Shift Design and Assignment via Linear MIP Transformation
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Solution Overview
Problem
Current methods for scheduling workers to cover demand are inefficient and fail to effectively model the complexity of shift design and shift assignment, often resulting in suboptimal solutions due to the inability to handle large multidimensional problems and express relevant constraints or cost functions easily.
Innovation Solution
A system that uses a processor to generate shift candidates, determine decision variables, and transform constraints and cost functions into linear forms, enabling the use of Mixed Integer Programming solvers to simultaneously design shifts and assign workers, thus optimizing the scheduling process while respecting labor laws, union contracts, and company policies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing approaches use complex decision variables to represent shift start/end time, then they can model shift design and assignment, but they cannot solve realistically sized problems and cannot express many relevant constraints or cost function terms easily
Solution Approach 1:
The patent segments the scheduling problem into two distinct components: shift design (determining shift patterns) and shift assignment (assigning workers to shifts). This is achieved by introducing binary decision variables that separately represent shift pattern selection and worker-shift assignment, allowing each component to be modeled and optimized independently while maintaining overall problem solvability for realistically sized instances
Solution Approach 2:
The patent introduces an intermediary element - a set of predefined shift patterns - that mediates between the labor demand requirements and worker assignments. These shift patterns serve as a bridge, allowing the model to express complex constraints and cost functions in terms of pattern selection and assignment decisions rather than directly modeling shift start/end times, thereby improving both modeling versatility and computational tractability
2Adaptability or versatility
If manual scheduling process is used, then it can handle constraints and objectives, but it consumes a great deal of time and cannot consider many objectives while ensuring constraints are not violated
Solution Approach 1:
The patent replaces the manual mechanical scheduling process with an automated mathematical optimization system. The mixed-integer programming model automatically considers multiple objectives (labor costs, overtime penalties, worker preferences) and numerous constraints (labor laws, union contracts, company policies) simultaneously, producing optimal schedules in computationally efficient time rather than requiring manual iteration through countless possibilities
3Productivity
If automated solution is used to solve large multidimensional problem, then it could reduce time consumption, but solving such large multidimensional problem is very difficult
Solution Approach 1:
The patent segments the large multidimensional scheduling problem into manageable components through the introduction of shift patterns as intermediate structures. By decomposing the problem into shift pattern definition, shift pattern selection, and worker assignment stages, the model reduces computational complexity while maintaining the ability to handle large-scale realistic scheduling problems efficiently
Solution Approach 2:
The patent changes the parameter representation from continuous shift start/end times to discrete shift pattern indices. This parameter transformation converts a complex continuous optimization problem into a more tractable discrete optimization problem that can be solved efficiently using mixed-integer programming, thereby improving productivity without sacrificing modeling accuracy
Data Source
AI summary
A system includes one or more processors; and at least one non-transitory machine-readable storage media comprising instructions which, when executed by the one or more processors, cause the one or more processors to: generate a set of shift candidates based on labor demand data; determine a set of decision variables representing whether a particular shift candidate is selected in a final schedule and whether a particular worker is assigned to the particular shift candidate; determine a set of constraints based at least in part on the set of decision variables, the set of shift candidates, the labor demand data, and scheduling configuration data, wherein a constraint of the set of constraints is transformed into linear form in terms of the set of decision variables; and determine simultaneously, using a MIP solver, a subset of the shift candidates selected in the final schedule and a set of shift assignments of which worker is assigned to which selected shift candidate of the subset of the shift candidates.