WGU D605 Optimization – Task 3
Amazon Air Fleet Optimization: Mixed-Integer Linear Programming Solution
The following report covers the implementation, solution analysis, development reflection,
references, and complete executable Python code.
Amazon Air Fleet Optimization: Mixed-
Integer Linear Programming Solution
WGU D605 – Optimization
Task 3 – Performance Assessment
Western Governors University
October 2026
Executive Summary
This report presents the implementation and evaluation of a mathematical optimization program
designed to improve aircraft routing and fleet utilization in an illustrative Amazon Air cargo
transportation network. The project builds on the optimization problem and mathematical model
developed in Task 2, translating the proposed solution into executable Python code and
evaluating its performance against operational requirements.
The optimization problem involves assigning available aircraft to cargo delivery routes while
minimizing the combined costs of flight operations, aircraft activation, ground handling, and late
deliveries. Each candidate route must satisfy aircraft capacity limitations, destination demand,
delivery time windows, and operational scheduling constraints.
The solution uses a mixed-integer linear programming (MILP) approach implemented in Python
with SciPy's optimization interface and the HiGHS solver. A route-enumeration technique
generates feasible aircraft-specific routes, after which an integer optimization model determines
the lowest-cost combination.
The program evaluated 38 feasible candidate routes and identified a minimum modeled operating
cost of $8,505.00. This represents a reduction of $305.00, or approximately 3.46%, compared
with a feasible baseline routing plan costing $8,810.00.
The optimal solution activates two of the three available aircraft, fulfills all 18 hypothetical cargo
units across four destinations, and satisfies all modeled capacity, time-window, and route-
continuity requirements without incurring late-delivery penalties.
,These findings demonstrate that integer optimization can improve resource allocation and
support transparent logistics decisions. The results are based on a clearly defined hypothetical
dataset and demonstrate the analytical method rather than actual Amazon Air cost savings.
1. Introduction
Aircraft fleet routing presents a challenging optimization problem because each assignment
affects costs, delivery performance, aircraft availability, and subsequent routing decisions. A
route that appears inexpensive when examined individually may prevent an aircraft from
servicing another destination or may violate its carrying capacity.
Amazon Air provides a relevant business setting for this analysis because of its extensive air
cargo operations. According to an August 2026 announcement, Amazon's Cincinnati/Northern
Kentucky International Airport hub processes substantial package volumes and supports more
than three dozen daily flights.
In this project, the Amazon Air business context is represented by a simplified network operating
from Cincinnati/Northern Kentucky International Airport (CVG). Four delivery destinations are
considered: Atlanta (ATL), Chicago O'Hare (ORD), Baltimore/Washington (BWI), and
Dallas/Fort Worth (DFW).
The purpose of Task 3 is to implement and evaluate the optimization methodology developed in
Task 2. The implementation must provide a reproducible program, determine optimal values for
decision variables, verify operational constraints, explain the computational results, and evaluate
the development process.
The analysis addresses the following question:
How can available aircraft be assigned to feasible delivery routes to minimize total
operational costs while satisfying cargo demand, aircraft capacity, delivery deadlines, and
route continuity?
The project objectives are to:
1. Implement the mathematical optimization model using Python.
2. Generate feasible aircraft routes satisfying the operational requirements.
3. Determine the combination of routes producing the minimum total cost.
4. Validate the optimization results independently.
5. Compare the optimized solution with an existing feasible planning alternative.
6. Evaluate the strengths, limitations, and practical implications of the proposed approach.
The analysis uses a deterministic, single-period model with hypothetical inputs. Real Amazon
Air operational records, aircraft manifests, fuel expenses, dispatch schedules, and contractual
service requirements were not supplied.
, A. Optimization Program Implementation
A1. Programming Language and Tools
Python was selected as the primary implementation language because it supports mathematical
modeling, numerical computation, data validation, and optimization using established open-
source libraries.
Its readability also makes the program easier to inspect and maintain. The model parameters,
decision variables, constraints, and solution-processing procedures can be separated into
functions, allowing individual components to be tested independently.
The implementation was executed using the following environment.
Component Version or technology Purpose
Programming language Python 3.13.5 Optimization application
Numerical computation NumPy 2.3.5 Matrices, vectors, and model coefficients
Optimization interface SciPy 1.17.0 Mixed-integer programming
MILP solver HiGHS through SciPy Find the minimum-cost feasible solution
Sparse matrix representation scipy.sparse Construct constraint matrices
Standard Python libraries itertools Generate aircraft route permutations
SciPy's milp() function accepts objective coefficients, integer-variable specifications, bounds,
and linear constraints. It solves these models using the HiGHS optimization software.
This implementation preserves the mixed-integer optimization approach identified in Task 2. The
reduced computational formulation uses binary variables only, making it a binary integer linear
program, which is a special case of MILP.
The original Task 2 recommendation also identified PuLP and CBC as suitable alternatives.
Those tools remain viable for operational implementations. However, the executed results
presented in this report were obtained using SciPy and HiGHS, not CBC.
A2. Mathematical Model Implementation
A2.1 Problem formulation
The system determines which aircraft should operate each delivery route while minimizing total
transportation costs. Aircraft may serve one or multiple destinations, provided that the combined
demand does not exceed their available cargo capacity.
Each activated aircraft begins at CVG, visits its assigned destinations, and returns to CVG before
the end of the scheduling horizon.
