Profit Maximization for a Robotics-as-a-Service Model

TL;DR

This work tackles profit maximization for a Robotics-as-a-Service operator managing a single robot under sequential customer demand. It integrates survival-analysis–based degradation modeling with inverse-optimization–driven learning to inform an MDP-based policy for joint pricing and robot replacement, with a three-phase online learning framework that first learns customer utilities, then degradation dynamics, and finally the optimal control policy. Empirical results from a discrete-time simulator demonstrate that the approach yields near-optimal profitability, with faster convergence for utility estimates than for degradation, and interpretable policy structure that balances revenue, holding costs, failures, and replacement costs. The framework offers a principled, data-driven method to manage pricing and lifecycle decisions in RaaS, with potential extensions to richer customer behaviors and stochastic decision rules.

Abstract

The growth of Robotics-as-a-Service (RaaS) presents new operational challenges, particularly in optimizing business decisions like pricing and equipment management. While much research focuses on the technical aspects of RaaS, the strategic business problems of joint pricing and replacement have been less explored. This paper addresses the problem of profit maximization for an RaaS operator operating a single robot at a time. We formulate a model where jobs arrive sequentially, and for each, the provider must decide on a price, which the customer can accept or reject. Upon job completion, the robot undergoes stochastic degradation, increasing its probability of failure in future tasks. The operator must then decide whether to replace the robot, balancing replacement costs against future revenue potential and holding costs. To solve this complex sequential decision-making problem, we develop a framework that integrates data-driven estimation techniques inspired by survival analysis and inverse optimization to learn models of customer behavior and robot failure. These models are used within a Markov decision process (MDP) framework to compute an optimal policy for joint pricing and replacement. Numerical experiments demonstrate the efficacy of our approach in maximizing profit by adaptively managing pricing and robot lifecycle decisions.

Figures (6)

• Figure 1: An example timeline illustrating the operational flow for the Robotics-as-a-Service (RaaS) provider. Upward arrows indicate the arrival of new customers ($x_i$). The robot's status alternates between being under rental ('R' in a green box) and idle ('I' in a purple box). The timeline also depicts key events like a price rejection from an arriving customer (diamond symbol), an unexpected robot failure during a job (star symbol), and a voluntary replacement initiated by the operator (heart symbol). The rewards associated with each period are shown above the timeline, reflecting revenues $\hat{u}^Tx_i$, holding costs $h\tau_i$, and costs for failure $F$ and replacement $R$.
• Figure 2: A diagram of the three-phase learning and control framework. Phase 1: The Projected Volume algorithm is run to obtain a reliable estimate of the customer utility vector, $\hat{u}$. Phase 2: This estimate is used to learn the degradation parameters $(\hat{\theta}, \hat{\lambda}_0)$ and train an initial control policy, $\hat{\pi}$. Phase 3: The system operates using this policy until a predefined number of new robot failures ($K$) occur. The data from these failures updates the dataset $\mathcal{D}_\theta$, which is then used to re-estimate the parameters and retrain the policy in a repeating cycle.
• Figure 3: Rolling average profit rate per time unit for the online learning policy and the oracle optimal policy, computed over a 10,000-unit window and averaged across 10 simulation runs with shaded standard deviations.
• Figure 4: $\ell_2$-norm estimation errors for utility vector $\widehat{u}$ (top) and degradation parameter $\widehat{\theta}$ (bottom) versus number of customers processed, showing means and standard deviations over 10 runs.
• Figure 5: Decision regions for job acceptance (purple) or shutdown (yellow) in the arrival phase, plotted against desired rental duration $T$ and cumulative degradation $\theta^\top X + \theta^\top x$, at selected percentiles of customer revenue $u^\top x$.

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3