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.

Hospital Scheduling

Assign hospital staff to shifts based on:

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

Examples: Hospital nurse scheduling, ward coverage planning, specialty rota planning

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:

Characteristic	Description	Example
Hard constraints	Must be satisfied	Legal requirements
Soft constraints	Should be optimized	Customer preferences
Planning entities	What gets assigned	Lessons, visits, shifts
Planning variables	The assignments	Timeslot, room, vehicle
Problem facts	Fixed data	Employees, rooms, skills

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 Getting Started section provides complete examples for common problem types.