Logistics Operations

Decision horizons · SCM functions · twenty-four models

Logistics operations research is the discipline of coordinating flows of goods, people, vehicles, and information across supply chains — from the strategic siting of a distribution centre that will stand for decades, to the tactical design of weekly inventory policies, to the operational routing of trucks, drones, and technicians at the start of the working day. It is one of the oldest branches of operations research: Monge (1781) formulated optimal transport; Kantorovich (1939) and Hitchcock (1941) gave it a linear-programming spine; Dantzig & Ramser (1959) inaugurated vehicle routing; Hakimi (1964) and Balinski (1965) opened facility location; and Harris (1913) had already solved inventory. This section presents twenty-four canonical logistics problems — each a live interactive solver — organised along the decision-horizon × SCM-function taxonomy codified by Chopra & Meindl (2019) and Ghiani, Laporte & Musmanno (2013), with SCOR, problem-family, and flow-direction views available through the lens toggle.

Why logistics OR matters

Scale of the problem · three anchor statistics

~12%
of global GDP is spent on logistics — transportation, warehousing, and inventory carrying costs total roughly US$ 10–12 trillion per year worldwide.
Armstrong & Associates; World Bank Logistics Performance Index · lpi.worldbank.org
~40%
of delivery costs in urban last-mile networks — the final leg between distribution centre and customer — is where small routing improvements compound into large savings.
McKinsey Parcel delivery: The future of last mile (2016) · mckinsey.com
~24%
of global CO₂ emissions come from the transport sector — routing, mode choice, and network design are now first-order climate levers as well as cost levers.
IEA Transport sector tracking · iea.org/transport

Decision framework

Four lenses on the same twenty-four applications

The primary taxonomy of Chopra & Meindl (2019) and Ghiani, Laporte & Musmanno (2013) decomposes logistics planning along two axes: the decision horizon (strategic, tactical, operational) and the SCM function (network design, inventory, transportation & routing, warehousing, crew & service). Every application in this section occupies one cell. Dashed cells are honest gaps — decisions that exist in practice but are not yet modelled here. Chips marked coming are canonical pages scheduled for the next build pass.

Horizon ↓  ·  Function →
Network & Facilityhubs, DCs, SCND
Inventorystock policy
Transportationrouting, dispatch
Warehousingterminals, slotting
Crew & Serviceduty, skills, gates
Strategic3–10 yr
Hub-and-Spoke Design p-Hub Median Distribution Centre Location UFLP Depot Location CFLP Fleet Sizing MIP Supply-Chain Network Design SCND · coming
Multi-Echelon Inventory Strategy ME-Inv · coming
Gap · mode / corridor selection
Folded into DC location
—
Tacticalmonths / quarter
—
Economic Order Quantity EOQ · coming Lot Sizing Wagner-Whitin · cross: manufacturing
Inventory-Routing Problem IRP · coming
Warehouse Slotting QAP
Driver Duty Scheduling Set Partitioning
Operationalday – week
—
Gap · real-time replenishment triggers
Capacitated VRP (canonical) CVRP · coming Delivery Route Planning CVRP · applied VRP with Time Windows VRPTW · coming Travelling Salesman TSP · coming Real-Time Dispatching Dynamic VRP Inbound / Milk-Run CVRP-inbound
Warehouse Packing 1D BP Order Picking Warehouse TSP
Technician Routing VRPTW + skills Airport Gate Assignment LAP

The SCOR (Supply Chain Operations Reference) model, maintained by the Association for Supply Chain Management, organises every supply-chain activity into five top-level processes: Plan, Source, Make, Deliver, Return. Logistics OR lives primarily in Plan, Source, Deliver, and (increasingly) Return. Make is dominated by the manufacturing domain; we cross-link there rather than duplicate.

Planstrategy · S&OP
Hub-and-Spoke Design p-Hub SC Network Design SCND · coming Fleet Sizing MIP Multi-Echelon Inventory ME-Inv · coming
Sourceprocurement · inbound
Inbound / Milk-Run CVRP-inbound Economic Order Quantity EOQ · coming Lot Sizing W-W · cross: manufacturing
Makeproduction
Primarily manufacturing domain.
Cross-link → Manufacturing Operations
Deliverfulfilment · outbound
DC Location UFLP Depot Location CFLP CVRP (canonical) CVRP · coming Delivery Routing CVRP · applied VRPTW VRPTW · coming Technician Routing VRPTW + skills Real-Time Dispatching Dynamic VRP Inventory-Routing IRP · coming Warehouse Packing 1D BP Warehouse Slotting QAP Order Picking Warehouse TSP Gate Assignment LAP Driver Scheduling Set Partitioning
Returnreverse logistics
Open gap in current coverage.
Cross-link → Waste Collection (arc-routing) · reverse-logistics canonical page planned.

