Discrete Optimization
Matching supply and demand in a sharing economy: Classification, computational complexity, and application

https://doi.org/10.1016/j.ejor.2019.04.032Get rights and content

Highlights

  • We analyze the structure of deterministic problems matching supply and demand in a sharing environment.

  • We provide a classification of these optimization problems.

  • We provide an analysis of computational complexity of several problems.

  • We consider the case of sharing parking space and explore the potential contribution of solving deterministic problems.

Abstract

The sharing economy, i.e., the cooperative consumption of goods and services offered by private households or companies via online market places, gains more and more attention. Most sharing platforms coordinate transactions by generating each consumer an individual list of suited and available resources to choose from. If plenty online requests arrive rather simultaneously and compete for the scarce shared resources, however, an optimization-based coordination of supply and demand promises much better matches (e.g., more satisfied requests). This paper focuses deterministic matching problems and provides a classification scheme for the resulting optimization problems occurring in different areas of the sharing economy. These matching problems vary, for instance, if immobile (e.g., parking space) or mobile resources (e.g., vehicles of a car sharing provider) are shared. With the help of this classification, we give a detailed overview on known and novel complexity results. Furthermore, we apply the example of sharing parking space and explore the potential contribution of deterministic matchings when applied in a dynamic, uncertain, and opportunistic environment.

Introduction

The sharing economy is said to be among the “10 ideas that will change the world” (Walsh, 2011). Online directory The Mesh currently lists almost 10,000 online platforms that use “modern technology and social networks to provide people with goods and services without the burden and expense of owning them outright” (Mesh, 2017). Examples range from crowded platforms such as Uber and Airbnb to niche providers like Freshneck.com for ties. Only in Europe, the sharing economy has generated revenues of nearly €4bn and facilitated €28bn of transactions in 2015 (Vaughan & Daverio, 2016). Assessments of the rapid diffusion of the sharing economy oscillate between the very extremes. Some commentators stress their potential to protect the environment by utilizing scarce resources more efficiently, others point out that many sharing platforms do not contribute to social welfare systems, obviate labor protection laws, and endanger established business models; see, for instance, (Ertz, Durif, Arcand, 2016a, Malhotra, Van Alstyne, 2014) for a closer discussion of these aspects.

A constituting element for the sharing economy is the central online platform that brings together offers of private households or companies (denoted providers) for goods as well as services and requests of other private households or companies (denoted consumers) aiming usage of these resources. Once offers on the supply side and requests on the demand side are collected, they need to be matched. The vast majority of online platforms currently applies a simple list-based solution as the basic matching mechanism. Consumers enter the websites or mobile apps of an online platform and specify the demanded characteristics of the requested resource. A typical information that is required by nearly all sharing platforms is the rental interval during which a resource is demanded. Car sharing providers like Car2Go additionally query the current GPS coordinates of the device placing a request to locate close-by cars. Other platforms, e.g., Flexe.com, require the specification of the demand for warehouse storage space and the preferred area. Given fully specified requests, a platform queries its offer database and presents the consumer an individual list of suited matches to choose from. The alternative to a list-based solution is a matching based on optimization procedures. Especially on crowded platforms with plenty offers and requests with varying preferences, matching supply and demand can be fully-automated by an optimization procedure.

On the positive side, an optimization-based matching promises better matches where – depending on the objective function – more requests can be satisfied or a higher commission fee for the platform provider can be generated. Furthermore, consumers need not scroll through the list of suited matches for the final selection but can, for instance, directly be navigated to the nearest vehicle of a car sharing provider. On the negative side, an optimization-based matching produces organizational overhead. To collect offers and requests in the meantime an optimization-based matching can be executed periodically, e.g., every minute, once per hour, or every day. This period of request collection is also dubbed the batching interval. Alternatively, a new optimization run can be started once a new offer or request (depending whether demand or supply constitutes the bottleneck) arrives. Both approaches require some patience of platform users until their matching result is finally announced. Depending on the type of shared resource and the competitive position, it may be hard for the provider of an online platform to give the right incentives for an early announcement of requests and offers. One example of such an incentive is the so-called handshake option just announced by German car sharing provider (DriveNow, 2017). Instead of a painstaking search for a parking space in a crowded city center, successive users can arrange the hand over of a car on the fly by quickly hopping off and on at the side of the road. Clearly, a handshake requires an arrangement via the central booking platform as well as an early and reliable specification of place and time. Another problem of an optimization-based matching is that some users may not be satisfied by the optimization result. In the worst case, unsatisfied users decline the match later on. Koutsoupias and Papadimitriou (1999) call the resulting loss of system performance, when participants reject proposed resources to form their own matches, the price of anarchy. One lever to avoid such behavior is a user reputation system which is often part of a sharing platform (Agatz, Erera, Savelsbergh, & Wang, 2012). In Section 5, we take a closer look on the increase of matching quality promised by an optimization-based matching compared to the list-based solution. These gains have to be traded off against the organizational overhead discussed above.

