Efficient Workforce Planning: A Challenge for Many Industries

Efficient staff scheduling is a pivotal challenge across a wide range of industries. Hospitals constitute a concrete example, as they must balance individual workloads while preventing short staffing and adhering to regulations by tracking medical certifications. The schedules must be highly resilient to sudden workforce changes and safeguard professionals from clinical errors caused by fatigue.

Hospitals employ this technique to ensure their staff is never overworked and always prepared to deliver the highest quality care. This is just one example industry, but it can be applied to many other industries as well.

How does Mixed Integer Linear Programming help with Workforce Scheduling?

Consider a workforce scheduling problem in a manufacturing workshop with four workstations that require a seven-day planning horizon with two shifts per day.

Each of the four workstations requires four qualified workers per shift. The workforce comprises two types of employees: temporary and contractual.

• Contractual Workers: Work five shifts per week, assigned based on eligibility for specific workstations, costing 150 Euros per shift. They cannot work more than one consecutive shift.
• Temporary Workers: Flexible, can be assigned to any workstation, costing 300 Euros per shift (this can also be the vacancy cost).

The objective is to create an optimal schedule that meets the following requirements:

• Satisfy the demand at each workstation (e.g., four workers per workstation)
• Adhere to labor regulations (e.g., working hour limits, no consecutive shifts)
• Comply with eligibility criteria (e.g., qualification for specific tasks)
• Minimize total labor costs

This tutorial equips healthcare administrators, industry managers, and staff planners to use Quantagonia’s HybridSolver for optimal workforce scheduling.

How to Implement Mixed Integer Linear Programming for Workforce Scheduling in Python

Implementing an optimization problem in Python is a straightforward process:

1. Define Problem Parameters (e.g., Salary and Capacity)
2. Define Objective Function (e.g., Minimize Cost)
3. Define Constraint Functions (e.g., Max Working Hours)
4. Run the Model (with HybridSolver)
5. Process the Results

Following this structured approach ensures clarity and makes it easier to understand and modify the code in the future.

Code Implementation: Optimizing Workforce Scheduling

At its core, we are tackling a workforce scheduling challenge using principles from operations research. This means optimizing shift assignments and ensuring qualified staff are available for each task while meeting all necessary constraints. The goal is to provide the highest quality outcome while ensuring employee satisfaction by combining several well-known Integer Programming problems:

• Shift Assignment (Assignment Problem)
• Workload Balancing (Load Balancing Problem)
• Worker Eligibility (Set Covering Problem)
• Maximal Shift Limit (Knapsack Problem)
• Non-Consecutive Shifts (Sequencing Problem)

In combination, the algorithm solves for an optimal shift plan that meets the demand while distributing work equitably among employees within a MILP Problem. Each shift is covered by a qualified professional, ensuring no worker exceeds the allowed workload.

Next, we utilize the HybridSolver to determine the most efficient workforce schedule.

The solution balances using temporary and contractual workers to meet operational demands cost-effectively. However, scheduling can become more complex with temporal variations in demand, additional constraints, and a larger workforce. Try it out for yourself. Here is the code implementation of the tutorial.