The Toth & Vigo (2014), Daskin (2013), and Zipkin (2000) research taxonomies organise logistics-OR around the canonical problem family each application instantiates. Five super-families cover this section: location, routing, inventory, scheduling & assignment, and packing. This is the view most familiar to operations-research readers; the previous two lenses translate it into SCM language.

Facility & Network Location
Where to put fixed infrastructure — hubs, depots, distribution centres, service networks.
Hub-and-Spoke Design p-Hub Median Hub Location (canonical) HLP · coming Depot Location CFLP CFLP (canonical) CFLP · coming DC Location UFLP UFLP (canonical) UFLP · coming p-Median PMP · coming SC Network Design SCND · coming
Vehicle & Arc Routing
TSP, VRP and its time-window / pickup-and-delivery / dynamic extensions. The heart of logistics-OR research.
Travelling Salesman TSP · coming Capacitated VRP (canonical) CVRP · coming Delivery Routing (applied) CVRP VRP Time Windows (canonical) VRPTW · coming Technician Routing VRPTW+skills Real-Time Dispatching Dynamic VRP Inbound Milk-Run CVRP Arc Routing / CPP cross: public-services
Inventory
Order quantities, reorder points, safety stock, and multi-echelon stocking under demand uncertainty.
Economic Order Quantity EOQ · coming Multi-Echelon Inventory ME-Inv · coming Inventory-Routing IRP · coming Lot Sizing (Wagner-Whitin) cross: manufacturing Newsvendor (seed example) cross: agriculture
Scheduling & Assignment
Duty rosters, gate and slot assignment — the polynomial-to-NP-hard spectrum of matching and partitioning.
Driver Duty Scheduling Set Partitioning Gate Assignment LAP / Hungarian Warehouse Slotting QAP Fleet Sizing MIP
Packing & Loading
Fitting demands into fixed-capacity containers — bin packing, cutting stock, cargo / container loading.
Warehouse Packing 1D Bin Packing Order Picking Warehouse TSP Cargo Loading (3D BP) cross: retail Cutting Stock cross: manufacturing Silo Packing cross: agriculture

A Bowersox, Closs & Cooper (2019) and Simchi-Levi et al. (2008) view follows the direction of physical flow: upstream (sourcing, inbound), midstream (transshipment, consolidation), downstream (fulfilment, last mile), and reverse (returns, recycling, closed-loop). This is the lens that makes reverse logistics and sustainability first-class citizens — the open frontier of the field.

Upstreamsourcing · inbound
Inbound / Milk-Run CVRP-inbound Economic Order Quantity EOQ · coming SC Network Design SCND · coming Lot Sizing cross: manufacturing
Midstreamcrossdock · transshipment
Hub-and-Spoke Design p-Hub Multi-Echelon Inventory ME-Inv · coming Inventory-Routing IRP · coming Fleet Sizing MIP
Downstreamfulfilment · last-mile
DC Location UFLP Depot Location CFLP CVRP (canonical) CVRP · coming Delivery Routing CVRP · applied VRPTW (canonical) VRPTW · coming Technician Routing VRPTW+skills Real-Time Dispatching Dynamic VRP Warehouse Packing 1D BP Warehouse Slotting QAP Order Picking Warehouse TSP Gate Assignment LAP Driver Scheduling Set Part.
Reversereturns · circular
Open research frontier.

Cross-link → Waste Collection (arc-routing).
Reverse-logistics, remanufacturing, and closed-loop network design are slated for a future build pass (see research frontiers below).

