7.5 Transportation Modes, Freight Economics & the Transshipment Model

7.5 Transportation Modes, Freight Economics & the Transshipment Model

The specification lists transportation modes (TL, LTL, air, rail, ship) and distribution models (transshipment, direct ship, cross docking, intermediate storage). Freight is often the largest logistics cost, and the mode choice also sets inventory in transit and the safety stock needed to cover transit variability.

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1. Mode Characteristics

Truckload notes:

• A 53-ft dry van holds 26 standard 48 × 40 in pallets single-stacked.
• Federal rules cap gross vehicle weight on the Interstate system at 80,000 lb, which typically leaves about 42,000–45,000 lb of payload.
• Dense freight weighs out (hits the weight limit first) and light freight cubes out (fills the space first). Know which applies when planning loads.

Containers: ocean capacity is counted in TEUs (twenty-foot equivalent units); a 40-ft container is 2 TEU.

Air freight charges the greater of actual weight and dimensional weight. The common international (IATA) divisor is 6,000 cm³ per kg, about 166 in³ per lb.

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2. LTL Pricing and the Deficit Weight Rule

LTL carriers price per hundredweight (cwt = 100 lb). Rates depend on:

• Freight class: under the National Motor Freight Classification there are 18 classes from 50 (dense, durable) to 500 (light, bulky, fragile), based on density, handling, stowability, and liability. Higher class means a higher rate.
• Weight breaks: the rate per cwt falls at heavier breaks (for example 500, 1,000, 2,000, 5,000, and 10,000 lb).
• Lane (origin and destination), plus minimum charges, fuel surcharges, and accessorial fees.

Deficit weight rule: a shipment may be billed at the next higher weight break, at that break's lower rate, when that is cheaper.

Example: The rate is $25.00/cwt for 5,000–9,999 lb and $20.00/cwt for 10,000 lb and over. An 8,500 lb shipment rated as is costs $85 \times 25 = \text{\textdollar}2{,}125$. Rated as 10,000 lb it costs $100 \times 20 = \text{\textdollar}2{,}000$, so the deficit weight rate applies and saves $125. The indifference weight is $10{,}000 \times 20/25 = 8{,}000$ lb: any shipment between 8,000 and 9,999 lb should be billed at the 10,000 lb break.

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3. Mode Selection by Total Logistics Cost

The cheapest freight rate is not always the cheapest mode. Goods in transit are inventory the company owns, and slower or less reliable modes need more safety stock.

$\text{Total annual cost} = \text{Freight} + \underbrace{D \times C \times i \times \frac{T}{365}}_{\text{in-transit inventory}} + \text{safety stock and other effects}$

where $D$ is annual units, $C$ is unit value, $i$ is the annual carrying rate, and $T$ is transit days.

Example: 50,000 units per year, each worth $200, carrying rate 25% per year.

Rail wins here. If the parts were worth $2,000 each, in-transit cost would be ten times larger. Rail would then cost $300{,}000 + 821{,}918 = \text{\textdollar}1{,}121{,}918$, against $450{,}000 + 273{,}973 = \text{\textdollar}723{,}973$ for truck, and truck would win. High-value goods favor faster modes.

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4. Distribution Network Options

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5. The Transshipment Problem

A transshipment model extends the transportation problem by allowing flow through intermediate nodes. Let $x_{ij}$ be the flow on arc $(i, j)$ with unit cost $c_{ij}$:

$\min \sum_{(i,j)} c_{ij} x_{ij}$

subject to:

• Supply nodes: $\sum_j x_{ij} - \sum_k x_{ki} \le s_i$ (net flow out at most the supply)
• Transshipment nodes: $\sum_k x_{ki} - \sum_j x_{ij} = 0$ (flow in equals flow out)
• Demand nodes: $\sum_k x_{ki} - \sum_j x_{ij} \ge d_i$
• $x_{ij} \ge 0$

It can be solved as an LP or converted to a transportation tableau by adding a buffer equal to total supply at each transshipment node.

Worked example: Plant P1 can ship 300 units and plant P2 200 units. Customers C1 and C2 each need 250. A cross-dock T is available. Unit costs:

Cheapest route for each plant–customer pair:

• P1 to C1: via T, $4 + 5 = 9$ (direct is 12).
• P1 to C2: via T, $4 + 4 = 8$.
• P2 to C1: via T, $6 + 5 = 11$.
• P2 to C2: direct, 9 (via T it is 10).

P1's cost advantage over P2 is $2 at C1 ($11 - 9$) and $1 at C2 ($9 - 8$), so P1's limited supply goes first to C1.

• P1 sends 250 to C1 via T: $250 \times 9 = \text{\textdollar}2{,}250$.
• P1 sends its remaining 50 to C2 via T: $50 \times 8 = \text{\textdollar}400$.
• P2 sends 200 to C2 directly: $200 \times 9 = \text{\textdollar}1{,}800$.

Minimum total cost = $4,450, with 300 units flowing through the cross-dock. Flow balance at T is 300 in and 300 out.