Sequential Job Assignment Using Non-Parametric Threshold Curves
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Solution Overview
Problem
Existing methods for assigning jobs with random arrival times, such as in financial fraud detection and cybersecurity, struggle to optimally allocate resources due to the impracticality of solving systems of ordinary differential equations (ODEs) and the impracticality of exhaustive manual inspection, especially when the job arrival process is unknown.
Innovation Solution
A non-parametric stochastic sequential allocation algorithm that generates time-varying threshold curves based on historical job data to determine whether to accept or decline jobs, maximizing the expected cumulative reward value by using an unknown cumulative distribution and mean shortage function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a system of ordinary differential equations (ODE) is used to optimally assign jobs, then the assignment optimality is improved, but the computational complexity and practical solvability deteriorate
Solution Approach 1:
The patent replaces the complex, expensive ODE-based solution with a simple, computationally inexpensive threshold-based rule. Each job is evaluated against a pre-computed threshold value, and the decision is made immediately without solving differential equations. This disposable, simple rule achieves near-optimal results with minimal computational overhead.
Solution Approach 2:
The patent substitutes the mechanical/mathematical system of solving ODEs with a statistical learning approach. Instead of using deterministic differential equations, the system learns optimal thresholds from historical data using empirical cumulative distribution functions, replacing complex mathematical mechanics with data-driven statistical mechanics.
2Measurement precision
If exhaustive manual inspection is performed on all jobs, then the detection accuracy is improved, but the time consumption and operational capacity deteriorate
Solution Approach 1:
The patent applies different inspection strategies to different jobs based on their characteristics. High-value jobs that exceed the threshold receive full manual inspection, while low-value jobs are automatically declined without inspection. This local differentiation of inspection quality optimizes both accuracy and time consumption by focusing resources on the most valuable cases.
Solution Approach 2:
Instead of performing exhaustive inspection on all jobs (excessive action), the system performs partial inspection only on jobs that meet certain criteria (those exceeding the threshold). This partial action approach achieves sufficient detection accuracy for the most valuable jobs while dramatically reducing overall time consumption and operational burden.
3Reliability
If the job arrival process is assumed to be known with closed-form expression, then the theoretical optimality is improved, but the adaptability to unknown processes deteriorates
Solution Approach 1:
The system is self-adapting and learns the job arrival process automatically from historical data without requiring external specification of the arrival process. The empirical cumulative distribution function is computed directly from observed data, allowing the system to serve itself by learning the underlying process characteristics and adjusting thresholds accordingly.
Solution Approach 2:
The patent changes the approach from assuming fixed known parameters (closed-form arrival process) to estimating parameters empirically from data. The threshold values are not fixed theoretically but are derived from the empirical distribution of historical job values, allowing the system to adapt to changing arrival processes and unknown distributions.
Data Source
AI summary
A method and a system for performing stochastic sequential assignment of jobs with random arrival times is provided. The method includes receiving a first plurality of jobs in a sequence; and sequentially applying, to each respective job from among the first plurality of jobs, a non-parametric sequential allocation algorithm in order to determine whether to accept the respective job or to decline the respective job. The application of the non-parametric sequential allocation algorithm includes calculating, for each respective job, a corresponding reward value that relates to a reward that is gained when the respective job is accepted; and maximizing an expected cumulative reward value based on the calculated reward values.