Workforce Scheduling via Shift Enumeration and MILP
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Solution Overview
Problem
Existing scheduling technologies face challenges in efficiently generating workforce schedules due to the complexity of NP-hard optimization problems, leading to high computational resource consumption and suboptimal solutions.
Innovation Solution
The implementation of heuristic approaches, including shift enumeration and mixed integer linear programming (MILP), to efficiently generate workforce schedules by decomposing the scheduling problem, enumerating candidate shifts, and applying mathematical programming techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If brute force or mathematical programming approaches are used to solve the scheduling problem, then solution quality may be improved, but computational resource consumption becomes prohibitively large
Solution Approach 1:
The scheduling problem is segmented into two distinct phases: (1) shift enumeration phase where candidate shifts are generated and stored, and (2) optimization phase where MILP is applied to select from pre-generated candidates. This segmentation allows the computationally intensive enumeration to be performed once, followed by more efficient optimization, thereby reducing overall computational resource consumption while maintaining solution quality.
Solution Approach 2:
Candidate shifts are enumerated and stored in advance before the optimization process begins. This preliminary action creates a ready pool of feasible shifts that can be quickly evaluated during optimization, eliminating the need to generate shifts during the optimization phase and significantly reducing computational resource requirements.
2Productivity
If traditional scheduling approaches are used, then computational resources are consumed, but the time required to generate schedules becomes prohibitively large
Solution Approach 1:
The schedule generation process is divided into shift enumeration and optimization phases, allowing parallel processing and more efficient utilization of computational resources. This segmentation enables the system to generate schedules faster by distributing the computational workload across different stages.
Solution Approach 2:
By pre-enumerating and storing candidate shifts before optimization, the system eliminates the time-consuming task of generating shifts during the optimization phase. This preliminary preparation significantly reduces the total time required to generate schedules while maintaining productivity.
3Reliability
If the scheduling problem is solved as a whole, then comprehensive optimization is achieved, but the problem complexity makes it NP-hard and difficult to solve
Solution Approach 1:
The complex NP-hard scheduling problem is segmented into a shift enumeration subproblem and an optimization subproblem. The enumeration phase generates feasible shifts without requiring complex optimization, while the MILP phase focuses on selecting optimal shifts from the pre-generated pool. This segmentation reduces problem complexity while maintaining optimization completeness.
Solution Approach 2:
The pool of enumerated candidate shifts acts as an intermediary between the enumeration phase and the optimization phase. This intermediary structure allows the system to bridge the gap between generating feasible schedules and optimizing them, reducing the overall problem complexity by breaking it into manageable stages.
Data Source
AI summary
An example method of workforce scheduling includes: identifying a plurality of variables associated with scheduling a plurality of workers to perform a plurality of jobs during respective shifts defined by corresponding time periods, wherein each variable is associated with a corresponding shift; identifying a scheduling problem for optimizing an objective function defined on the plurality of variables subject to a plurality of constraints; identifying, based on a historic schedule assigning at least a subset of the plurality of workers to perform at least a subset of the plurality of jobs during a plurality of past time periods, a subset of the plurality of variables; determining, based on the subset of the plurality of variables, a tentative solution of the scheduling problem; responsive to determining that the tentative solution fails a predefined quality criterion, modifying the tentative solution; and generating a schedule based on the modified tentative solution.