the transportation network in conjunction with the route taken must be considered, especially when the optimization objectives include the delivery time/delay.
Beyond the assignment and scheduling of delivery tasks, there are several other parameters to consider. For instance, the delivery zones of the restaurants can be adjusted dynamically depending on the rate of incoming orders and the number of drivers that are in service in the area at a certain time. The charging of the customers can also be dynamic, given the instantaneous service demand and resource capacity of the aggregator.
So far, the problem is primarily examined from the aggregator’s point of view. Some objectives are desirable for others as well. For example, minimizing the delay in deliveries is desirable for everyone. Nevertheless, the fact that different actors are selfish, with often conflicting goals, is mostly overlooked. In general, there is a lack of alternative problem formulations that either address the problem from another actor’s perspective or consider relationships and interdependencies among different actors. For example, the driver’s perspective entails some complex decisions. It is known that, in reality, many drivers work simultaneously for more than one aggregator to maximize their income; they sometimes even decide to bundle orders offered by different aggregators. To maximize one’s day-long earnings, the decision of a driver about whether to accept a delivery task or not is a stand-alone stochastic optimization problem. It depends on whether a better delivery offer is likely to arrive in the near future, either from the same or from a different aggregator, and, subsequently, where the driver will end up after delivering the order (i.e., in a popular area with high order demand or away from restaurants, where new delivery tasks will be scarce). The selection of location when idle is also a strategic decision for a driver, including the decision about whether to relocate after a delivery. For all of the aforementioned decisions, a decision-support tool for drivers could increase their efficiency.
All four actors of the problem act independently, and none of them controls the decisions of the others. However, strong interdependencies exist among them. Identifying and modeling these interdependencies will enable the formulation of more realistic optimization scenarios. For example, the number of drivers that will be collaborating with a particular aggregator and, therefore, the capacity of the aggregator to respond timely to delivery tasks at a certain time is dependent upon the drivers’ satisfaction with the aggregator, a factor that is not yet quantified in the existing literature. Further, to accurately estimate the total delivery time, the aggregator must be able to make a fairly good estimation of the ready-to-pickup time at the restaurant, which concerns the operation of the restaurant. Specifically, it depends on all incoming orders from all sources (dine-in, takeout, other aggregators, etc.) in combination with the restaurant’s kitchen capacity. So far, only a few works have taken such relationships into account (e.g., Hildebrandt and Ulmer, 2022, and Paul et al., 2020).
In reality, several aggregators operate within a certain area. An interesting extension of the MDP is to introduce an “aggregator of aggregators” service, that is, a level of cooperation among aggregators. Instead of delaying orders when an aggregator’s capacity is reached or sending a driver far away to deliver a single order during peak hours, it is worth exploring models of cooperation among aggregators so that delivery tasks of different aggregators are combined, or delivery tasks are simply outsourced from one aggregator to another. Evidently, to model such scenarios, it is implied that a formulation of the MDP accounting for multiple aggregators in an area is considered.
In the foreseeable future, autonomous vehicles are expected to be widely adopted as a means of transportation. The future of deliveries will likely be driverless, with autonomous robots, cars, and unmanned aerial vehicles (UAVs), as illustrated in Figure 3. Moreover, such delivery services will not stay confined to the delivery of food from restaurants, but they will expand to the delivery of other goods from nearby shops or from close-by warehouses. Large vendors, such as Amazon, have already started considering the idea of establishing smaller warehouses close to larger urban centers. Actually, to serve a contemporary lifestyle, this service has the potential to expand to any point-to-point delivery of small-sized items.
Fig 3 The future of transportation with autonomous, driverless means of transportation.
Technology companies, such as Nuro and Yandex, are working on developing so-called last-mile delivery robots, which are small, wheeled, autonomous bots rolling along sidewalks at walking speed. A few companies have already deployed robot deliveries commercially in a few confined areas around the world. The small sidewalk robots are functional and promising, but not all areas have adequate sidewalk infrastructure. Furthermore, an abundance of these robots may disrupt primary sidewalk users, namely, pedestrians, cyclists, and disabled individuals. Such discussions have already been initiated in cities where robot deliveries were deployed.
To this end, we foresee that the future of deliveries by means of autonomous, driverless cars will also have its place. Several optimization factors—typical in the domain of transportation for autonomous fleets—arise, such as route optimization, charging station placement, vehicle recharging decisions, positioning of the vehicles while idle, etc. Moreover, autonomous cars are foreseen to transform personal mobility through car-sharing schemes and transport-as-a-service concepts. Services that combine both meal delivery and personal mobility can be developed, and requests for person rides and meal deliveries can be jointly optimized and served by joint routes.
