The Optimal Contract Design And Scheduling With Dual Sources In Ride-hailing Services

The ride-hailing services have become popular options for urban citizens because of the widespread use of smart mobile devices and great achievements in communications technologies.The demand for ride-hailing services usually exhibits high uncertainty and fluctuates considerably across time and space.Mitigating the temporal or spatial imbalances between demand and supply has become a critical issue for ride-hailing platforms.Currently,platforms rely on freelancers to provide services,who enjoy high flexibility in choosing when and where to provide services.Moreover,these freelancers usually make self-interested decisions and feature heterogeneous preferences for service locations or working hours.It has been a challenge for the platforms to guide or incentivize drivers to provide services when and where they are most needed.This poses a great challenge for platforms to manage the workforce and balance demand and supply.Although extensive research has been conducted on the ride-hailing market’s pricing and scheduling optimization,most studies primarily considered single sourcing.A theoretical modeling framework of pricing and scheduling optimization for heterogeneous labor sources has not been developed.To ensure a reliable labor supply while retaining flexible scheduling for those freelancers,this paper investigates dual sourcing.In addition to existing freelancers,platforms can recruit a certain number of contractual drivers who are required to work at specific hours and follow the platform’s guidance on idle movements.In the context of two-sided markets,this paper investigates how to optimize the contract design and schedule and dispatch contractual drivers such that the market demand and supply becomes more balanced and platforms’ profits are maximized.Leveraging equilibrium analysis and optimization theory,this paper examines contract design and scheduling optimization under dual sourcing.We follow an approach of ”market equilibrium analysis-contract design and scheduling or dispatching optimization-algorithm design-case study” and discuss dual sourcing on two levels.First,at the strategic level,we discuss the optimal contract and analyze the applicability conditions of dual sourcing.Second,at the planning level,we consider spatiotemporal demand-supply imbalances and investigate the optimal empty vehicle dispatch and working hour scheduling of contractual drivers.In more detail,our study models dual sourcing from four aspects.First,to cope with demand uncertainty,this paper develops an aggregate modeling framework to examine the practicability of such a dual-sourcing strategy.We characterize the market equilibrium and investigate the optimal contract design of dual sourcing under the varying price sensitivity of freelancers and heterogeneity in drivers’ risk attitudes.More specifically,assuming contractual drivers are paid fixed salaries for hedging risks,the upper-level contract design optimizes service price for customers,freelancer’s earnings per completed order,and contractual driver’s salary.The lower market equilibrium characterizes the interaction between market demand,drivers’ contractual choices,and freelancers’ participating decisions.We prove the existence of market equilibrium under dual sourcing and analyze the price structure of optimal dual sourcing supply contracts.Via analytical models and numerical experiments,we examine the applicable conditions of the dual sourcing strategy and its impacts on various market stakeholders.This work provides a theoretical foundation for implementing dual sourcing in ride-hailing markets.Second,to address the spatial demand-supply mismatch,we explore how to optimize contractual drivers’ idle movements to control supply distribution over the network.Freelancers and contractual drivers feature heterogeneous cruising behaviors,with freelancers searching for customers following their preferences whilst contracted drivers repositioning in a centralized manner as system actuators.We devise a mixed equilibrium model to capture the interplay between the idle repositioning movements of both parties,and their impacts on the market demand.A fixed-point algorithm is developed to solve the market equilibrium and the real-world data is invited to quantify the impacts of dual sourcing on various market sectors.Our numerical results confirm the effectiveness of the dual sourcing strategy in balancing spatial demand and supply.This work provides theoretical support for the platform’s dispatching decisions.Third,to address the temporal demand-supply mismatch,we explore how to schedule contractual drivers’ working hours to control supply distribution over the temporal dimension.We develop a bi-level model to optimize the schedules of contractual drivers and characterize the interaction between two types of drivers.The schedule optimization is transformed into a network design problem.The lower-level market equilibrium model takes drivers’ working-time preferences and freelancers’ strategic behaviors into account.We use the routes over a time-expanded network to represent workers’ schedules and a network flow model as a proxy for the freelancers’ scheduling decisions.The upper level optimizes the schedules of contractual drivers and their salaries considering the reaction of freelancers.Our numerical results identify the working-time preferences as key factors impacting the potential of the dual sourcing strategy.This work provides theoretical support for the platform’s scheduling decisions.Finally,we further introduce dual sourcing into oligopoly markets where several platforms compete with other.We investigate the contract design and optimal scheduling decisions for contractual drivers.We model the contract design problem as a hierarchical single-leader multi-follower game and explore the impacts of localized scheduling coordination on the competition among platforms.Given the contract,we model the platform competition as a non-cooperative game.Each platform is a strategic player that schedules its contractual drivers to maximize total utility under drivers’ individual rationality conditions.At the upper level,we propose a novel contract design to guide the market equilibrium and balance demand and supply.We formulate the contract design problem as a program of mathematical programming with equilibrium constraints.A solution algorithm integrating Bayesian optimization and quasi-variational inequalities is developed to obtain the optimal contract design.Our numerical results identify key factors impacting the competition outcomes and contract design.This work provides a theoretical foundation for implementing dual sourcing in oligopoly markets.This study attempts to explore the potential of the dual sourcing strategy considering the heterogeneity of contractual drivers and freelancers.We develop the model framework covering the aggregated model,spatial dispatching,and temporal scheduling decisions.This work extends previous studies on ride-hailing services and provides theoretical foundations for applying the dual sourcing strategy in the ride-hailing market.