3.1 Supply Chain Network Design & Facility Location

Supply Chain Network Design & Facility Location

Supply chain network design is the strategic configuration of physical nodes (manufacturing plants, warehouses, distribution centers, cross-docks) and interconnecting transportation links. The overarching objective of network optimization is to establish an operational infrastructure that minimizes Total Logistics Cost while consistently fulfilling customer service level agreements (SLAs) and delivery lead time expectations. Sourcing professionals operating within the ISM CPSM framework must balance quantitative financial modeling with qualitative operational and risk factors when determining facility locations.

---

The Core Logistics Cost Trade-Off Framework

Designing a supply chain network requires balancing four interconnected cost categories that react in opposing directions as the number of network nodes changes:

1. Facility Fixed & Operating Costs: Lease payments, property taxes, utility infrastructure, material handling equipment (MHE), management labor, and maintenance overhead. Operating more facilities increases aggregate network fixed costs in a step-variable function.
2. Inventory Carrying Costs: Aggregate pipeline cycle stock remains relatively constant based on customer demand, but safety stock increases exponentially as nodes multiply. Safety stock across multiple locations scales according to the Square Root Rule of Inventory:

$SS_{\text{total}} = SS_{\text{base}} \times \sqrt{\frac{N_{\text{new}}}{N_{\text{existing}}}}$

1. Inbound Transportation Costs: Moving bulk raw materials or finished goods from factories and suppliers to distribution centers (DCs). As DC nodes increase, inbound freight transitions from consolidated, full truckload (TL) rail or motor carriage into smaller, less-than-truckload (LTL) shipments, causing inbound transportation costs per unit to rise.
2. Outbound Transportation Costs: Moving goods from DCs to end-customer destinations. Operating more DCs places inventory closer to end markets, reducing final-mile delivery distances, enabling local motor transport or parcel delivery, and significantly decreasing outbound freight costs.

Network Configuration Trade-Off Summary Table

---

Mathematical Facility Location Modeling: Continuous vs. Discrete Models

Facility location modeling falls into two broad categories: continuous location models and discrete location models. Continuous models evaluate an infinite number of geographic points across a continuous coordinate plane to find the theoretical cost-minimizing center. Discrete models evaluate a finite set of pre-selected candidate sites against specific operational constraints, transportation tariffs, and site-specific cost functions.

---

Center of Gravity (CoG) Continuous Location Model

The Center of Gravity (CoG) method is a foundational mathematical continuous location technique used to identify the single optimal geographic facility location that minimizes total transportation costs based on volume and distance. Coordinates ($X_i, Y_i$) of existing supply points or demand centers are weighted by their annual shipment volumes ($W_i$).

Mathematical Formulas

$C_x = \frac{\sum_{i=1}^n (W_i \cdot X_i)}{\sum_{i=1}^n W_i}$

$C_y = \frac{\sum_{i=1}^n (W_i \cdot Y_i)}{\sum_{i=1}^n W_i}$

Step-by-Step Worked Numerical Calculation: Central Warehousing Location

A supply chain director is evaluating where to build a new central distribution center to serve four primary regional markets across North America. The demand locations, grid coordinates, and annual freight volumes are detailed below:

• Market A (Atlanta): Grid Coordinate $(20, 30)$, Annual Volume $W_1 = 5,000\text{ tons}$
• Market B (Boston): Grid Coordinate $(80, 90)$, Annual Volume $W_2 = 3,000\text{ tons}$
• Market C (Chicago): Grid Coordinate $(40, 70)$, Annual Volume $W_3 = 8,000\text{ tons}$
• Market D (Dallas): Grid Coordinate $(30, 20)$, Annual Volume $W_4 = 4,000\text{ tons}$

Step 1: Calculate Total Network Freight Weight

$\sum_{i=1}^4 W_i = 5,000 + 3,000 + 8,000 + 4,000 = 20,000\text{ tons}$

Step 2: Compute Weighted X-Coordinate Sum & Center ($C_x$)

$\sum (W_i \cdot X_i) = (5,000 \times 20) + (3,000 \times 80) + (8,000 \times 40) + (4,000 \times 30)$ $\sum (W_i \cdot X_i) = 100,000 + 240,000 + 320,000 + 120,000 = 780,000$ $C_x = \frac{780,000}{20,000} = 39.0$

Step 3: Compute Weighted Y-Coordinate Sum & Center ($C_y$)

$\sum (W_i \cdot Y_i) = (5,000 \times 30) + (3,000 \times 90) + (8,000 \times 70) + (4,000 \times 20)$ $\sum (W_i \cdot Y_i) = 150,000 + 270,000 + 560,000 + 80,000 = 1,060,000$ $C_y = \frac{1,060,000}{20,000} = 53.0$

Operational Interpretation

The mathematically optimal Center of Gravity location for the new warehouse is grid coordinate $(39.0, 53.0)$. By placing the facility at this continuous coordinate, the total ton-mile transportation burden across all four markets is minimized.

---

Inventory Consolidation & The Square Root Rule

When restructuring a network, supply chain managers must calculate the exact inventory impact of consolidating or expanding facilities. The Square Root Rule demonstrates that total safety stock scales proportional to the square root of the ratio of new to existing facilities.

Worked Example: Inventory Expansion Calculation

An electronics distributor currently operates 1 centralized distribution center carrying $$4,000,000$ in safety stock. The company plans to decentralize its network by building 4 identical regional distribution centers to achieve same-day delivery SLAs.

$SS_{\text{new}} = SS_{\text{existing}} \times \sqrt{\frac{N_{\text{new}}}{N_{\text{existing}}}} = \$4,000,000 \times \sqrt{\frac{4}{1}} = \$4,000,000 \times 2 = \$8,000,000$

Expanding from 1 to 4 locations doubles the required total safety stock inventory across the network from $$4\text{M}$ to $$8\text{M}$, tying up additional working capital.

---

Qualitative & Multi-Criteria Site Selection Matrix

While mathematical models pinpoint optimal freight coordinates, actual site selection must integrate non-monetary operational criteria using a Weighted Factor Rating Matrix. Sourcing teams assign weights ($\sum W = 1.0$) to key qualitative and quantitative criteria, rate candidate sites on a standard scale (e.g., 1 to 10), and compute weighted composite scores.

Weighted Site Selection Matrix Example

Candidate Site A achieves a higher overall score ($7.70$ vs $6.85$) due to superior labor pool depth, intermodal transport access, and lower climate risk, overcoming Site B's favorable tax environment.

---

Strategic Real-World CPSM Scenario: Omnichannel Network Restructuring

Consider an industrial manufacturer transitioning to an omnichannel fulfillment strategy. To meet 24-hour customer delivery SLAs, leadership proposes building 6 regional micro-fulfillment centers. The CPSM sourcing professional must present a total logistics cost audit showing that while outbound parcel costs drop by $35%$, safety stock holding costs will rise by $145%$ ($\sqrt{6/1} \approx 2.45$), and facility overhead will increase by $$3.2\text{M}$ annually. By presenting this trade-off analysis, the sourcing leader guides the executive team toward a hybrid network model combining 2 regional DCs with 3PL cross-dock nodes, achieving SLA targets at optimal total landed cost.