Routing, Scheduling and Load Planning

Introduction

Transportation performance depends not only on the availability of vehicles and infrastructure but also on the quality of operational decisions. A shipment may be moved over a technically feasible route and still create excessive cost because vehicles return empty, deliveries miss customer time windows, loads are poorly consolidated, or schedules ignore loading and unloading constraints. Routing, scheduling and load planning therefore form an integrated decision problem within transportation systems.

Routing determines the paths or sequences followed by vehicles or shipments. Scheduling assigns activities to time periods and specifies when vehicles depart, arrive, load, unload and return. Load planning determines which consignments are placed on which vehicles and where they are positioned. At postgraduate level, these decisions should be understood as interdependent optimisation problems rather than isolated clerical tasks.

A useful managerial principle is that the objective is not simply to minimise distance. A practical plan must balance transport cost, service quality, fleet utilisation, safety, emissions, labour regulations, risk and resilience.

Learning Objectives

After studying this chapter, the learner should be able to:

1. Formulate shortest-path, transportation and transshipment models.
2. Distinguish vehicle-routing variants and select suitable solution methods.
3. Construct feasible schedules under capacity and time-window constraints.
4. Estimate fleet requirements and evaluate utilisation.
5. Apply load-consolidation and load-sequencing principles.
6. Interpret optimisation results critically, including their assumptions and limitations.
7. Explain the role of transport-management systems, analytics and artificial intelligence in operational planning.

1. The Decision Architecture

Transportation planning is commonly organised into three horizons:

These horizons interact. A depot located far from demand may force longer routes; an undersized fleet may make a mathematically efficient schedule infeasible; and a vehicle configuration may limit the type of cargo that can be consolidated.

A transportation plan can be represented as a network G = (V, A), where V is the set of nodes and A is the set of directed links or arcs. Nodes may represent suppliers, plants, depots, cross-docks, customers, ports or terminals. Each arc may have distance, travel time, monetary cost, capacity, reliability and emissions attributes.

Important terminology includes:

• Origin and destination: the starting and ending points of a movement.
• Node: a location in a transportation network.
• Arc or link: a feasible movement between two nodes.
• Demand: quantity requiring movement between specified points.
• Lead time: elapsed time between order release and receipt.
• Time window: an interval during which service must begin or be completed.
• Deadhead movement: travel without revenue-generating cargo.
• Backhaul: a return movement, preferably carrying useful freight.
• Consolidation: combining compatible consignments into one movement.
• Transshipment: transferring cargo through an intermediate node.
• Route: an ordered sequence of nodes visited by a vehicle or shipment.

2. Shortest-Path and Network Models

2.1 Shortest-path problem

The shortest-path problem seeks a least-cost path from an origin node o to a destination node d. If cᵢⱼ is the cost of traversing arc (i, j), and xᵢⱼ is 1 when that arc is selected and 0 otherwise, the objective is:

Subject to flow conservation:

where bₒ = 1, b_d = −1, and bᵢ = 0 for all other nodes. The variable xᵢⱼ is binary. Costs must use consistent units, such as kilometres, minutes or monetary units. The model assumes known arc costs and a static network. It does not by itself represent vehicle capacity, multiple customers or delivery time windows.

For non-negative arc costs, Dijkstra’s algorithm efficiently solves the single-source shortest-path problem. If negative arc costs exist, Bellman–Ford may be required; negative cycles require special treatment. In practical transport networks, dynamic travel times, congestion and turn restrictions often require time-dependent or resource-constrained shortest-path methods.

2.2 Transportation model

The transportation model allocates quantities from several origins to several destinations. Let sᵢ be supply at origin i, dⱼ be demand at destination j, cᵢⱼ be unit shipping cost, and xᵢⱼ be the quantity shipped. The balanced model is:

subject to:

When total supply equals total demand and all supply and demand must be used, the inequalities become equalities. The model is appropriate for divisible flows, such as pallets or tonnes, but not automatically for indivisible loads or detailed vehicle tours.

2.3 Transshipment model

A transshipment model allows flow through intermediate nodes. It is useful for hub-and-spoke networks, cross-docking, rail-road interfaces and multimodal transport. Flow conservation at an intermediate node k is:

unless the node has a permitted gain or loss, such as handling loss or inventory accumulation. Transshipment can reduce line-haul costs through consolidation, but it adds handling, delay, damage exposure and coordination requirements.

