Server Scheduling via Integer Programming Model Segmentation
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Solution Overview
Problem
Existing server scheduling systems face challenges in optimizing schedules due to the large number of variables and constraints in mixed integer linear programming models, making them impractical for industrial use, despite potential cost savings, as they exceed the cost savings and require significant computational resources.
Innovation Solution
A computer-implemented method and system that generates a mixed integer programming model with reduced variables and constraints by defining shift variables to include break times, allowing for optimized server scheduling with fewer variables, thus simplifying computational requirements and improving processor capability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional mixed integer linear programming models are used for server scheduling, then scheduling optimization can be achieved, but the large number of variables and constraints makes the system impractical for industrial use
Solution Approach 1:
The patent segments the scheduling problem by dividing the set of all possible shifts into a core set of representative shifts. Instead of considering every possible shift combination, the model segments the variable space by selecting only essential shifts that capture the fundamental scheduling patterns, thereby reducing complexity while maintaining optimization capability.
Solution Approach 2:
The patent extracts and removes non-essential variables and constraints from the traditional mixed integer linear programming model. By identifying and eliminating redundant shift variables and less critical constraints, the model achieves practical industrial applicability while retaining the core optimization functionality needed for reliable scheduling.
2Adaptability or versatility
If traditional mixed integer linear programming models with many variables are used, then comprehensive scheduling coverage is achieved, but computational resources are exceeded and costs outweigh savings
Solution Approach 1:
The patent segments the comprehensive set of shift variables into a manageable core set. By dividing the full variable space into essential and non-essential components, the model maintains adequate scheduling coverage for different service types and time periods while dramatically improving computational efficiency to practical levels.
Solution Approach 2:
The patent applies partial action by considering only the most critical shift variables and constraints needed for effective scheduling, rather than exhaustively modeling every possible scenario. This selective approach achieves sufficient scheduling coverage without the computational burden of complete coverage, making the system economically viable.
3Manufacturing precision
If break times are defined as separate variables from shift variables, then detailed break scheduling is achieved, but the number of variables increases significantly
Solution Approach 1:
The patent merges break time definition into the shift variable structure itself. Instead of creating separate variables for break times, the model integrates break scheduling directly within the shift variable definitions, thereby maintaining precise break scheduling capability while avoiding the variable explosion that would result from separate break variables.
Solution Approach 2:
The shift variables are designed to serve multiple functions simultaneously: they define both the work periods and the break periods within a single variable structure. This multi-functionality eliminates the need for separate break variables, reducing overall model complexity while preserving the precision needed for detailed break scheduling.
Data Source
AI summary
A system for scheduling servers is provided. The system receives a scheduling period, staffing requirements in planning intervals during the scheduling period, skill groups with one or more servers in each skill group, location, tour group, shift templates and associated scheduling rules for each server to be scheduled. The system generates a Mixed Integer Linear Programming model using this information. The system continues searching feasible solutions to the Mixed Linear Integer Programming model until one or more stopping criteria are satisfied by a terminal solution. The system generates detailed server schedules using the terminal solution to the Mixed Integer Linear Programming model.