Prescriptive Analytics Toolbox — Optimization & Simulation Recipes

Why this toolbox matters

If you can predict demand but not recommend what to do next, your analytics stop short. This toolbox helps teams move from forecasts and models to feasible, cost‑aware actions that consider constraints, risk, and human realities. The recipes are intentionally small, repeatable, and pragmatic so you can prototype recommendations, show trade‑offs, and iterate with stakeholders.

What you get

• Problem templates: concise, runnable formulations for common operational decisions (inventory reorder, routing, shift staffing).
• Modeling recipes: how to choose objectives, define variables and constraints, and pick solvers (or lightweight alternatives).
• Simulation templates: Monte Carlo and scenario methods to quantify risk, sensitivity, and value of additional information.
• Communication templates: one‑page summaries, trade‑off tables, and visualization suggestions that make recommendations actionable.

How to use a recipe (quick 5‑step pattern)

1. Define the decision — what action will be taken, who acts, and what constraints bind them.
2. Choose the objective — minimize cost, maximize fill rate, minimize unmet demand, maximize throughput, or a weighted combination.
3. Model inputs — identify required forecasts, estimates of cost/benefit, variability distributions and implementation constraints (lead times, vehicle capacity, labour rules).
4. Formulate and solve — write variables & constraints, choose solver or heuristic, record solution and feasible alternatives.
5. Test with simulation — inject realistic uncertainty, run scenarios, compute performance metrics, and produce sensitivity and value‑of‑information analysis for decision robustness.

Recipe 1 — Inventory reorder (small SKU, periodic review)

When to reorder and how much for a small set of SKUs where stockouts and holding costs matter.

Recipe 2 — Routing (single depot, vehicle routing)

Plan daily routes to serve known stops with capacity and time windows.

Recipe 3 — Staffing and shift scheduling

Assign people to shifts to meet time‑varying demand with labour rules.

Modeling recipes — a short reference

• Objectives: cost minimization, service maximization, weighted multi‑objective (use scalarization or Pareto front for trade‑offs).
• Variables: continuous for flows, integer for counts, binary for on/off decisions. Keep an eye on integrality — binary variables drive solve complexity.
• Constraints: feasibility (supply/demand), capacity, time, regulatory and human constraints. Explicitly represent implementation limits (e.g., max 3 route changes per driver per week).
• Solver guidance: start with LP relaxations to test feasibility; move to MIP only when necessary. Use open source tools (OR‑Tools, COIN‑OR) for prototyping. Document solver tolerances and time limits for stakeholder transparency.

Simulation & sensitivity templates

Always test recommended decisions against realistic uncertainty.

• Monte Carlo scenario simulation: sample demand, lead times, or travel times; apply the candidate policy or plan; collect KPIs (cost, fill rate, service level).
• Scenario analysis: construct small sets of plausible futures (best case, base, worst case, key risk scenarios) and evaluate outcomes.
• Sensitivity sweeps: vary a single input (e.g., holding cost, fuel price) across a range to find breakpoints where the recommended action changes.
• Value of Information (VOI): compute expected value of perfect information (EVPI) or expected value of sample information (EVSI) for key uncertain parameters to prioritize data collection efforts.

Communication templates — turn technical output into decisions

Stakeholders need clear trade‑offs and a recommended next step, not model internals.

• One‑page executive summary: recommendation, expected benefit (monetary & service), main risks, required actions, and confidence level.
• Trade‑off table: rows = candidate options; columns = cost, service metric, implementation difficulty, sensitivity rating. Highlight Pareto‑efficient options.
• Visualizations: fan charts for KPI distributions, tornado chart for sensitivity, Pareto front scatter plotting cost vs service, and small route map snapshots for routing recommendations.
• Implementation checklist: data required, operational changes, pilot scope, success metrics, rollback criteria, and owner/contact.

Common pitfalls & how to avoid them

• Avoid black‑box recommendations: always return a small set of alternative feasible options and explain sensitivities.
• Beware unrealistic data needs: prioritize minimal sufficient inputs and use VOI to justify expensive data collection.
• Don’t ignore human factors: include operational constraints and stakeholder incentives in the model or show how they change results.
• Test for brittleness: run many simulations and present the probability of worse‑than‑acceptable outcomes, not only expected values.

Practical next steps (starter checklist)

1. Pick one decision problem you can pilot in a single site or SKU group.
2. Assemble minimal data and assumptions; run a baseline model and a heuristic alternative.
3. Simulate both under uncertainty and produce the trade‑off table and one‑page summary.
4. Run a short operational pilot with clear metrics and rollback criteria.
5. Capture results, lessons, and update the model or process before scaling.

Starter assets to create or request

• Excel template: inventory (demand, costs, reorder rule) with Monte Carlo sampling.
• Notebook (Python/OR‑Tools): small VRP example and a staffing MIP with sample data.
• Communication slide template: one‑page recommendation, trade‑off table, and sensitivity visuals.

Where this toolbox fits in your domain

Use these recipes to rapidly prototype prescriptive recommendations that are feasible, explainable, and resilient. The emphasis is on actionable output: recommended actions with quantified trade‑offs and a clear plan to pilot, measure, and iterate.