3. Vehicle-Routing Models

The vehicle-routing problem (VRP) extends shortest-path logic to multiple customers and vehicles. In the capacitated VRP, each customer must be visited, each vehicle begins and ends at a depot, and vehicle capacity cannot be exceeded.

Let xᵢⱼᵏ equal 1 if vehicle k travels from i to j. Let cᵢⱼ be travel cost, qᵢ be customer demand, and Qᵏ be the capacity of vehicle k. A typical objective is:

subject to customer-visit constraints, route-continuity constraints and capacity constraints:

where yᵢᵏ equals 1 if customer i is assigned to vehicle k. Additional constraints eliminate subtours, which are disconnected cycles that do not include the depot.

Common variants include:

• CVRP: capacitated VRP.
• VRPTW: VRP with time windows.
• MDVRP: multi-depot VRP.
• HVRP: heterogeneous-fleet VRP, where vehicles differ in capacity or cost.
• Pickup-and-delivery VRP: pickups and deliveries are paired and precedence must be respected.
• Periodic VRP: customers are served on specified recurring days.
• Open VRP: vehicles need not return to the starting depot.
• Stochastic VRP: demand or travel time is uncertain.

VRP is generally computationally difficult as problem size grows. Exact mixed-integer programming is valuable for small and medium instances or for benchmarking. For larger operational problems, constructive heuristics, savings methods, local search, tabu search, simulated annealing, genetic algorithms and large-neighbourhood search are commonly used. A sophisticated method is not automatically superior: data quality, feasibility controls and response time often determine practical value.

Time windows and service times

If vehicle k reaches customer i at time tᵢᵏ, service must occur within [aᵢ, bᵢ]. Waiting may be allowed:

and:

Here sᵢ is service time at i, τᵢⱼ is travel time from i to j, and M is a sufficiently large constant. The equation is active only when arc (i, j) is used. Excessively large M values can weaken optimisation performance; tighter bounds are preferable.

Time windows may be hard, meaning violation is prohibited, or soft, meaning violation incurs a penalty. A soft-window objective may include:

where α and β are penalty rates. Usually β is greater than α when late delivery is more damaging than early arrival.

4. Scheduling and Fleet Sizing

Routing answers “where should the vehicle go?” Scheduling answers “when should each activity occur?” A schedule includes loading, dispatch, travel, breaks, unloading, return and maintenance. Ignoring non-driving time produces systematically optimistic plans.

For a vehicle route, total cycle time may be estimated as:

All terms must use the same unit, normally hours. The buffer protects against congestion, queueing and operational variation.

If a daily workload requires H vehicle-hours and each available vehicle provides E productive hours, a basic fleet estimate is:

The ceiling function ensures that a fraction of a vehicle is rounded upward. This estimate assumes workload and vehicle hours are measured consistently and ignores vehicle heterogeneity. If demand is uncertain, a service-level or scenario-based model is preferable.

A utilisation ratio can be defined as:

Utilisation must be interpreted carefully. Very high utilisation may indicate efficiency, but it may also imply inadequate resilience, missed time windows and excessive driver overtime. Load factor is different:

A vehicle can have high load factor but poor time utilisation, or the reverse.

Scheduling must comply with driver-hours regulations, mandatory rest, maximum working hours, vehicle maintenance windows, appointment slots and terminal operating hours. Regulatory requirements vary by jurisdiction and vehicle type; therefore, planners must consult current law rather than rely on generic assumptions.

5. Load Planning and Consolidation

Load planning has three related objectives: use vehicle capacity effectively, preserve cargo integrity and ensure safe, feasible unloading. Capacity is multidimensional:

• Weight capacity: tonnes or kilograms.
• Volume capacity: cubic metres.
• Floor or pallet positions: loading locations.
• Axle capacity: allowable weight distribution.
• Compatibility capacity: restrictions involving hazardous, perishable or incompatible goods.

A simple load-consolidation model selects consignments for a vehicle. Let vᵢ be the volume of shipment i, wᵢ its weight, pᵢ its contribution or avoided cost, and zᵢ a binary selection variable. With vehicle volume V and weight W:

subject to:

This is a multidimensional knapsack representation. It is useful for selection, but it does not guarantee that selected freight can be physically arranged or unloaded in the required sequence.

A feasible load plan should consider:

1. Delivery sequence: goods for the first delivery should generally be accessible first.
2. Stability: heavy items should be low and properly restrained.
3. Axle loading: weight must be distributed within legal axle limits.
4. Fragility and compatibility: hazardous, odorous, wet or fragile products may require separation.
5. Temperature control: cold-chain products require validated temperature conditions.
6. Cube and weight balance: filling volume while exceeding weight is infeasible.
7. Reverse logistics: returns, packaging and rejected goods require space.

