Multi-Warehouse Inventory Allocation: Split-Shipment Reduction and Regional Fulfillment Node Optimization

## Algorithmic Distribution in Modern Omni-Channel Logistics

Expanding from a centralized fulfillment facility to a distributed 3-node or 5-node warehouse network drastically cuts parcel transit times and carrier shipping zones. However, unoptimized inventory allocation creates frequent split shipments, wiping out transit cost savings through duplicate fulfillment overhead.

### 1. Carrier Shipping Zone Cost Structure (2 lb Standard Parcel)

| Shipping Zone | Distance Radius | Average Ground Transit | Baseline Rate | Fuel & Peak Surcharges | Total Delivered Cost |
|:--------------|:---------------:|:----------------------:|:-------------:|:----------------------:|:--------------------:|
| Zone 2 | 0 - 150 miles | 1 Business Day | $7.45 | $1.22 | $8.67 |
| Zone 4 | 301 - 600 miles | 2 Business Days | $9.15 | $1.54 | $10.69 |
| Zone 6 | 1,001 - 1,400 miles | 3 Business Days | $11.85 | $1.98 | $13.83 |
| Zone 8 | 1,801+ miles | 4-5 Business Days | $14.90 | $2.45 | $17.35 |

### 2. Multi-Node Inventory Optimization Model

To optimize fulfillment across nodes $N$ for demand points $D$, we formulate the objective function:

$$\min \sum_{i \in N} \sum_{j \in D} \left( c_{ij} \cdot x_{ij} \right) + \sum_{k \in \text{Orders}} S_k \cdot P_{\text{split}}$$

Where $c_{ij}$ is shipping cost between node $i$ and customer $j$, $x_{ij}$ is units shipped, $S_k$ is a binary indicator of whether order $k$ required multiple fulfillment nodes, and $P_{\text{split}}$ is the handling penalty.