mcp-optimizer

This tool solves general linear programming problems where you want to optimize a linear objective function subject to linear constraints. Use cases: - Resource allocation: Distribute limited resources optimally - Diet planning: Create nutritionally balanced meal plans within budget - Manufacturing mix: Determine optimal product mix to maximize profit - Investment planning: Allocate capital across different investment options - Supply chain optimization: Minimize transportation and storage costs - Energy optimization: Optimize power generation and distribution Args: objective: Objective function with 'sense' ("minimize" or "maximize") and 'coefficients' (dict mapping variable names to coefficients) variables: Variable definitions mapping variable names to their properties (type: "continuous"/"integer"/"binary", lower: bound, upper: bound) constraints: List of constraints, each with 'expression' (coefficients), 'operator' ("<=", ">=", "=="), and 'rhs' (right-hand side value) solver: Solver to use ("CBC", "GLPK", "GUROBI", "CPLEX") time_limit_seconds: Maximum time to spend solving (optional) Returns: Optimization result with status, objective value, variable values, and solver info Example: # Maximize 3x + 2y subject to 2x + y <= 20, x + 3y <= 30, x,y >= 0 solve_linear_program( objective={"sense": "maximize", "coefficients": {"x": 3, "y": 2}}, variables={ "x": {"type": "continuous", "lower": 0}, "y": {"type": "continuous", "lower": 0} }, constraints=[ {"expression": {"x": 2, "y": 1}, "operator": "<=", "rhs": 20}, {"expression": {"x": 1, "y": 3}, "operator": "<=", "rhs": 30} ] )

This tool solves optimization problems where some or all variables must take integer values, which is useful for discrete decision problems. Use cases: - Facility location: Decide where to build warehouses or service centers - Project selection: Choose which projects to fund (binary decisions) - Crew scheduling: Assign integer numbers of staff to shifts - Network design: Design networks with discrete components - Cutting stock: Minimize waste when cutting materials - Capital budgeting: Select investments when partial investments aren't allowed Args: objective: Objective function with 'sense' and 'coefficients' variables: Variable definitions with types "continuous", "integer", or "binary" constraints: List of linear constraints solver: Solver to use ("CBC", "GLPK", "GUROBI", "CPLEX") time_limit_seconds: Maximum time to spend solving (optional) Returns: Optimization result with integer/binary variable values Example: # Binary knapsack: select items to maximize value within weight limit solve_integer_program( objective={"sense": "maximize", "coefficients": {"item1": 10, "item2": 15}}, variables={ "item1": {"type": "binary"}, "item2": {"type": "binary"} }, constraints=[ {"expression": {"item1": 5, "item2": 8}, "operator": "<=", "rhs": 10} ] )

Args: variables: List of variable definitions with bounds and types constraints: List of constraint definitions with coefficients and bounds objective: Objective function definition with coefficients and direction solver_name: Solver to use ("SCIP", "CBC", "GUROBI", "CPLEX") time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with optimal variable values and objective

Solve assignment problem using OR-Tools Hungarian algorithm. Args: workers: List of worker names tasks: List of task names costs: 2D cost matrix where costs[i][j] is cost of assigning worker i to task j maximize: Whether to maximize instead of minimize (default: False) max_tasks_per_worker: Maximum tasks per worker (optional) min_tasks_per_worker: Minimum tasks per worker (optional) Returns: Dictionary with solution status, assignments, total cost, and execution time

Solve transportation problem using OR-Tools. Args: suppliers: List of supplier dictionaries with 'name' and 'supply' keys consumers: List of consumer dictionaries with 'name' and 'demand' keys costs: 2D cost matrix where costs[i][j] is cost of shipping from supplier i to consumer j Returns: Dictionary with solution status, flows, total cost, and execution time

This tool solves knapsack problems where items need to be selected to maximize value while staying within capacity constraints. Use cases: - Cargo loading: Optimize loading of trucks, ships, or planes by weight and volume - Portfolio selection: Choose optimal set of investments within budget constraints - Resource allocation: Select projects or activities with limited budget or resources - Advertising planning: Choose optimal mix of advertising channels within budget - Menu planning: Select dishes for a restaurant menu considering costs and popularity - Inventory optimization: Decide which products to stock in limited warehouse space Args: items: List of items, each with 'name', 'value', 'weight', and optionally 'volume', 'quantity' capacity: Weight capacity constraint volume_capacity: Volume capacity constraint (optional) knapsack_type: Type of knapsack problem ('0-1', 'bounded', 'unbounded') max_items_per_type: Maximum items per type for bounded knapsack Returns: Knapsack result with total value and selected items Example: # Select items to maximize value within weight limit solve_knapsack_problem( items=[ {"name": "Item1", "value": 10, "weight": 5, "volume": 2}, {"name": "Item2", "value": 15, "weight": 8, "volume": 3}, {"name": "Item3", "value": 8, "weight": 3, "volume": 1} ], capacity=10, volume_capacity=5 )

Args: locations: List of location dictionaries with name and coordinates distance_matrix: Optional pre-calculated distance matrix start_location: Index of starting location (default: 0) return_to_start: Whether to return to starting location (default: True) time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with route and total distance

Args: locations: List of location dictionaries with name, coordinates, and demand vehicles: List of vehicle dictionaries with capacity constraints distance_matrix: Optional pre-calculated distance matrix time_matrix: Optional pre-calculated time matrix depot: Index of depot location (default: 0) time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with routes for all vehicles

Args: jobs: List of job dictionaries with tasks and constraints machines: List of available machine names horizon: Maximum time horizon for scheduling objective: Optimization objective ("makespan" or "total_completion_time") time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with job schedule and machine assignments

Args: employees: List of employee names shifts: List of shift dictionaries with time and requirements days: Number of days to schedule employee_constraints: Optional constraints and preferences per employee time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with employee schedules and coverage statistics

Args: assets: List of asset dictionaries with expected return, risk, and sector objective: Optimization objective ("maximize_return", "minimize_risk", "maximize_sharpe", "risk_parity") budget: Total budget to allocate (default: 1.0) risk_tolerance: Maximum acceptable portfolio risk (optional) sector_constraints: Maximum allocation per sector (optional) min_allocation: Minimum allocation per asset (default: 0.0) max_allocation: Maximum allocation per asset (default: 1.0) solver_name: Solver to use ("CBC", "GLPK", "GUROBI", "CPLEX") time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with optimal portfolio allocation

Args: products: List of product dictionaries with costs and resource requirements resources: List of resource dictionaries with capacity constraints periods: Number of planning periods demand: List of demand requirements per product per period objective: Optimization objective ("maximize_profit", "minimize_cost", "minimize_time") inventory_costs: Optional inventory holding costs per product setup_costs: Optional setup costs per product solver_name: Solver to use ("CBC", "GLPK", "GUROBI", "CPLEX") time_limit_seconds: Maximum solving time in seconds (default: 30.0) Returns: Optimization result with optimal production plan

Args: problem_type: Type of optimization problem input_data: Input data to validate Returns: Validation result with errors, warnings, and suggestions