mcp-optimizer

# Routing & Scheduling - Usage Examples ## Description Routing and scheduling problems optimize the sequence of operations, route construction, and resource allocation over time to minimize costs and time. ## Example Prompts for LLM ### Example 1: Traveling Salesman Problem (TSP) ``` Help me solve a traveling salesman problem using MCP Optimizer. A sales representative must visit 8 cities and return to the starting point: Cities: New York, Boston, Philadelphia, Washington, Baltimore, Richmond, Norfolk, Raleigh Distance matrix (miles): NYC BOS PHL WAS BAL RIC NOR RAL New York 0 215 95 230 185 290 340 480 Boston 215 0 310 440 395 500 550 690 Philadelphia 95 310 0 135 100 205 255 395 Washington 230 440 135 0 40 110 160 300 Baltimore 185 395 100 40 0 150 200 340 Richmond 290 500 205 110 150 0 50 190 Norfolk 340 550 255 160 200 50 0 140 Raleigh 480 690 395 300 340 190 140 0 Additional conditions: - Start and end route in New York - Working hours: 8 hours per day - Average speed: 60 mph - Need to spend 1 hour in each city Find the shortest route to visit all cities. ``` ### Example 2: Vehicle Routing Problem (VRP) ``` Use MCP Optimizer to plan delivery routes. A delivery service has: - 4 trucks with different capacities - 15 delivery points - Central warehouse Trucks: - Truck 1: capacity 5 tons, cost $200/day - Truck 2: capacity 3 tons, cost $150/day - Truck 3: capacity 8 tons, cost $300/day - Truck 4: capacity 2 tons, cost $120/day Delivery points (cargo weight in tons): 1. Store A: 0.8 tons 2. Store B: 1.2 tons 3. Office C: 0.3 tons 4. Warehouse D: 2.5 tons 5. Restaurant E: 0.6 tons 6. Pharmacy F: 0.2 tons 7. School G: 0.9 tons 8. Hospital H: 1.1 tons 9. Factory I: 3.2 tons 10. Store J: 0.7 tons 11. Office K: 0.4 tons 12. Warehouse L: 1.8 tons 13. Cafe M: 0.5 tons 14. Gym N: 0.6 tons 15. Library O: 0.3 tons Delivery time windows: - Morning (9-12): points 1,3,5,7,11,15 - Afternoon (12-15): points 2,4,6,8,12,14 - Evening (15-18): points 9,10,13 Constraints: - Working day: 8 hours - Maximum distance per truck: 200 km - Mandatory return to warehouse Minimize total delivery costs. ``` ### Example 3: Employee Shift Scheduling ``` Solve a shift scheduling problem with MCP Optimizer. A 24/7 call center requires coverage with minimum staff: Shifts: - Morning (8-16): minimum 15 operators - Evening (16-24): minimum 20 operators - Night (0-8): minimum 8 operators Available employees (25 people): - Full-time: 15 people (can work any shift) - Part-time: 10 people (day shifts only) Constraints: - Maximum 5 shifts per week per person - Minimum 2 consecutive days off - Cannot work consecutive shifts - Night shifts only for full-time employees Additional requirements: - Increase coverage by 20% on weekends - Experienced operators (5 people) must be in each shift - New hires (3 people) cannot work nights Minimize total working hours while ensuring coverage. ``` ### Example 4: Production Order Scheduling ``` Help schedule production orders with MCP Optimizer. A factory has 5 machines and 12 orders to complete: Machines: - Machine A: universal, 16 hours/day - Machine B: lathe, 20 hours/day - Machine C: milling, 18 hours/day - Machine D: drilling, 22 hours/day - Machine E: grinding, 14 hours/day Orders (processing time in hours on each machine): A B C D E Due Priority Order 1 8 6 - 4 2 3days 1 Order 2 12 - 10 6 4 5days 2 Order 3 6 4 8 - 3 2days 1 Order 4 - 8 12 10 6 7days 3 Order 5 10 6 - 8 5 4days 2 Order 6 4 - 6 3 2 1day 1 Order 7 14 10 16 12 8 10days 3 Order 8 8 6 10 - 4 6days 2 Order 9 - 4 8 6 3 3days 1 Order 10 12 8 - 10 6 8days 3 Order 11 6 - 4 2 1 2days 1 Order 12 10 8 12 8 5 9days 2 Constraints: - Priority 1 orders must be completed first - Some operations cannot be done on certain machines (-) - Machine setup between orders: 1 hour - Late penalty: $100/day Minimize total completion time and penalties. ``` ### Example 5: School Bus Routing ``` Optimize school bus routes with MCP Optimizer. A school district serves 3 schools with 6 buses: Schools: - Elementary: 450 students, hours 8:00-15:00 - Middle: 600 students, hours 8:30-15:30 - High: 800 students, hours 9:00-16:00 Buses: - Bus 1: 45 seats, depot A - Bus 2: 60 seats, depot A - Bus 3: 45 seats, depot B - Bus 4: 72 seats, depot B - Bus 5: 45 seats, depot C - Bus 6: 60 seats, depot C Stops (number of students by school): Stop 1: [25, 15, 20] - elementary, middle, high Stop 2: [30, 25, 35] Stop 3: [20, 30, 25] Stop 4: [35, 20, 30] Stop 5: [15, 25, 20] Stop 6: [25, 35, 40] Stop 7: [40, 30, 35] Stop 8: [20, 15, 25] Stop 9: [30, 40, 45] Stop 10: [25, 20, 30] Constraints: - Travel time to school: maximum 45 minutes - Bus can serve only one school per trip - Need 2 trips: morning and afternoon - Distance between stops: 5-15 minutes Minimize total travel time and number of buses used. ``` ### Example 6: Medical Procedure Scheduling ``` Help schedule medical