Teacher(s)
Language
English
Prerequisites
Students are expected to have a strong background in the following areas:
• Foundations of Linear and Integer Programming
• Basic knowledge of graph theory
• Probability theory and stochastic processes
• Programming skills in Python and experience in implementing or SCIP.
• Foundations of Linear and Integer Programming
• Basic knowledge of graph theory
• Probability theory and stochastic processes
• Programming skills in Python and experience in implementing or SCIP.
Main themes
This course introduces foundational principles and advanced mathematical and algorithmic methods for designing, analyzing, and optimizing complex networked systems, including supply chains, infrastructure networks, and digital platforms. It integrates large-scale optimization, uncertainty modeling, decomposition techniques, and AI-assisted decision methods, with applications in transportation, telecommunications, logistics, and strategic resource systems.
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | 1. Model complex real-world logistic and supply chain systems as mathematical optimization programs (MILP, MINLP, and bilevel formulations) integrating discrete decisions, flows, and complex constraints. 2. Critically analyze optimization models, assessing correctness, scalability, sensitivity to parameters, and structural strength. 3. Design advanced solution strategies, including relaxations, decomposition methods, cutting-plane approaches, and controlled heuristics. 4. Evaluate robustness and structural resilience of decision systems under uncertainty, disruptions, adversarial events, or demand shocks. 5. Formulate and analyze network-based decision systems across physical, digital, and hybrid infrastructures. 6. Interpret AI methods within optimization pipelines, understanding machine learning and reinforcement learning as tools for approximating optimal decisions or accelerating optimization procedures. 7. Implement computational optimization workflows using modern modeling environments, solvers, and simulation tools. 8. Make informed strategic decisions in complex networked environments balancing efficiency, risk, resilience, and economic performance. |
Content
This course introduces the mathematical and algorithmic foundations of supply chain network
design and optimisation. Its starting point is a simple observation: the decisions that
shape a logistics network (where to open a warehouse or a plant, which facility serves
which market, how much capacity to install and when, which route a vehicle should follow,
how much redundancy to buy against a disruption) are discrete, and the number of
admissible configurations grows so quickly with the size of the network that no exhaustive
evaluation is possible. The course builds the theory needed to state such decisions as
integer optimisation problems, the machinery needed to certify how good a candidate
solution is, and the modelling judgement needed to decide what deserves to enter a model in
the first place.
The approach is deliberately twofold. On one side, the course develops the structural
mathematics that explains why some network problems are tractable and others are not:
systems of linear Diophantine inequalities, relaxations and bounds, total unimodularity and
the integrality of network polyhedra, valid inequalities and their separation. On the other
side, it applies this machinery to concrete strategic and operational questions, through
case studies based on real or realistic data drawn from manufacturing, retail distribution,
energy infrastructure, digital services, emergency response and humanitarian logistics.
The course is organised in two parts.
PART I — Network structure and demand
- Total unimodularity and the integrality of network polyhedra; Seymour's decomposition
theorem.
- Minimum-cost flow, transportation and transshipment problems; the max-flow/min-cut
theorem; multi-commodity flows and the loss of integrality; valid inequalities (cutset,
metric, lifted cover).
- Estimating demand: types of demand, forecasting horizon and aggregation, moving average,
exponential smoothing, linear and convex regression, measures of forecast quality.
PART II — Supply chain network design
- Strategic decisions in network design: the role of geography, why multiple warehouses and
multiple plants, data precision versus significance, non-quantifiable data.
- Facility location: centre of gravity, distance-based models, service levels and
sensitivity analysis.
- Transportation costs, capacities, facility fixed and variable costs, multi-echelon and
multi-product models, multi-period network design.
- Optimisation under uncertainty: two-stage stochastic programming, robust optimisation
with budgeted uncertainty, scenario-based robust location.
- Facility location with endogenous pricing and its linearisation.
- Service-oriented location: set covering and maximal covering location, p-centre and
p-median, hub-and-spoke networks, last-mile micro-hubs and parcel lockers, humanitarian
and reverse logistics.
- Reliable and survivable network design: the reliable facility location problem, the
k-survivable connected facility location problem, resilience versus cost trade-offs.
- Routing: asymmetric and symmetric travelling salesman problems, subtour elimination and
its separation, reduction to min-cut, branch-and-cut; the capacitated vehicle routing
problem and its variants.
At the end of the course, the participant will be able to recognise the combinatorial
structure hidden inside a managerial decision problem and to translate it into a rigorous
mathematical model; to assess the quality of that model, by deriving bounds and by
understanding what makes a relaxation strong or weak; to implement it with a professional
solver and to interpret the numerical output, including its sensitivity to demand, capacity
and cost estimates; and to discuss the resulting decisions with the awareness that a
solution is optimal only with respect to the assumptions that were written down. This last
point — the distinction between the precision of a number and its significance, and the
treatment of what cannot be quantified — is cultivated throughout the course as carefully
as the technique itself.
design and optimisation. Its starting point is a simple observation: the decisions that
shape a logistics network (where to open a warehouse or a plant, which facility serves
which market, how much capacity to install and when, which route a vehicle should follow,
how much redundancy to buy against a disruption) are discrete, and the number of
admissible configurations grows so quickly with the size of the network that no exhaustive
evaluation is possible. The course builds the theory needed to state such decisions as
integer optimisation problems, the machinery needed to certify how good a candidate
solution is, and the modelling judgement needed to decide what deserves to enter a model in
the first place.