Amazon Air Fleet Optimization: Mixed-Integer Linear Programming Solution
The following report covers the implementation, solution analysis, development reflection,
references, and complete executable Python code.
Amazon Air Fleet Optimization: Mixed-
Integer Linear Programming Solution
WGU D605 – Optimization
Task 3 – Performance Assessment
Western Governors University
October 2026
Executive Summary
This report presents the implementation and evaluation of a mathematical optimization program
designed to improve aircraft routing and fleet utilization in an illustrative Amazon Air cargo
transportation network. The project builds on the optimization problem and mathematical model
developed in Task 2, translating the proposed solution into executable Python code and
evaluating its performance against operational requirements.
The optimization problem involves assigning available aircraft to cargo delivery routes while
minimizing the combined costs of flight operations, aircraft activation, ground handling, and late
deliveries. Each candidate route must satisfy aircraft capacity limitations, destination demand,
delivery time windows, and operational scheduling constraints.
The solution uses a mixed-integer linear programming (MILP) approach implemented in Python
with SciPy's optimization interface and the HiGHS solver. A route-enumeration technique
generates feasible aircraft-specific routes, after which an integer optimization model determines
the lowest-cost combination.
The program evaluated 38 feasible candidate routes and identified a minimum modeled operating
cost of $8,505.00. This represents a reduction of $305.00, or approximately 3.46%, compared
with a feasible baseline routing plan costing $8,810.00.
The optimal solution activates two of the three available aircraft, fulfills all 18 hypothetical cargo
units across four destinations, and satisfies all modeled capacity, time-window, and route-
continuity requirements without incurring late-delivery penalties.
,These findings demonstrate that integer optimization can improve resource allocation and
support transparent logistics decisions. The results are based on a clearly defined hypothetical
dataset and demonstrate the analytical method rather than actual Amazon Air cost savings.
1. Introduction
Aircraft fleet routing presents a challenging optimization problem because each assignment
affects costs, delivery performance, aircraft availability, and subsequent routing decisions. A
route that appears inexpensive when examined individually may prevent an aircraft from
servicing another destination or may violate its carrying capacity.
Amazon Air provides a relevant business setting for this analysis because of its extensive air
cargo operations. According to an August 2026 announcement, Amazon's Cincinnati/Northern
Kentucky International Airport hub processes substantial package volumes and supports more
than three dozen daily flights.
In this project, the Amazon Air business context is represented by a simplified network operating
from Cincinnati/Northern Kentucky International Airport (CVG). Four delivery destinations are
considered: Atlanta (ATL), Chicago O'Hare (ORD), Baltimore/Washington (BWI), and
Dallas/Fort Worth (DFW).
The purpose of Task 3 is to implement and evaluate the optimization methodology developed in
Task 2. The implementation must provide a reproducible program, determine optimal values for
decision variables, verify operational constraints, explain the computational results, and evaluate
the development process.
The analysis addresses the following question:
How can available aircraft be assigned to feasible delivery routes to minimize total
operational costs while satisfying cargo demand, aircraft capacity, delivery deadlines, and
route continuity?
The project objectives are to:
1. Implement the mathematical optimization model using Python.
2. Generate feasible aircraft routes satisfying the operational requirements.
3. Determine the combination of routes producing the minimum total cost.
4. Validate the optimization results independently.
5. Compare the optimized solution with an existing feasible planning alternative.
6. Evaluate the strengths, limitations, and practical implications of the proposed approach.
The analysis uses a deterministic, single-period model with hypothetical inputs. Real Amazon
Air operational records, aircraft manifests, fuel expenses, dispatch schedules, and contractual
service requirements were not supplied.
, A. Optimization Program Implementation
A1. Programming Language and Tools
Python was selected as the primary implementation language because it supports mathematical
modeling, numerical computation, data validation, and optimization using established open-
source libraries.
Its readability also makes the program easier to inspect and maintain. The model parameters,
decision variables, constraints, and solution-processing procedures can be separated into
functions, allowing individual components to be tested independently.
The implementation was executed using the following environment.
Component Version or technology Purpose
Programming language Python 3.13.5 Optimization application
Numerical computation NumPy 2.3.5 Matrices, vectors, and model coefficients
Optimization interface SciPy 1.17.0 Mixed-integer programming
MILP solver HiGHS through SciPy Find the minimum-cost feasible solution
Sparse matrix representation scipy.sparse Construct constraint matrices
Standard Python libraries itertools Generate aircraft route permutations
SciPy's milp() function accepts objective coefficients, integer-variable specifications, bounds,
and linear constraints. It solves these models using the HiGHS optimization software.
This implementation preserves the mixed-integer optimization approach identified in Task 2. The
reduced computational formulation uses binary variables only, making it a binary integer linear
program, which is a special case of MILP.
The original Task 2 recommendation also identified PuLP and CBC as suitable alternatives.
Those tools remain viable for operational implementations. However, the executed results
presented in this report were obtained using SciPy and HiGHS, not CBC.
A2. Mathematical Model Implementation
A2.1 Problem formulation
The system determines which aircraft should operate each delivery route while minimizing total
transportation costs. Aircraft may serve one or multiple destinations, provided that the combined
demand does not exceed their available cargo capacity.
Each activated aircraft begins at CVG, visits its assigned destinations, and returns to CVG before
the end of the scheduling horizon.
