Unlocking 100% Fill Rates with Dynamic Bonusing

At WorkWhile, our mission is simple yet powerful: Help workers earn a better living by revolutionizing how workers and companies connect. The Data Science team supports this mission by designing and developing algorithms that intelligently and dynamically adjust our various marketplace levers to ensure that every work opportunity is filled and every worker reaches their full potential.

One common challenge that all labor marketplaces face is unexpected fluctuations to supply and demand conditions, which is compounded by significant variability in the type of work being requested (shift characteristics such as long distances, odd hours, etc.). To address both the random movements in supply-demand conditions and predictability in shift attractiveness, we've developed a Dynamic Bonusing System designed to adaptively incentivize workers based on real-time market conditions and taking into account specific shift characteristics. This approach helps ensure a marketplace that can absorb transient shocks and maintain the very best fill rates across all types of work.

Supply-Demand Dynamics

As a large and diverse marketplace, we naturally see strong day-to-day movements in supply – proxied by workers viewing shift listings – and demand – represented by the number of workers requested. If there’s unexpected inclement weather in a particular market, for example, workers may be less engaged and interested in work. On the company side, if there’s an unexpected surge in warehouse orders, for example, the company will request more workers from our platform to close their staffing gap.

The histogram plot below shows the probability density distribution of the supply-demand ratio for each day of the week, with the ratio scaled to equal 1 at its peak per geographical market. Based on this plot, there’s strong evidence of temporary shocks, where across the same days of the week there’s wide dispersion in the distribution of the supply-demand ratio, indicating the occurrence of extreme values. Such shocks, without intervention, set the stage for too little supply to meet demand.

Again, such variance is common across all labor marketplaces, and WorkWhile has invested in building out a bonus system that reacts to such shocks and scales effectively toward 100% fill rates.

Introducing Dynamic Bonusing

The core principle behind our bonus system is that we want to discover the true market clearing bonus amount by searching across different bonus amounts until the shift appears attractive enough to fill. This optimization process leverages a data-driven model of shift attractiveness and real-time market signals that predict the likelihood of a shift filling, and based on the estimated relationship between total shift earnings and fill we balance the benefit of successfully filled shifts against the cost of additional bonuses.

System Overview

1. Data Ingestion: We pull data around key parameters of the shift needed for our subsequent modeling. These include:

   • Dynamic state of shift such as historical and current sign-up rates
   • Static shift features such as base hourly wage, market, job type
   • Overall historical data in the market conditions of the specific shift such as show rates, effective hourly wages etc. This effectively adds in marketplace context and incorporates seasonality and trends for a more robust and adaptive model

2. Sign-Up Rate Interpolation: Using the historical data of the selected shift, we leverage a simple interpolation approach to predict future sign-up rates. Historical data has proven the following fit to most accurately represent the relationship between future and past states.

   $$X = Signup\ Rate_{(t)} = \beta_1 \cdot Signup\ Rate{(t-1)} - \beta_2 \cdot Signup\ Rate{(t-2)}$$

3. Markup Function: Assuming a strong causal relationship between bonus magnitude and the sign-up rate, it becomes essential to quantify how far a shift is from its fulfillment target in order to calibrate incentives effectively. This is precisely why our markup function is anchored to the observed sign-up rate at each point in time. By conditioning the markup on real-time sign-up performance, the model serves a dual role:

   • Proactive, by establishing an initial bonus informed by historical norms and market characteristics.
   • Reactive, by adjusting the bonus dynamically in response to lagging sign-ups as the shift start time approaches.

   The markup is computed via the equation below, with 𝛼, 𝛽, and 𝛾 being learned through optimization. This markup is conservative at first to limit costs and becomes progressively aggressive if worker sign-ups remain below requirements as the shift approaches. This ensures that we remain economical with bonuses, providing just enough incentive to clear the market effectively.

   $$\mathit{Markup} = 1 + (\alpha \cdot e^{-\beta X} - \gamma)$$

   By coupling time sensitivity with real-time fulfillment signals, the markup acts as a dynamic economic control mechanism, ensuring we offer just enough incentive to achieve market clearance — without overspending.

4. Objective Function: We employ an objective function that incorporates two key components: the cost of bonuses and the economic impact of gaps in shift fill. For each bonus amount, we calculate the margin between these two components, and conduct a search for the bonus amount that optimizes for the following negative-margin loss function:

   $$MIN \left( \mathit{Bonus} - \mathit{ShowRate} \times \mathit{Wages} \right)$$ $$\mathit{s.t.} \ \mathit{Bonus} \geq 0$$

5. Show-Rate Regression Model: Unlike sign-up rate, which reflects interest, the show rate reflects true labor fulfillment – the outcome that directly impacts operational success and cost efficiency. We fit a nonlinear regression model based on historical show-rate data, segmented by market, job position, and shift type, in order to map the causal relationship between wage and worker reliability.

   $$\mathit{Show Rate}_{\mathit{Shift}} = f(\mathit{Bonus}, \mathit{Position}, \mathit{Market}, \mathit{Wage})$$

   This model layer effectively decouples worker interest from worker attendance or reliability, with the former being used to gauge the model aggressiveness, while the latter is used to make sure we optimize for reliability and not just intent.

6. Minimization: We leverage the Nelder-Mead algorithm to find the minimum of our objective function. Nelder-Mead is a derivative-free optimization algorithm that uses geometric operations (reflection, expansion etc.) to minimize a set of candidate solutions. In our case, with every single evaluation, the algorithm hops around different parameters to compute bonus amounts in order to discover the global minimum of the negative margin.

7. Deployment & Feedback Loop: Our model runs automatically every 30 minutes for every listed shift, starting 24 hours before the shift begins. This frequent iteration ensures rapid responsiveness to changes in worker signup trends, therefore allowing for dynamic corrections if needed.

Challenges and Mitigations

Systems that rely on fitted regression models rely heavily on historical data. This dependency can be problematic in newly entered markets or job categories with sparse data. To mitigate this, we implement conservative initial bonus assumptions, gradually becoming more aggressive as we gather sufficient market response data.

Results and Benefits

The implementation of our Dynamic Bonusing System has shown substantial benefits:

Higher Shift Fill Rates: We consistently achieve significantly improved fill rates compared to manual, nondynamic methods, closely approaching our 100% target Enhanced Worker Satisfaction: Workers perceive bonuses positively, recognizing a marketplace that values the time, effort, and other intrinsics of a shift accurately

Looking Ahead

Moving forward, we plan to further refine our Dynamic Bonusing System. Areas for improvement include incorporating even richer real-time data and experimenting with more sophisticated optimization techniques such as reinforcement learning.

At WorkWhile, we remain committed to harnessing data and technology to unlock economic opportunities. Our dynamic bonusing system is just one of the many steps towards achieving optimal market conditions where every shift is reliably filled. All of these levers are in service of helping workers find work that works for them, ultimately helping them earn a better living and live better lives. We invite you to check out our careers page, follow us on LinkedIn, and join us on this journey in building the future of work.