Problem Types

SolverForge can solve a wide variety of planning and scheduling problems. Here are some common categories:

Scheduling Problems

Assign activities to time slots and resources.

Employee Scheduling (Rostering)

Assign employees to shifts based on:

• Skills and qualifications
• Availability and preferences
• Labor regulations (max hours, rest periods)
• Fairness (balanced workload)

Examples: Hospital nurse scheduling, retail staff scheduling, call center scheduling

School Timetabling

Assign lessons to timeslots and rooms:

• Teachers can only teach one class at a time
• Rooms have limited capacity
• Student groups shouldn’t have conflicts
• Preference for consecutive lessons

Examples: University course scheduling, school class scheduling

Meeting Scheduling

Find optimal times for meetings:

• Required attendees must be available
• Rooms must be available and large enough
• Minimize conflicts with other meetings
• Consider timezone differences

Job Shop Scheduling

Schedule jobs on machines:

• Operations must follow a specific order
• Machines can only do one job at a time
• Minimize total completion time (makespan)

Examples: Manufacturing scheduling, print shop scheduling

Routing Problems

Plan routes and sequences for vehicles or resources.

Vehicle Routing Problem (VRP)

Plan delivery or service routes:

• Vehicle capacity constraints
• Time windows for deliveries
• Minimize total travel distance/time
• Multiple depots possible

Variants:

• CVRP - Capacitated VRP
• VRPTW - VRP with Time Windows
• PDPTW - Pickup and Delivery with Time Windows

Examples: Delivery route planning, field service scheduling, waste collection

Traveling Salesman Problem (TSP)

Visit all locations exactly once with minimum travel:

• Single vehicle
• Return to starting point
• Minimize total distance

Examples: Sales territory planning, circuit board drilling

Assignment Problems

Assign entities to resources or positions.

Task Assignment

Assign tasks to workers or machines:

• Match skills/capabilities
• Balance workload
• Meet deadlines
• Minimize cost

Examples: Project team assignment, warehouse task allocation

Bin Packing

Pack items into containers:

• Items have sizes/weights
• Containers have capacity limits
• Minimize number of containers used

Examples: Truck loading, cloud server allocation, cutting stock

Resource Allocation

Allocate limited resources to competing demands:

• Budget allocation
• Equipment assignment
• Space allocation

Complex Planning Problems

Real-world problems often combine multiple problem types:

Field Service Scheduling

Combines:

• Routing - Travel between customer locations
• Scheduling - Time windows and appointment slots
• Assignment - Match technician skills to job requirements

Project Planning

Combines:

• Task scheduling - Activities with durations and dependencies
• Resource assignment - Assign people/equipment to tasks
• Constraint satisfaction - Deadlines, budgets, availability

Problem Characteristics

When modeling your problem, consider these characteristics:

Choosing the Right Model

When modeling your problem:

1. Identify entities - What things need to be assigned or scheduled?
2. Identify variables - What values are you assigning?
3. Identify constraints - What rules must be followed?
4. Define the score - How do you measure solution quality?

The Quickstarts section provides complete examples for common problem types.