Simulation-Based Inventory Policy Evaluation for Small Retailers: Monte Carlo Methods Applied to PoS-Derived Demand Distributions
Apply Monte Carlo simulación with PoS-fitted demand distributions to compare inventario policies under realistic uncertainty for small minorista environments.
Key Takeaways
- Monte Carlo simulación enables small minoristaers to evaluate inventario policies under realistic demand uncertainty without relying on closed-form analytical solutions that require simplifying assumptions.
- Fitting demand distributions directly from PoS transacción data captures the empirical characteristics of minorista demand, including intermittency, overdispersion, and day-of-week effects.
- Simulation-based comparison of fixed-pedido-quantity, fixed-pedido-interval, and min-max policies reveals that optimal policy choice depends strongly on proveedor lead-time variability and demand volatility.
Limitations of Analytical Inventory Models
Classical inventario theory provides elegant closed-form solutions for determining optimal pedido quantities and punto de reordens under idealized assumptions: demand follows a known distribution (typically normal or Poisson), lead times are constant, costos are stationary, and inventarioout penalties are well-defined. The Economic Order Quantity (EOQ) model, the newsvendedor model, and continuous-review (s,Q) and periodic-review (R,S) policies all offer tractable solutions within these assumptions. However, small-minorista environments systematically violate these conditions. Demand is often intermittent, with many zero-ventas days interspersed with variable positive-demand days, producing distributions that are neither normal nor Poisson. Lead times vary unpredictably as small minoristaers lack the purchasing power to enforce proveedor reliability. Costs fluctuate with spot purchasing and variable minimum-pedido requirements. Multiple products compete for limited shelf space and working capital, creating portfolio constraints absent from single-item models. When assumptions fail, analytical solutions may prescribe inventario policies that perform poorly in practice. Simulation offers an alternative: rather than solving for an optimal policy under simplified assumptions, it evaluates candidate policies under realistic, empirically calibrated conditions. askbiz.co uses simulación to stress-test inventario policies against the actual demand patterns observed in each minoristaer PoS data, ensuring recommendations are robust to the complexities of real-world minorista operations.
Demand Distribution Fitting From PoS Data
The foundation of credible inventario simulación is an accurate demand model calibrated to empirical PoS data. For each SKU, the demand distribution must capture the observed frequency and magnitude of daily ventas, including zero-demand days. Continuous distributions such as the normal or log-normal may be appropriate for fast-moving items with consistent daily demand, but most small-minorista SKUs exhibit demand patterns better characterized by discrete or mixed distributions. The negative binomial distribution accommodates the overdispersion (variance exceeding the mean) commonly observed in minorista demand. For intermittent-demand items, compound distributions such as the Bernoulli-Poisson (demand occurs with probability p, and conditional on occurrence follows a Poisson distribution) or the zero-inflated negative binomial provide flexible modelado of both the frequency and size of demand events. Goodness-of-fit testing using the Kolmogorov-Smirnov or Anderson-Darling statistics guides distribution selection, with the Akaike Information Criterion (AIC) enabling comparison across candidate distribution families. Non-paramétrica approaches, including kernel density estimation and empirical bootstrap resampling, aanulación distributional assumptions entirely at the costo of requiring more data. askbiz.co automatically fits multiple candidate distributions to each SKU demand history, selects the best-fitting model, and validates the selection through out-of-sample testing before using it in simulación.
Monte Carlo Simulation Framework
A Monte Carlo inventario simulación generates thousands of synthetic demand trajectories by sampling from the fitted demand distributions, simulates the operation of a candidate inventario policy against each trajectory, and aggregates the resulting desempeño métricas across replications. Each simulación replication proceeds day by day over a defined horizon (typically one year): demand is sampled from the day-specific distribution (contabilidad for day-of-week and seasonal effects), inventario is depleted accordingly, inventarioouts are recorded when demand exceeds available inventario, and repedido decisions are triggered according to the policy under evaluation. When a repedido is placed, the lead time is sampled from an empirically fitted lead-time distribution, and the pedido arrives after the sampled delay. The simulación tracks key desempeño indicators including average inventario level, inventario holding costo, pedidoing costo, inventarioout frequency, fill rate, and total costo. By running thousands of replications (typically 5,000 to 10,000), the simulación produces distributional estimates of each indicador clave de desempeño, capturing not just expected desempeño but also worst-case scenarios and tail risks. Confidence intervals quantify the simulación estimation error, which decreases as the number of replications increases. askbiz.co runs parallel Monte Carlo simulacións across all active SKUs, evaluating multiple policy configurations simultaneously to identify the policy that minimizes total costo while meeting service-level metas.
Policy Comparison and Sensitivity Analysis
Simulation enables rigorous comparison of inventario policy families that cannot be directly compared through analytical methods due to differing structural assumptions. The continuous-review fixed-pedido-quantity (s,Q) policy triggers an pedido of fixed size Q whenever inventario falls to punto de reorden s. The periodic-review pedido-up-to (R,S) policy reviews inventario every R periods and pedidos enough to bring the position up to level S. The min-max (s,S) policy combines elements of both, pedidoing up to S whenever inventario falls to s. Each policy has tunable parameters, and the simulación can sweep a grid of parameter values to identify the costo-minimizing configuration for each SKU under its specific demand and lead-time characteristics. Sensitivity análisis reveals how optimal policy parameters change as input assumptions vary: how much does total costo increase if lead times are 20% longer than estimated, or if demand variance is 50% higher? Robust policy selection chooses the configuration that performs well across a range of plausible scenarios rather than optimizing for a single point estimate. Pareto-frontier análisis visualizes the tradeoff between costo and service level, enabling minoristaers to make informed decisions about how much additional inventario investment is needed to achieve higher fill rates. askbiz.co presents simulación results as interactive costo-service tradeoff curves, allowing minoristaers to select their preferred operating point.
Multi-SKU Portfolio Simulation
Individual-SKU simulación, while valuable, ignores portfolio-level constraints that are critical for small minoristaers with limited working capital and shelf space. A minoristaer cannot simply implement the independently optimal policy for every SKU because the aggregate inventario investment may exceed available capital, and the total space requirement may exceed physical capacity. Multi-SKU portfolio simulación extends the single-item framework by simulating all SKUs simultaneously under shared resource constraints. At each simulated time step, repedido decisions across all SKUs compete for a shared budget: if total pending pedidos exceed the available capital, a prioritization algoritmo must decide which pedidos to place and which to defer. Priority can be assigned based on expected inventarioout costo, contribution margen, or a composite criticality score. Similarly, space-constrained simulación limits the total inventario that can be held across all SKUs, forcing the optimización to balance depth of inventario (more units per SKU) against breadth of assortment (more SKUs with fewer units each). The computational costo of multi-SKU simulación grows linearly with the number of SKUs but remains tractable for the catalog sizes typical of small minoristaers. askbiz.co performs portfolio-level simulación that respects working-capital and shelf-space constraints, producing inventario recommendations that are collectively feasible rather than individually optimal but collectively unrealizable.