Example: Ampido.com is a sharing platform for parking space (see Fig. 1(a)). Offers stem from private households that lend their private parking space, e.g., during their holidays, or parking lots with unoccupied space. In the current solution, consumers seeking parking space specify their target position and rental interval. Then, they are presented a list (supported by a map) of available offers they can choose from. Once such a platform is widely accepted and dozens of requests arrive (almost) concurrently, placed by drivers already on their way via the navigation apps on their smartphones, a matching based on sophisticated optimization may lead to much better matches compared to the current list solution. The resulting optimization problem can be defined as follows: Given a set of parking spaces, each defined by the geographic position and its availability over time, these offers need to be matched with a given set of parking requests. Each request of a consumer has a target defining the ideal parking position, a radius specifying the maximum accepted walking distance (between assigned parking space and ideal position), and a rental interval. Given fixed parking fees per hour and a proportional commission fee for the platform, we seek a matching, i.e., a list of accepted requests and their assigned parking spaces, such that rental periods at no parking space overlap, each accepted request receives a parking space within the respective maximum walking distance, and the total revenue of accepted requests is maximized. Fig. 1(b) and (c) present an example instance for this optimization task and a solution, respectively. Note that this solution is optimal (as long as the parking fee per hour is positive), because all requests are accepted. With a list-based matching, there is the threat that an optimal solution is missed. If consumer A is the first to place the request and selects parking space #2 from the resulting list, an optimal solution where all requests are accepted will inevitably be missed.

This paper is dedicated to an optimization-based matching of supply and demand in a sharing economy, and we further restrict our scope on static and deterministic matchings. Our main contribution is a classification scheme for potential matching problems in the wide spectrum of sharing applications analogously to the famous classification schemes for machine scheduling and queuing systems introduced by Graham, Lawler, Lenstra, and Rinnooy Kan (1979) and Kendall (1953), respectively. This classification scheme is applied to present elementary complexity results in a systematic and compact form. Some complexity results are directly taken over from other applications (e.g., interval scheduling), others constitute new results. Another main contribution is to systematically explore, how solving deterministic and static matching problems can nonetheless contribute, if the environment these matching problems are solved in is indeed neither static, nor deterministic, nor altruistic. With the help of our example of sharing parking space, we explore how deterministic matchings can successfully be applied in a dynamic, stochastic, and opportunistic environment.

The remainder of the paper is structured as follows. Section 2 precisely defines the scope of our survey. Then, Section 3 presents our classification scheme, which is applied in Section 4 to provide elementary complexity results. Section 5 takes a closer look on how optimization can be applied during the daily operations of a sharing platform. Applying our parking example from Fig. 1, we quantify the value of optimization (compared to the list-based approach) for different batching intervals by a computational experiment. Furthermore, we apply our deterministic matchings in a dynamic, stochastic, and opportunistic environment. Finally, Section 6 elaborates future research needs and concludes the paper.

Section snippets

Scope of paper

The sharing economy is also denoted as collaborative consumption, collaborative economy, or peer economy. Some argue that the name is misleading, because sharing implies a social exchange without profit aims, so that for the profit-oriented and market-mediated access to a stranger’s goods or services the term access economy is better suited (Eckhardt & Bardhi, 2015). The term sharing economy should, thus, be reserved for a non-profit, peer-to-peer exchange. This vivid discussion comes along

Classification scheme

Classification schemes based on a so-called tuple-notation are often applied in the scientific literature to structure a field of optimization problems, such that each subproblem can concisely be identified and described by a tuple shortcut. The most prominent examples are those for machine scheduling and queuing systems initially introduced by Graham et al. (1979) and Kendall (1953), respectively. Further tuple-notations have, for instance, been provided for project scheduling (Brucker, Drexl,

Analysis of computational complexity

This section applies our classification scheme to systematically consider the resulting problem settings. Our focus is on analyzing the computational complexity of static and deterministic problem settings. For each single case we specify the tuple of our classification, give a brief example from the sharing economy, and settle the computational complexity by either providing a polynomial time algorithm or proving NP-hardness. We structure this section according to the movability of resources.

How to apply deterministic optimization-based matching on a sharing platform

This paper is dedicated to static and deterministic matching problems only. The real world, however, is typically dynamic, uncertain, and the participating agents behave opportunistic. This section assesses the suitability of a static and deterministic optimization-based planning in the aforementioned (i.e., dynamic, uncertain, and opportunistic) environments. Furthermore, we explore the potential of matchings resulting from sophisticated optimization compared to those based on customer choices

Future research needs and conclusion

This section concludes the paper by specifying important future research needs. We start with missing complexity results and proceed with issues on the successful application of optimization in the sharing economy.

Complexity issues: Although quite a few complexity results are obtained by identifying equivalent problems in the literature (and others by our own analysis in this paper), there are still problem settings left whose computational complexity remains open. Maybe the most interesting

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