procedures with MCP Optimizer. A hospital has 4 operating rooms and 15 scheduled surgeries: Operating Rooms: - OR 1: general surgery, 12 hours/day - OR 2: cardiac surgery, 10 hours/day - OR 3: neurosurgery, 8 hours/day - OR 4: universal, 14 hours/day Surgeries: 1. Appendectomy: 2 hours, OR 1 or 4, medium priority 2. Heart surgery: 6 hours, OR 2 only, high priority 3. Brain tumor removal: 8 hours, OR 3 only, high priority 4. Cholecystectomy: 3 hours, OR 1 or 4, low priority 5. Coronary bypass: 5 hours, OR 2 only, high priority 6. Hernia repair: 1.5 hours, OR 1 or 4, low priority 7. Spine surgery: 4 hours, OR 3 or 4, medium priority 8. Gastric resection: 4 hours, OR 1 or 4, medium priority 9. Valve replacement: 7 hours, OR 2 only, high priority 10. Craniotomy: 6 hours, OR 3 only, high priority 11. Laparoscopy: 2 hours, OR 1 or 4, low priority 12. Stenting: 3 hours, OR 2 only, medium priority 13. Cataract removal: 1 hour, OR 4, low priority 14. Arthroscopy: 2.5 hours, OR 4, low priority 15. Tonsillectomy: 1.5 hours, OR 1 or 4, low priority Constraints: - High priority surgeries must be completed first - 30 minutes preparation between surgeries - Some surgeries require special equipment - Working day: 7:00-19:00 Maximize number of completed surgeries considering priorities. ``` ### Example 7: Tournament Scheduling ``` Plan a tournament schedule with MCP Optimizer. A football league runs a championship with 12 teams: Teams: A, B, C, D, E, F, G, H, I, J, K, L Stadiums: - Stadium 1: capacity 50,000, rent $10,000/day - Stadium 2: capacity 30,000, rent $6,000/day - Stadium 3: capacity 40,000, rent $8,000/day - Stadium 4: capacity 25,000, rent $5,000/day Constraints: - Each team plays every other team twice (home and away) - Season lasts 22 rounds (6 matches per round) - Matches on weekends only - Minimum 2 weeks between home matches for each team - Derby matches (A-B, C-D, E-F) at large stadiums Team popularity (expected attendance): A: 45,000, B: 40,000, C: 35,000, D: 30,000 E: 25,000, F: 20,000, G: 18,000, H: 15,000 I: 12,000, J: 10,000, K: 8,000, L: 6,000 Ticket price: $50 (average) Maximize ticket revenue minus stadium rent. ``` ### Example 8: Equipment Maintenance Scheduling ``` Optimize equipment maintenance schedule with MCP Optimizer. A manufacturing plant has 20 pieces of equipment and 5 service teams: Equipment (hours until scheduled maintenance): 1. Machine A1: 120 hours, high criticality 2. Machine A2: 80 hours, medium criticality 3. Conveyor B1: 200 hours, high criticality 4. Conveyor B2: 150 hours, high criticality 5. Press C1: 60 hours, medium criticality 6. Press C2: 90 hours, medium criticality 7. Furnace D1: 300 hours, high criticality 8. Furnace D2: 250 hours, high criticality 9. Compressor E1: 100 hours, low criticality 10. Compressor E2: 140 hours, low criticality 11. Pump F1: 50 hours, medium criticality 12. Pump F2: 70 hours, medium criticality 13. Generator G1: 180 hours, high criticality 14. Generator G2: 160 hours, high criticality 15. Fan H1: 40 hours, low criticality 16. Fan H2: 30 hours, low criticality 17. Crane I1: 110 hours, medium criticality 18. Crane I2: 130 hours, medium criticality 19. Robot J1: 220 hours, high criticality 20. Robot J2: 190 hours, high criticality Service Teams: - Team 1: mechanics, 8 hours/day, $500/day - Team 2: electricians, 8 hours/day, $600/day - Team 3: universal, 10 hours/day, $700/day - Team 4: robot specialists, 6 hours/day, $800/day - Team 5: emergency, 12 hours/day, $1000/day Maintenance time (hours): - Machines: 4 hours (teams 1,3) - Conveyors: 6 hours (teams 1,2,3) - Presses: 3 hours (teams 1,3) - Furnaces: 8 hours (teams 2,3) - Compressors: 2 hours (teams 1,2,3) - Pumps: 2 hours (teams 1,2,3) - Generators: 5 hours (teams 2,3) - Fans: 1 hour (teams 1,2,3) - Cranes: 3 hours (teams 1,3) - Robots: 6 hours (teams 3,4) Constraints: - Critical equipment cannot be stopped simultaneously - 4-week planning horizon - Emergency team only for urgent cases - Weekends: emergency work only Minimize maintenance costs while meeting schedule. ``` ## Request Structure for MCP Optimizer ```python # Example for routing problem result = solve_routing_problem( locations=["A", "B", "C", "D"], distance_matrix=[ [0, 10, 15, 20], [10, 0, 35, 25], [15, 35, 0, 30], [20, 25, 30, 0] ], problem_type="TSP", # or "VRP" constraints={ "time_windows": [(8, 17), (9, 16), (10, 18), (8, 15)], "capacity": 100 } ) ``` ## Typical Activation Phrases - "Solve a traveling salesman problem" - "Optimize delivery routes" - "Schedule employee shifts" - "Find optimal operation sequence" - "Help with resource planning" - "Create work schedule" - "Optimize time intervals" ## Applications Routing and scheduling problems are used in: - Logistics and delivery - Production planning - Personnel management - Medical scheduling - Transportation systems - Sports tournaments - Equipment maintenance