Application catalog

All twenty-four pages · thirteen live · eleven coming · dashed cards are upcoming canonical pages

CVRP Operational Crossover: agri · construction
Delivery Route Planning
Plan outbound delivery routes from a depot to customers under vehicle-capacity constraints, using Clarke-Wright Savings, Sweep, and Nearest Neighbor on a Quebec City road network.
Open solver
VRPTW + skills Operational Crossover: healthcare
Technician Visit Scheduling
Assign service technicians to customer appointments with hard time windows and skill-matching requirements, via Solomon I1 insertion and Nearest-Neighbor-TW heuristics on a real road map.
Open solver
Dynamic VRP Operational
Real-Time Dispatching
Rolling-horizon simulation comparing myopic, cheapest-insertion, and delay-and-batch dispatch policies as new customer requests arrive over the day.
Open solver
CVRP-inbound Operational
Inbound Logistics & Milk-Run
Consolidate inbound pickups from multiple suppliers into milk-run routes, using Clarke-Wright Savings, Nearest Neighbor, and 2-opt improvement.
Open solver
CVRP Operational Coming
Capacitated Vehicle Routing (canonical)
The abstract CVRP on CVRPLIB benchmarks (Uchoa et al.): minimise total tour length for a fleet of identical vehicles serving customers with known demands from a single depot. Dantzig & Ramser 1959.
Coming in Phase 4
TSP Operational Coming
Travelling Salesman Problem
The canonical problem of OR: find the shortest Hamiltonian tour through n cities. Held-Karp DP, Branch & Bound with 1-tree bounds, and 2-opt/3-opt local search on TSPLIB instances.
Coming in Phase 4
VRPTW Operational Coming
Vehicle Routing with Time Windows (canonical)
CVRP extended with customer time windows. Solomon I1 insertion, Nearest-Neighbor-TW, and Simulated Annealing on Solomon benchmarks. Solomon 1987.
Coming in Phase 4
1D Bin Packing Operational Crossover: agri · retail
Warehouse Packing
Pack orders of varying size into fixed-capacity bins / totes, comparing First Fit, First Fit Decreasing, and Best Fit Decreasing against theoretical 11/9 approximation bounds.
Open solver
QAP Tactical
Warehouse Slotting
Assign SKUs to storage slots to minimise picker travel distance, using the Quadratic Assignment Problem (Koopmans-Beckmann 1957) with Simulated Annealing.
Open solver
Warehouse TSP Operational
Warehouse Order Picking
Route pickers through warehouse aisles using S-shape (Ratliff & Rosenthal 1983), Nearest Neighbor, and 2-opt heuristics on a rectangular-aisle layout.
Open solver
p-Hub Median Strategic
Hub-and-Spoke Design
Select p hub locations and assign spokes to hubs to minimise total transportation cost with consolidation discounts, via Greedy, Exhaustive, and Swap Local Search (O'Kelly 1987).
Open solver
UFLP Strategic Crossover: agri
Distribution Centre Location
Uncapacitated Facility Location: select which candidate DC sites to open, minimising fixed opening cost plus customer-assignment cost. Balinski 1965. Greedy add/drop with Local Search.
Open solver
CFLP Strategic
Depot Location
Capacitated Facility Location: open depots subject to capacity limits while meeting customer demand. Greedy, Lagrangian Relaxation (Erlenkotter-style), and Local Search.
Open solver
CFLP Strategic Coming
Capacitated Facility Location (canonical)
Abstract CFLP on OR-Library benchmarks. Cornuéjols-Fisher-Sridharan dual ascent, LP relaxation, and Lagrangian heuristics.
Coming in Phase 4
UFLP Strategic Coming
Uncapacitated Facility Location (canonical)
Abstract UFLP with Erlenkotter's DUALOC dual-ascent (1978), 1.488-approximation Li (2013), and LP relaxation.
Coming in Phase 4
p-Median Strategic Crossover: healthcare · public Coming
p-Median Problem
Select p facilities to minimise weighted distance from demand nodes. Hakimi 1964. Teitz-Bart interchange, Lagrangian relaxation.
Coming in Phase 4
HLP Strategic Coming
Hub Location (canonical)
Abstract single- and multiple-allocation hub location on CAB and AP benchmarks. O'Kelly 1987; Campbell 1994; Alumur-Kara 2008 survey.
Coming in Phase 4
MIP Strategic
Fleet Sizing & Vehicle Composition
Mixed-integer programming to choose the optimal mix of small, medium, and large vehicles given demand patterns and fixed/variable cost trade-offs.
Open solver
Set Partitioning Tactical
Driver Duty Scheduling
Build minimum-cost driver duties from a set of valid duty patterns using Greedy Chaining, Column Generation, and manual drag-and-drop construction.
Open solver
EOQ Tactical Coming
Economic Order Quantity
The classical square-root formula Q* = √(2DS/h). Harris 1913; Wilson 1934. Sensitivity analysis, quantity discounts, backorder extension.
Coming in Phase 4
ME-Inv Strategic Coming
Multi-Echelon Inventory
Coordinated stocking across a serial / arborescent multi-echelon system with stochastic demand. Clark-Scarf 1960; Axsäter 2015 base-stock.
Coming in Phase 4
IRP Tactical Crossover: healthcare Coming
Inventory-Routing Problem
Jointly decide replenishment quantities and vehicle routes under vendor-managed inventory. Bell et al. 1983 (Exxon); Coelho-Cordeau-Laporte 2014 survey.
Coming in Phase 4
SCND Strategic Coming
Supply-Chain Network Design
Multi-echelon strategic network: suppliers → plants → DCs → customers. Multi-commodity MIP with capacity and service-level constraints.
Coming in Phase 4
LAP Operational
Airport Gate Assignment
Assign arriving flights to gates to minimise passenger walking distance, via Random, Greedy, and Hungarian algorithms (Kuhn 1955) — polynomial-time optimal.
Open solver