Consolidation produces economies when fixed dispatch costs are shared. However, excessive consolidation can increase dwell time, handling, route complexity and service risk. The correct decision compares total logistics cost, not merely cost per loaded vehicle.

6. Integrated Planning Workflow

A professional planning process can follow these stages:

1. Clean the data: validate addresses, demand units, vehicle dimensions, service times and operating calendars.
2. Define the service promise: specify delivery windows, priorities and acceptable lateness.
3. Generate feasible arcs: remove roads, terminals or vehicle movements that violate restrictions.
4. Assign demand to facilities or lanes: use transportation or transshipment models where appropriate.
5. Construct routes: apply exact optimisation or heuristics according to scale and urgency.
6. Schedule routes: insert appointments, breaks, loading and unloading activities.
7. Check load feasibility: verify weight, cube, axle loads, compatibility and unloading sequence.
8. Validate operationally: obtain driver, warehouse and customer-service feedback.
9. Dispatch and monitor: compare planned versus actual progress.
10. Re-optimise: respond to traffic, cancellations, breakdowns and urgent orders.
11. Review performance: measure cost, service, utilisation, empty kilometres, emissions and safety.

A route is feasible only if it passes all relevant checks. A mathematically optimal route that cannot be loaded, driven legally or serviced at the customer is not an operational solution.

7. Worked Example: Small Delivery Plan

An illustrative distributor operates one depot and must serve four customers. Vehicle capacity is 1,000 kg and 8 m³. The route is planned in delivery order A–B–C–D. Data are:

Total weight is:

Total volume is:

Thus, the route satisfies both vehicle capacities, with 100 kg and 1 m³ remaining. Suppose the depot loading takes 0.5 h, travel times are depot–A 0.5 h, A–B 0.4 h, B–C 0.3 h, C–D 0.4 h and D–depot 0.6 h. The vehicle departs at 07:30.

Arrival at A is 08:00, within its window. Departure is 08:15. Arrival at B is 08:39, before the opening time of 09:00, so the vehicle waits 21 minutes and begins service at 09:00. Departure is 09:12. Arrival at C is 09:30, so the vehicle waits until 10:00. Departure is 10:18. Arrival at D is 10:42, so it waits until 11:00. Departure is 11:12. Return to the depot occurs at 11:48, excluding any additional unloading time.

The example demonstrates that capacity feasibility does not guarantee time efficiency. Waiting accounts for 21 + 30 + 18 = 69 minutes. An alternative sequence or later departure might reduce waiting, but it must preserve all time windows and the loading sequence. If customer A had required delivery by 08:00, the plan would need a departure earlier than 07:30 or a different route structure.

8. Applied Case: Urban Grocery Distribution

This is an illustrative case based on common industry conditions.

Background

A regional grocery distributor serves 86 stores from one metropolitan distribution centre. It operates a mixed fleet of refrigerated trucks and vans. Store deliveries have appointment windows, and vehicles carry both ambient and chilled products.

Problem

The company experiences 14% empty kilometres, frequent late arrivals at large stores and vehicle overloading on high-volume days. Planners use spreadsheets, and routes are often modified manually after dispatch. The main difficulty is not lack of demand data but inconsistent master data: service times are understated, vehicle capacities are recorded only by weight, and store receiving hours are not always current.

Analysis

A diagnostic study separates the problem into three layers. First, a transportation model allocates store demand to the distribution centre and possible satellite cross-dock. Second, a heterogeneous-fleet VRPTW constructs routes using vehicle type, refrigeration requirements and store time windows. Third, a load-planning module checks weight, cube, pallet positions and delivery sequence.

Historical GPS data are used to estimate travel-time distributions rather than a single average. For example, a route may use the 85th-percentile travel time during a congested period. The company also distinguishes hard windows, such as legal receiving hours, from soft windows, where a penalty is applied for deviation.

Approach and solution

The distributor implements the following policy:

• Cluster stores geographically before route construction, while allowing cross-cluster reassignment when it improves feasibility.
• Reserve refrigerated capacity before filling residual ambient capacity.
• Use realistic loading and service times based on observed data.
• Penalise late delivery more heavily than early arrival.
• Sequence pallets in reverse delivery order, subject to axle and stability constraints.
• Maintain a daily exception list for breakdowns, traffic incidents and urgent orders.
• Re-optimise only affected routes when possible, avoiding unnecessary disruption to all drivers.

