Marketing Resource Allocation Optimizer

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Quick Start Guide

(click to collapse)

Upload Your Data

Provide a CSV with 3 columns: resource_id, input (spending/allocation), and output (results). Each row is one historical observation.

Example: Sales rep data with monthly spending and revenue, or ad channel data with impressions and conversions.

Fit Response Models

Choose how to model each resource's response curve. Recommended: "Auto-select BEST model for EACH resource" to let the tool pick optimal models.

What it does: Fits mathematical functions (linear, logarithmic, power, etc.) that predict output from input for each resource.

Set Constraints

Define business rules: total budget, min/max per resource, equity requirements, etc. Start simple (just budget), then add advanced constraints as needed.

Pro tip: Use "Reset All" button to quickly return to defaults when experimenting.

Optimize & Analyze

Click "Run optimization" to find the best allocation. Review results in tables and charts, compare scenarios, and export recommendations as CSV.

Key output: Optimal allocation per resource, predicted total output, ROI, and marginal returns analysis.

OPTIMIZATION OVERVIEW & METHODOLOGY

This tool helps marketers allocate limited budgets across multiple resources (sales reps, ad channels, regions, etc.) to maximize total output (revenue, conversions, leads). The optimization finds the best way to distribute your budget based on each resource's individual response curve—the relationship between spending and results.

The Four-Step Process:

Model Fitting: For each resource $i$, fit a response function $Y_i = f_i(X_i)$ where:
- $X_i$ = input allocation (dollars, hours, impressions) for resource $i$
- $Y_i$ = predicted output (sales, conversions, leads) from resource $i$
- $f_i(\cdot)$ = the model type (linear, log, power, quadratic, sqrt, logistic, or bounded log)
Constraint Definition: Set business rules like total budget $B$, minimum/maximum per resource, equity requirements, or output ceilings.
Optimization: Find allocations $x_1, x_2, \ldots, x_n$ that maximize total predicted output while respecting all constraints.
Scenario Comparison: Save multiple allocations and compare outcomes, ROI, and marginal returns to support decision-making.

Objective function (maximize total output): $$\text{Maximize } Z = \sum_{i=1}^{n} f_i(x_i)$$ where:

$Z$ = total predicted output across all resources (the objective we're maximizing)
$n$ = number of resources (reps, channels, regions, etc.)
$f_i(x_i)$ = predicted output from resource $i$ given allocation $x_i$
$x_i$ = decision variable (how much to allocate to resource $i$)

Subject to constraints: $$\sum_{i=1}^{n} x_i \leq B$$ $$L_i \leq x_i \leq U_i \quad \forall i$$ where:

$B$ = total budget available for allocation
$L_i$ = minimum required allocation for resource $i$ (can be 0)
$U_i$ = maximum allowed allocation for resource $i$

Optimization method: Greedy marginal returns allocator

This tool uses a greedy marginal returns algorithm: it repeatedly allocates small budget increments ($100 at a time) to whichever resource currently offers the highest marginal return—the additional output per additional dollar spent at that resource's current allocation.

Why this method? It's transparent, respects all constraints naturally, and guarantees feasible solutions. For smooth response curves with diminishing returns (most marketing scenarios), it often finds the optimal or near-optimal allocation. The diagnostics section reports iterations, convergence, and constraint satisfaction for your specific allocation.

Marginal returns intuition: In an optimal allocation, marginal returns are roughly equal across all funded resources. If one resource had much higher marginal returns than another, you could improve total output by shifting budget from the low-return resource to the high-return one.

Model types and when to use them

Linear: $Y = a + bX$ — Constant returns. Use when each additional dollar produces roughly the same output increase.

Logarithmic: $Y = a + b \cdot \ln(X)$ — Strong diminishing returns. Output increases quickly at first, then plateaus.

Power: $Y = a \cdot X^b$ — Flexible growth/decay. $b > 1$ = accelerating returns, $b < 1$ = diminishing returns.

Quadratic: $Y = a + bX + cX^2$ — Non-monotonic. Can capture peak performance at mid-range spending.

Square Root: $Y = a + b\sqrt{X}$ — Moderate diminishing returns. Less aggressive than logarithmic.

Logistic (S-curve): $Y = L/(1 + e^{-k(X-X_0)})$ — Slow start, rapid growth, then saturation at ceiling $L$. Perfect for market saturation scenarios.

Bounded Logarithmic: $Y = \text{ceiling} - (\text{ceiling} - a) \cdot e^{-bX}$ — Exponential approach to a known ceiling. Use when you can specify maximum achievable output (e.g., total market size).

MARKETING SCENARIOS

Load a preset marketing use case:

Select a preset to auto-populate historical data for common resource allocation problems (sales team budgets, channel spend, regional marketing). Each scenario includes fitted models and suggested constraints.