Logistics OR in context

A short history · landmarks that shaped the field

Logistics is one of the oldest branches of operations research — arguably the oldest. Many of its problems predate the term “operations research” itself. The timeline below anchors each problem family in this section to the paper that introduced it.

1781

Optimal Transport

Moving earth with minimum total effort — a continuous relaxation that later fuels Kantorovich and modern OT.

Gaspard Monge
1913

Economic Order Quantity

The closed-form formula Q* = √(2DS/h) — arguably the first OR result.

Ford W. Harris
1939–41

Transportation Problem

Linear-programming formulation of minimum-cost flow on a bipartite supplier–demand network.

L. Kantorovich; F. Hitchcock
1954

TSP as LP + cuts

Dantzig, Fulkerson & Johnson solve a 49-city instance — the first practical cutting-plane algorithm.

Dantzig, Fulkerson, Johnson
1955–58

Assignment & Lot Sizing

Kuhn's Hungarian method (1955) makes LAP polynomial. Wagner-Whitin (1958) solves dynamic lot sizing by DP.

H. Kuhn; Wagner & Whitin
1959

Vehicle Routing

“The Truck Dispatching Problem” — the paper that launched an entire OR sub-discipline.

Dantzig & Ramser
1964–65

Facility Location

Hakimi introduces p-median; Balinski formulates UFLP as an integer program.

Hakimi; Balinski
1987

VRPTW & Hubs

Solomon I1 inserts customers under time windows; O'Kelly formulates the hub-location problem.

Solomon; O'Kelly

Current research frontiers

Where logistics OR is actively evolving

Dynamic & stochastic routing

Online and anticipatory VRP variants for e-commerce, ride-hailing, and on-demand delivery — routing decisions that must commit before demand is fully revealed. Gendreau & Potvin 1998; Pillac et al. 2013; Psaraftis, Wen & Kontovas 2016.

Green & electric vehicle routing

Pollution-routing (Bektaş & Laporte 2011) and electric-vehicle routing with charging decisions: routing choices now optimise CO₂ and kWh as well as distance. Dekker, Bloemhof & Mallidis 2012.

City logistics & last-mile innovation

Consolidation hubs, drone & autonomous delivery, micro-fulfilment, and curb-space management — the operational research of ever-denser urban freight. Taniguchi, Thompson & Yamada 2014.

Reverse logistics & closed-loop networks

Returns processing, remanufacturing, and circular supply-chain network design. Rapidly growing under e-commerce return rates of 20–30% and extended-producer-responsibility regulation.

ML-assisted OR

Learning-augmented heuristics (pointer networks, graph neural networks, RL for VRP) and predict-then-optimize pipelines. Powell 2022; Kool et al. 2019; Bengio, Lodi & Prouvost 2021.

Robust & distributionally robust logistics

Routing, location, and inventory decisions hedged against ambiguous demand & travel-time distributions. Wasserstein-DRO formulations for facility location and VRP.