A rolling weekly review compares planned and actual service times. Drivers can report access restrictions through a mobile application, and changes are approved by a transport planner rather than inserted without governance.

Outcome

After three months, the illustrative programme reduces empty kilometres, improves appointment adherence and lowers emergency vehicle use. The improvement is attributed less to the optimisation algorithm alone than to better data, explicit constraints and operational adoption. The company also discovers that pushing utilisation above a safe threshold increases late deliveries; therefore, it introduces a resilience buffer rather than maximising utilisation unconditionally.

Learning points

1. Data governance is a prerequisite for optimisation.
2. Weight-only capacity measures are inadequate for grocery distribution.
3. Human review remains important when conditions change rapidly.
4. Service reliability and safety may justify a higher nominal transport cost.
5. Load planning, routing and scheduling should be evaluated as one system.

9. Technology, AI and Contemporary Developments

Transport-management systems integrate orders, maps, vehicle data, warehouse appointments, proof of delivery and billing. A modern system may use GPS, telematics, electronic proof of delivery, geofencing and real-time traffic feeds.

Artificial intelligence can support demand forecasting, travel-time prediction, address correction, anomaly detection and dynamic re-routing. Machine-learning predictions should not be confused with optimisation: a predictive model estimates what may happen, while an optimisation model chooses an action subject to constraints. Combining the two is useful, but predictions must be monitored for drift and bias.

Digital twins can simulate fleet, depot and network changes before implementation. Internet-of-Things sensors can monitor temperature, door opening, shock and location. However, technology introduces cybersecurity, privacy, vendor-dependence and data-quality risks. Automated re-routing should have rules that protect customer commitments, driver safety and regulatory compliance.

10. Limitations, Governance and Ethical Considerations

Models simplify reality. Travel times vary; customer demand changes; loading may be slower than planned; and road conditions can make an optimal route infeasible. Common modelling errors include:

• treating average travel time as guaranteed travel time;
• omitting loading, waiting and service time;
• using nominal rather than usable vehicle capacity;
• ignoring driver breaks and legal restrictions;
• allowing mathematically feasible but physically impossible loading;
• measuring cost while neglecting service and safety.

Governance requires version-controlled data, documented assumptions, approval rights, audit trails and exception procedures. Driver-monitoring data should be collected proportionately and handled according to privacy law and organisational policy. Algorithms should not systematically assign unsafe or excessively burdensome work to particular drivers or locations. Environmental claims should use transparent boundaries, including empty travel, refrigeration energy and outsourced movements where relevant.

Best-Practice Principles

1. Model the complete operational process, not only travel distance.
2. Use hard constraints for safety, law and physical feasibility.
3. Use explicit penalties for soft service preferences.
4. Separate strategic, tactical and operational decisions but link their data.
5. Validate solutions with dispatchers, drivers, warehouses and customers.
6. Measure total cost, service, safety, emissions and resilience together.
7. Use scenario analysis for congestion, demand peaks and vehicle failure.
8. Re-plan selectively when disruption occurs.
9. Treat master-data maintenance as a continuing management process.
10. Prefer a robust, explainable plan to a fragile theoretical optimum.

Chapter Summary

Routing identifies feasible and economical movement paths; scheduling assigns times to loading, travel, service, breaks and return; and load planning allocates freight while respecting weight, volume, axle, compatibility and unloading requirements. Shortest-path, transportation and transshipment models address network flows, while vehicle-routing models represent multi-customer vehicle tours. Time windows, service times and driver regulations convert a distance problem into a time-constrained operational problem.

Fleet sizing can begin with the ratio of workload hours to productive vehicle hours, but uncertainty and resilience must also be considered. Consolidation reduces fixed movement cost when shipments are compatible, yet excessive consolidation can increase waiting and service risk. Effective practice integrates optimisation with accurate data, operational validation, digital monitoring and governance. The best transportation plan is therefore not merely the least-distance plan; it is a feasible, safe, service-compliant and economically robust plan.

Key Terms

Shortest path: Least-cost path between an origin and destination in a network.

Transportation model: Model allocating flow from multiple origins to multiple destinations.

Transshipment: Movement through one or more intermediate nodes.

Vehicle-routing problem: Optimisation of routes for vehicles serving multiple customers.

Capacitated VRP: Vehicle-routing problem with vehicle-load limits.

Time window: Permitted interval for starting or completing service.

