Inbound Logistics & Parts Delivery
CVRP — Clarke-Wright Savings / NP-Hard
A manufacturer receives daily parts from 8–15 suppliers. A fleet of 3 trucks (each 12 tonnes) must collect components and deliver to the plant. Poor routing wastes 15–25% in excess fuel and driver time compared to optimized collection routes.
Where This Decision Fits
Manufacturing operations chain — the highlighted step is what this page optimizes
The Problem
From factory floors to optimization theory
A manufacturing plant operates as the single depot. 8 supplier nodes are scattered across the region, each holding components of varying weight ready for collection. The plant dispatches a fleet of 3 trucks, each with a 12-tonne capacity Q. The objective is to minimize total collection distance while ensuring every supplier is visited exactly once and no truck exceeds its weight limit.
This maps directly to the Capacitated Vehicle Routing Problem (CVRP): given n supplier nodes with demands, a single plant depot, and a fleet of identical vehicles each with capacity Q, find routes starting and ending at the depot that visit each supplier exactly once without exceeding vehicle capacity.
subject to
Σk Σj xijk = 1 // each supplier visited exactly once
Σj x0jk = Σi xi0k = 1 // each truck starts & ends at plant
Σi qi · Σj xijk ≤ Q // truck capacity Q not exceeded
xijk ∈ {0, 1} // binary routing variables
Where dij is the distance between locations, qi is the parts weight at supplier i, Q is the truck capacity (12t), and xijk indicates whether truck k travels from i to j.
The CVRP is NP-hard — it generalizes both the Traveling Salesman Problem (single vehicle, no capacity) and the Bin Packing Problem (assignment only, no routing). Even with 8 suppliers and 3 trucks, the number of feasible route permutations explodes combinatorially.
See full CVRP theory and all algorithmsTry It Yourself
Route collection trucks across supplier locations
Inbound Logistics Optimizer
8 Suppliers · 3 Trucks · 12t CapReady. Click “Solve & Compare All Algorithms” to run.
| Algorithm | Distance | Routes | Time |
|---|---|---|---|
| Click Solve & Compare All Algorithms | |||
The Algorithms
Constructive heuristics and local search for vehicle routing
Nearest Neighbor
O(n²)Build routes one at a time. Starting from the plant depot, repeatedly visit the nearest unvisited supplier whose parts weight fits within remaining truck capacity. When no more suppliers can be added, return to the depot and start a new route. Simple and fast, but tends to produce longer routes due to greedy local decisions that ignore the global picture.
Clarke-Wright Savings
O(n² log n)Start with each supplier on its own route (depot → supplier → depot). Compute savings for merging every pair of routes: s(i,j) = d(0,i) + d(0,j) − d(i,j). Sort savings in descending order and greedily merge route pairs whenever the combined load does not exceed truck capacity. The algorithm produces high-quality solutions quickly and is the most widely used CVRP heuristic in practice.
2-opt Improvement
O(n²) per passTake an existing solution (e.g., from Nearest Neighbor) and improve it by repeatedly reversing sub-segments within each route. For every pair of edges in a route, check whether removing them and reconnecting the route segments in reverse order reduces total distance. Continue until no further improvement is found. This local search operator often reduces route length by 10–20% compared to the initial constructive heuristic.
Real-World Complexity
Why inbound logistics goes beyond the basic CVRP
Beyond Standard CVRP
- Time windows — Suppliers have loading docks available only during specific hours; late arrivals cause production line stoppages
- Heterogeneous fleet — Refrigerated trucks, flatbeds, and box trucks differ in capacity, speed, and compatibility with supplier loading bays
- Multi-commodity loads — Fragile electronics, heavy castings, and hazardous chemicals cannot share the same vehicle
- Just-in-time pressure — Parts must arrive within a narrow window before assembly; early arrival wastes buffer space, late arrival halts the line
- Backhaul opportunities — Empty trucks returning to suppliers can carry returnable containers, packaging, or defective parts for rework
- Consolidation points — Cross-dock facilities allow partial loads from nearby suppliers to be merged before the final plant delivery
- Dynamic disruptions — Supplier shortages, traffic incidents, and weather require real-time route re-optimization
Key References
Foundational works in vehicle routing
- (1964). “Scheduling of vehicles from a central depot to a number of delivery points.” Operations Research, 12(4), 568–581.
- (1959). “The truck dispatching problem.” Management Science, 6(1), 80–91.
- (1958). “A method for solving traveling-salesman problems.” Operations Research, 6(6), 791–812.
- (2014). “Vehicle Routing: Problems, Methods, and Applications.” 2nd ed., SIAM.
- (2008). “The Vehicle Routing Problem: Latest Advances and New Challenges.” Springer.
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