Key references

Cited above · DOIs & permanent URLs

Chopra, S., & Meindl, P. (2019).
Supply Chain Management: Strategy, Planning, and Operation (7th ed.).
Pearson. ISBN 978-0-13-453245-2 · pearson.com
Ghiani, G., Laporte, G., & Musmanno, R. (2013).
Introduction to Logistics Systems Management (2nd ed.).
Wiley · doi:10.1002/9781118492185
Bowersox, D. J., Closs, D. J., & Cooper, M. B. (2019).
Supply Chain Logistics Management (5th ed.).
McGraw-Hill.
Simchi-Levi, D., Kaminsky, P., & Simchi-Levi, E. (2008).
Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies (3rd ed.).
McGraw-Hill.
Toth, P., & Vigo, D. (Eds.) (2014).
Vehicle Routing: Problems, Methods, and Applications (2nd ed.).
SIAM / MOS-SIAM Series on Optimization · doi:10.1137/1.9781611973594
Daskin, M. S. (2013).
Network and Discrete Location: Models, Algorithms, and Applications (2nd ed.).
Wiley · doi:10.1002/9781118537015
Laporte, G., Nickel, S., & Saldanha-da-Gama, F. (Eds.) (2019).
Location Science (2nd ed.).
Springer · doi:10.1007/978-3-030-32177-2
Zipkin, P. H. (2000).
Foundations of Inventory Management.
McGraw-Hill.
Axsäter, S. (2015).
Inventory Control (3rd ed.).
Springer · doi:10.1007/978-3-319-15729-0
Dantzig, G. B., & Ramser, J. H. (1959).
“The truck dispatching problem.”
Management Science, 6(1), 80–91. doi:10.1287/mnsc.6.1.80
Clarke, G., & Wright, J. W. (1964).
“Scheduling of vehicles from a central depot to a number of delivery points.”
Operations Research, 12(4), 568–581. doi:10.1287/opre.12.4.568
Solomon, M. M. (1987).
“Algorithms for the vehicle routing and scheduling problems with time window constraints.”
Operations Research, 35(2), 254–265. doi:10.1287/opre.35.2.254
Hakimi, S. L. (1964).
“Optimum locations of switching centers and the absolute centers and medians of a graph.”
Operations Research, 12(3), 450–459. doi:10.1287/opre.12.3.450
Balinski, M. L. (1965).
“Integer programming: Methods, uses, computation.”
Management Science, 12(3), 253–313. doi:10.1287/mnsc.12.3.253
Harris, F. W. (1913).
“How many parts to make at once.”
Factory, The Magazine of Management, 10(2), 135–136. (Reprinted in Operations Research, 38(6), 1990, 947–950.)
Kuhn, H. W. (1955).
“The Hungarian method for the assignment problem.”
Naval Research Logistics Quarterly, 2(1–2), 83–97. doi:10.1002/nav.3800020109
O'Kelly, M. E. (1987).
“A quadratic integer program for the location of interacting hub facilities.”
European Journal of Operational Research, 32(3), 393–404. doi:10.1016/S0377-2217(87)80007-3
Alumur, S., & Kara, B. Y. (2008).
“Network hub location problems: The state of the art.”
European Journal of Operational Research, 190(1), 1–21. doi:10.1016/j.ejor.2007.06.008
Coelho, L. C., Cordeau, J.-F., & Laporte, G. (2014).
“Thirty years of inventory routing.”
Transportation Science, 48(1), 1–19. doi:10.1287/trsc.2013.0472
Bektaş, T., & Laporte, G. (2011).
“The Pollution-Routing Problem.”
Transportation Research Part B, 45(8), 1232–1250. doi:10.1016/j.trb.2011.02.004
Pillac, V., Gendreau, M., Guéret, C., & Medaglia, A. L. (2013).
“A review of dynamic vehicle routing problems.”
European Journal of Operational Research, 225(1), 1–11. doi:10.1016/j.ejor.2012.08.015
Crainic, T. G., & Laporte, G. (1997).
“Planning models for freight transportation.”
European Journal of Operational Research, 97(3), 409–438. doi:10.1016/S0377-2217(96)00298-6
ASCM (Association for Supply Chain Management).
SCOR Digital Standard (Plan · Source · Make · Deliver · Return · Enable).
scor.ascm.org
World Bank.
Logistics Performance Index.
lpi.worldbank.org
International Energy Agency (IEA).
Transport sector tracking — CO₂ emissions.
iea.org/energy-system/transport

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