Service time: Time spent loading, unloading or serving a customer.

Subtour: Disconnected cycle in a routing solution that does not connect properly to the depot.

Deadhead: Vehicle movement without revenue-generating freight.

Backhaul: Return movement carrying freight after an outbound trip.

Consolidation: Combining shipments into a larger movement.

Load factor: Actual payload divided by rated payload.

Fleet utilisation: Productive vehicle-hours divided by available vehicle-hours.

Heterogeneous fleet: Fleet containing vehicles with different capacities or costs.

Hard constraint: Requirement that cannot be violated.

Soft constraint: Preference whose violation is permitted with a penalty.

Cross-docking: Transfer of goods through a facility with little or no storage.

Rolling horizon: Planning method that repeatedly updates future decisions as new information arrives.

Review Questions

Short Answer Questions

1. Distinguish routing from scheduling.
2. What is the purpose of a transshipment node?
3. Define a vehicle time window.
4. Why can weight capacity alone be insufficient for load planning?
5. State two limitations of using average travel time in route planning.

Long Answer Questions

1. Explain the structure and assumptions of the shortest-path, transportation and transshipment models.
2. Compare CVRP, VRPTW, MDVRP and heterogeneous-fleet VRP.
3. Discuss how loading sequence, axle limits and compatibility affect load planning.
4. Explain the relationship between fleet sizing, utilisation and resilience.
5. Evaluate the role of transport-management systems and AI in integrated transportation planning.

Analytical / Application Questions

1. A depot must deliver to customers with different demands, service times and time windows. Design a method for constructing and validating a feasible route, identifying the data required.
2. A company has high vehicle utilisation but increasing late deliveries and driver overtime. Diagnose the likely causes and recommend operational and modelling changes.
3. Compare direct delivery with a cross-docking alternative when consolidation reduces line-haul cost but adds handling time. Specify the cost, service and risk factors that should be included in the decision.

Multiple Choice Questions with Answers

Question 1

Which model is primarily designed to allocate quantities from several origins to several destinations?

A. Shortest-path model

B. Transportation model

C. Assignment-only model

D. Inventory-review model

Correct Answer: B. Transportation model

Question 2

In a shortest-path formulation, what does xᵢⱼ = 1 normally indicate?

A. Arc (i, j) is selected

B. Node i has zero demand

C. Vehicle j is unavailable

D. Customer i is late

Correct Answer: A. Arc (i, j) is selected

Question 3

Which constraint is central to a capacitated vehicle-routing problem?

A. Every vehicle must visit every customer

B. Total assigned demand must not exceed vehicle capacity

C. All routes must have equal distance

D. All customers must be served at the same time

Correct Answer: B. Total assigned demand must not exceed vehicle capacity

Question 4

A vehicle has 1,000 kg rated payload and carries 750 kg. Its load factor is:

A. 25%

B. 50%

C. 75%

D. 133%

Correct Answer: C. 75%

Question 5

If a route requires 42 productive vehicle-hours and each vehicle provides 8 productive hours, the minimum fleet estimate is:

A. 4 vehicles

B. 5 vehicles

C. 6 vehicles

D. 8 vehicles

Correct Answer: C. 6 vehicles

Question 6

Which statement best describes a hard time window?

A. It may be violated without consequence

B. It can be violated only when fuel prices rise

C. Violation is prohibited in the model

D. It applies only to warehouse loading

Correct Answer: C. Violation is prohibited in the model

Question 7

What is a major purpose of load sequencing?

A. To maximise empty kilometres

B. To ensure freight is accessible in delivery order

C. To eliminate all service times

D. To make every vehicle identical

Correct Answer: B. To ensure freight is accessible in delivery order

Question 8

Which movement is called deadheading?

A. A return trip carrying a backhaul

B. Travel without revenue-generating cargo

C. A refrigerated delivery

D. A transshipment through a hub

Correct Answer: B. Travel without revenue-generating cargo

Question 9

Why are subtour-elimination constraints used in vehicle-routing models?

A. To prevent disconnected customer cycles

B. To increase vehicle speed

C. To calculate fuel density

D. To remove all time windows

Correct Answer: A. To prevent disconnected customer cycles

Question 10

Which statement about AI in transportation planning is most accurate?

A. Prediction automatically guarantees an optimal route

B. AI removes the need for operational constraints

C. AI can predict travel times, while optimisation selects constrained actions

D. AI makes data governance unnecessary

Correct Answer: C. AI can predict travel times, while optimisation selects constrained actions