The volume of autonomous car deliveries in the future will be sufficiently large to add to the congestion problem during certain hours. Congestion from delivery traffic will rise by more than 21% according to the World Economic Forum (Deloison et al., 2020). Congestion will also affect the service itself by increasing delivery times. Therefore, solutions taking traffic into consideration will be required. Joint optimization of multiple point-to-point delivery services with different delivery time requirements can be considered in combination with opportunistic scheduling and routing based on a time-dependent route reservation concept aiming to minimize congestion (Menelaou et al., 2017). This can be additionally combined with dynamic pricing schemes offering the option for customers to relax time requirements in return for lower delivery prices, especially for the delivery of goods other than meals.
Further, as meal delivery services are becoming ubiquitous in the contemporary urban lifestyle, they can be employed in the context of easing modern challenges related to the food system, as these are recognized by relevant official organizations (Froidmont-Görtz, 2020). The concept of food sharing was introduced a few years ago; however, its logistics is a difficult aspect that can be facilitated through autonomous delivery services. Extending the concept of a service like meal delivery to cover grocery and other shopping can contribute to the reduction of food and other waste as the idea of “buy as you need” instead of stockpiling is promoted. The cost of the service for the customer may become an issue; however, the more frequently delivery services and routes are jointly optimized and covered by the same fleet, the more the delivery costs can drop. Moreover, other modern concepts, such as the circular economy, can be effectively combined with point-to-point delivery services.
Finally, this discussion would not be complete without referring to the utilization of UAVs. Falling under the general umbrella of autonomous delivery services, a major difference is that UAVs do not use the regular transportation infrastructure. It is, therefore, a promising area for future research, with many open challenges. We anticipate that UAV-based deliveries will become a reality in the future, coexisting with vehicular deliveries of all kinds. To optimize different coexisting delivery means, designing a dynamic delivery-means selection strategy is also an interesting topic, taking into consideration the availability of each as well as current conditions in the air, on sidewalks, and on the road network.
This work was supported by the European Union’s Horizon 2020 research and innovation program under Grant 739551 (KIOS Centre of Excellence) and by the Government of the Republic of Cyprus through the Directorate General for European Programmes, Coordination, and Development.
Maria Michalopoulou is the corresponding author for this article.
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Maria Michalopoulou (michalopoulou.maria@ucy.ac.cy) earned her B.Sc. degree in informatics and telecommunications from the University of Athens, Greece. She subsequently earned her M.Sc. and a doctoral (Dr.-Ing.) degrees in communication engineering from the Rheinisch-Westfälische Technische Hochschule Aachen University, Germany. Since September 2017, she has been a research associate at the KIOS Research and Innovation Center of Excellence, University of Cyprus, 2109 Nicosia, Cyprus. Her research interests include a variety of topics in the domains of wireless networks and intelligent transportation networks. She is a Member of IEEE.
Panayiotis Kolios (pkolios@ucy.ac.cy) earned his B.Eng. and Ph.D. degrees in telecommunications engineering from King’s College London in 2008 and 2011, respectively. He is a research assistant professor with the KIOS Research and Innovation Center of Excellence, University of Cyprus, 2109 Nicosia, Cyprus. His research interests include both basic and applied research on networked intelligent systems (e.g., intelligent transportation systems, autonomous unmanned aerial systems, and the plethora of cyberphysical systems that arise within the Internet of Things). He is a Member of IEEE.
Tania Panayiotou (panayiotou.tania@ucy.ac.cy) earned her diploma degree in computer engineering and informatics from the University of Patras, Patras, Greece, in 2005 and her Ph.D. degree in computer engineering from the University of Cyprus (UCY) in 2013. She is a research associate with the KIOS Research and Innovation Center of Excellence, UCY, 2109 Nicosia, Cyprus. She has authored more than 40 articles, conference papers, and book chapters. Her research interests include optical networks and transportation networks. She is a Member of IEEE.
Georgios Ellinas (gellinas@ucy.ac.cy) earned his B.S., M.Sc., M.Phil., and Ph.D. degrees in electrical engineering from Columbia University. He is a professor at the Electrical and Computer Engineering Department and a founding member of the KIOS Research and Innovation Center of Excellence at the University of Cyprus, 2109 Nicosia, Cyprus. Prior to joining the University of Cyprus, he also served as an associate professor of electrical engineering at City College/City University of New York, as a senior network architect at Tellium Inc., and as a research scientist at Bell Communications Research (Bellcore). His research interests are in telecommunication networks, intelligent transportation systems, the Internet of Things, and unmanned aerial systems. He is a Member of IEEE.
Digital Object Identifier 10.1109/MPOT.2023.3327798