Agent Scheduling MILP Model with Shift Length Constraints
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Solution Overview
Problem
Existing resource scheduling methods, such as those described in U.S. Pat. No. 7,725,339, do not allow for the specification of a minimum and maximum number of daily shifts with a specific length in agent schedules, limiting flexibility and adherence to agent availability and service targets.
Innovation Solution
A Mixed Integer Linear Programming (MILP) model and solution algorithm are developed to generate agent schedules that include constraints for minimum and maximum daily shifts, allowing for more flexible scheduling by formulating decision variables and objective functions to optimize scheduling criteria like cost and agent preference.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a MILP model allows varying daily shifts lengths, then scheduling flexibility is improved, but the ability to specify minimum and maximum number of daily shifts with specific length is lost
Solution Approach 1:
The patent segments the scheduling problem by introducing separate decision variables for different shift length categories (e.g., short shifts, long shifts) within the MILP model. This allows the system to specify minimum and maximum numbers of daily shifts with specific lengths while maintaining overall scheduling flexibility through the optimized allocation of these segmented shift types.
2Reliability
If agent schedules include minimum and maximum daily shift constraints, then adherence to agent availability is improved, but model complexity increases
Solution Approach 1:
The patent transforms the scheduling constraints into parameter-based formulations within the MILP model. By defining minimum and maximum shift counts as adjustable parameters rather than fixed structural constraints, the model achieves better adherence to agent availability while managing complexity through parameter optimization rather than complex constraint logic.
3Productivity
If the MILP model optimizes multiple scheduling criteria, then scheduling effectiveness is improved, but computational complexity increases
Solution Approach 1:
The patent creates a universal MILP model framework that can optimize multiple scheduling criteria simultaneously (e.g., coverage, cost, agent preference, skill matching) through a single integrated objective function. This multi-functional approach improves overall scheduling effectiveness while avoiding the computational complexity of multiple separate optimization runs by consolidating all criteria into one unified model.
Data Source
AI summary
A computer implemented method for agent scheduling using a Mixed Integer Programming (MILP) model, and a Mixed Integer Programming and Search Heuristic (MILP&SH) algorithm. The MILP model of the invention comprises of an objective function, decision variables, and constraints expressing tour group and shift template rules and required staffing levels as equations and inequalities. The MILP&SH algorithm comprises of an MILP solution algorithm and a search heuristic. The MILP solution algorithm applied to the MILP model to generate a plurality of solutions. If a solution generated by the MILP solution algorithm is an integer feasible solution, the search heuristic generates agent schedules. If a solution is not an integer feasible solution, the steps of the search heuristic are executed to find an integer feasible solution. The search heuristic compares the objective function value for an integer feasible solution found with the objective value for the best solution. If the integer feasible solution has a better objective function value, the best solution is replaced with the integer feasible solution. The MILP&SH algorithm iterates to generate integer feasible solutions, and updating the best solution and associated agent schedules. The MILP&SH algorithm terminates with a best solution found when one or more stopping conditions are satisfied.