stochastic-optimization

What it does

Provides a stochastic-optimization skill that helps solve optimization problems under uncertainty in supply chains. It addresses two-stage stochastic programming for production planning with recourse, chance-constrained inventory optimization, and a Sample Average Approximation (SAA) approach for general stochastic problems. It includes concrete code examples and formulations for each method, guiding users through modeling, objective construction, and solution extraction.

How it works

• Two-Stage Stochastic Programming: Defines Stage 1 production decisions before uncertainty and Stage 2 recourse decisions after uncertainty. Builds an extensive form deterministic equivalent with variables for Stage 1 production and for each scenario's inventory and backorder. Objective combines Stage 1 cost and expected Stage 2 cost, then enforces capacity and scenario-specific balance constraints. Solves using a MILP solver and extracts production plans, plus per-scenario inventories and backorders.
• Chance-Constrained Optimization: For each product, uses a service level to convert a probabilistic constraint into a deterministic stock level via a normal approximation: s = μ + zα σ. Computes holding costs based on this stock level and reports per-product results including safety stock and service level.
• Sample Average Approximation (SAA): Outlines a procedure to approximate E[f(x,ξ)] by averaging over samples. Repeats generation of scenarios, solving the deterministic problem, and evaluating on out-of-sample tests to select a best solution.

When to use it

Use when the user explicitly mentions stochastic optimization, scenario-based optimization, chance constraints, two-stage stochastic programming, or uncertainty modeling in supply chain contexts. Also applicable when modeling demand uncertainty, lead times, prices, or other parameters with probabilistic treatment and a recourse structure is desired.

What it can touch

• Tools: claude-code
• It provides code blocks in Python illustrating usage with common libraries (numpy, PuLP, scipy) and shows how to structure models, variables, constraints, and objective formulations.

Caveats

• License: MIT
• The skill provides sample code and placeholder problem structures; real deployment requires adapting to specific data formats, solver availability, and problem sizes.
• It assumes availability of scenario data and, in the Chance-Constrained section, normal distribution assumptions for a closed-form solution of safety stock.