DATA UPLOAD & MODEL FITTING

Upload Historical Data

Provide a CSV file with columns: resource_id (name/label for each resource), input (historical budget/hours), and output (historical sales/conversions/leads).

Drag & Drop historical data file (.csv, .tsv, .txt)

Three columns: resource_id, input, output. Each row represents one resource's historical performance. Up to 500 resources supported.

No file uploaded yet.

Optimization Constraints

Set the rules: Constraints define the business rules and practical limits for your allocation. The optimizer will find the best allocation that respects all these constraints. Start with basic constraints (total budget, min/max per resource), then explore advanced options for more realistic scenarios.

Total budget available (total $ to allocate across all resources)

Minimum per resource (ensure every resource gets at least this much)

Maximum per resource (leave blank for no maximum)

Force integer allocations (round to whole dollars, no cents)

Allow extrapolation beyond historical range

⚠️ OVERRIDES min/max per resource: When unchecked, all allocations are strictly capped at each resource's historical range (min to max observed input), regardless of the "Maximum per resource" and "Minimum per resource" settings above. This ensures predictions stay within reliable data ranges but may conflict with budget requirements.

Cost Structure (Variable & Fixed Costs)

Variable costs: If your input units are NOT dollars (e.g., hours, impressions, people), specify the cost per unit. This converts input units to actual budget dollars (e.g., $50/hour means 100 hours = $5,000 budget).
Fixed costs: One-time or baseline costs incurred for activating each resource (e.g., salary, platform fees). These are added to the total budget calculation when a resource receives any allocation above the minimum.

Variable cost per input unit (leave 1.0 if inputs are already in dollars)

Fixed cost per active resource (e.g., $30,000 salary per rep; leave 0 if no fixed costs)

Advanced constraints

Limit number of resources funded (focus budget on top performers)

What it does: Forces the optimizer to allocate $0 to some resources. For example, max=5 means only the 5 most productive resources receive funding, all others get $0.

Apply equity constraint (prevent extreme inequality in allocations)

What it does: Enforces max_allocation ≤ ratio × min_allocation. For example, ratio=10 means if the smallest funded resource gets $1,000, the largest can't exceed $10,000. Resources with $0 are excluded from this comparison.

Limit deviation from baseline (avoid drastic changes from historical spending)

What it does: Constrains each resource's allocation to stay within ±X% of its maximum historical input. For example, 50% means if a resource's max observed input was $10,000, allocation must be between $5,000-$15,000.

VISUAL OUTPUT

Response Curves with Optimal Allocations

View:

Each curve shows a resource's predicted output for different input levels. Red diamonds indicate the optimal allocation from the current solution. Grey circles show historical data points used to fit each model.

Allocation Comparison

Compare allocated budgets across resources. Longer bars indicate higher allocations.

Marginal Returns Analysis

Shows the marginal return (additional output per additional dollar) at the optimal allocation point. In an efficient allocation, marginal returns should be equalized across funded resources.

Scenario Comparison

Compares predicted total output under different allocation strategies: (1) Historical averages, (2) Current levels (most recent data), (3) Budget-only optimization (no other constraints), and (4) Your constrained optimization (with all active constraints).

▸ Additional Info: What Each Strategy Represents

Historical Averages: Allocates the average spending level from your historical data to each resource. Represents the "typical" allocation pattern based on past behavior. This baseline shows what output you'd expect if you maintained average historical spending.

Current Levels: Uses the most recent allocation (last row of your data) for each resource. Shows the output from your current/latest spending pattern. Useful for comparing "where we are now" versus optimized strategies.

Budget-Only Optimization: Runs optimization with only the total budget constraint active—no min/max per resource, no cardinality limits, no equity requirements, no baseline maintenance, and extrapolation enabled. This represents the theoretical maximum output achievable if you had complete flexibility. The gap between this and constrained optimization shows the "cost" of your constraints.

Constrained Optimization: Your actual optimization result with all active constraints applied. Active constraints include:

Total Budget constraint

This scenario represents the realistic optimized allocation given your business rules and operational constraints.

Visual output settings

Show historical data points on response curves Max resources to display in charts:

These settings update charts immediately when changed. Use the dropdown on each chart to view individual resources.

Marketing Resource Allocation Optimizer

Quick Start Guide

Upload Your Data

Fit Response Models

Set Constraints

Optimize & Analyze

OPTIMIZATION OVERVIEW & METHODOLOGY

MARKETING SCENARIOS

DATA UPLOAD & MODEL FITTING

Upload Historical Data

Model Fitting Options

Model Fit Results

Optimization Constraints

OPTIMIZATION RESULTS

Allocation Summary

Resource Allocation Details

VISUAL OUTPUT

Response Curves with Optimal Allocations

Allocation Comparison

Marginal Returns Analysis

Scenario Comparison

OPTIMIZATION DIAGNOSTICS

SCENARIO COMPARISON & WAR GAMING

Saved Scenarios

Scenario Comparison Results

Sensitivity Analysis