The approach is deliberately twofold. On one side, the course develops the structural
mathematics that explains why some network problems are tractable and others are not:
systems of linear Diophantine inequalities, relaxations and bounds, total unimodularity and
the integrality of network polyhedra, valid inequalities and their separation. On the other
side, it applies this machinery to concrete strategic and operational questions, through
case studies based on real or realistic data drawn from manufacturing, retail distribution,
energy infrastructure, digital services, emergency response and humanitarian logistics.
The course is organised in two parts.
PART I — Network structure and demand
- Total unimodularity and the integrality of network polyhedra; Seymour's decomposition
theorem.
- Minimum-cost flow, transportation and transshipment problems; the max-flow/min-cut
theorem; multi-commodity flows and the loss of integrality; valid inequalities (cutset,
metric, lifted cover).
- Estimating demand: types of demand, forecasting horizon and aggregation, moving average,
exponential smoothing, linear and convex regression, measures of forecast quality.
PART II — Supply chain network design
- Strategic decisions in network design: the role of geography, why multiple warehouses and
multiple plants, data precision versus significance, non-quantifiable data.
- Facility location: centre of gravity, distance-based models, service levels and
sensitivity analysis.
- Transportation costs, capacities, facility fixed and variable costs, multi-echelon and
multi-product models, multi-period network design.
- Optimisation under uncertainty: two-stage stochastic programming, robust optimisation
with budgeted uncertainty, scenario-based robust location.
- Facility location with endogenous pricing and its linearisation.
- Service-oriented location: set covering and maximal covering location, p-centre and
p-median, hub-and-spoke networks, last-mile micro-hubs and parcel lockers, humanitarian
and reverse logistics.
- Reliable and survivable network design: the reliable facility location problem, the
k-survivable connected facility location problem, resilience versus cost trade-offs.
- Routing: asymmetric and symmetric travelling salesman problems, subtour elimination and
its separation, reduction to min-cut, branch-and-cut; the capacitated vehicle routing
problem and its variants.
At the end of the course, the participant will be able to recognise the combinatorial
structure hidden inside a managerial decision problem and to translate it into a rigorous
mathematical model; to assess the quality of that model, by deriving bounds and by
understanding what makes a relaxation strong or weak; to implement it with a professional
solver and to interpret the numerical output, including its sensitivity to demand, capacity
and cost estimates; and to discuss the resulting decisions with the awareness that a
solution is optimal only with respect to the assumptions that were written down. This last
point — the distinction between the precision of a number and its significance, and the
treatment of what cannot be quantified — is cultivated throughout the course as carefully
as the technique itself.
Teaching methods
The course is delivered through blackboard lectures, complemented by a set of slides that
follow the same structure. The slides are not a substitute for the lectures: students are
expected to study them together with the reference textbooks.
Each chapter alternates three registers:
1. Construction of the mathematical model and of its structural properties at the
blackboard, with explicit attention to why a formulation is correct, how strong its
relaxation is, and what makes it tractable or intractable.
2. Case studies based on real or realistic data — a global telecommunications
manufacturer's distribution network, a Belgian chocolate producer, electric-vehicle
charging infrastructure, edge servers of a streaming platform, cloud region selection,
emergency medical services, parcel lockers, humanitarian logistics — in which modelling
choices are discussed together with their managerial consequences.
3. Implementation sessions, in which models are written and solved with a professional
solver (FICO Xpress, through both the Mosel language and its Python interface) and the
numerical output is interpreted, including sensitivity analysis on demand and capacity.
Exercise sets close the main chapters and are corrected in class.
follow the same structure. The slides are not a substitute for the lectures: students are
expected to study them together with the reference textbooks.
Each chapter alternates three registers:
1. Construction of the mathematical model and of its structural properties at the
blackboard, with explicit attention to why a formulation is correct, how strong its
relaxation is, and what makes it tractable or intractable.
2. Case studies based on real or realistic data — a global telecommunications
manufacturer's distribution network, a Belgian chocolate producer, electric-vehicle
charging infrastructure, edge servers of a streaming platform, cloud region selection,
emergency medical services, parcel lockers, humanitarian logistics — in which modelling
choices are discussed together with their managerial consequences.
3. Implementation sessions, in which models are written and solved with a professional
solver (FICO Xpress, through both the Mosel language and its Python interface) and the
numerical output is interpreted, including sensitivity analysis on demand and capacity.
Exercise sets close the main chapters and are corrected in class.
Evaluation methods
Written examination (indicatively 65%). Assesses the mastery of the mathematical content: modelling a
verbally described decision problem as an integer program, deriving and comparing bounds,
reasoning on the structure of a formulation, and interpreting the properties of the
models seen in class. Closed book.
Case study (indicatively 35%, but this percentage can change from year to year in function of the complexity of the case chosen). Students formulate and solve a network design or location problem
related to the topics of the course, on real or realistic data, individually or in small
groups. The deliverable must include the mathematical model, its implementation with a
solver, an analysis of computational behaviour, an interpretation of the results, and a
justification of the resulting decisions.
The final grade is the weighted sum of the two components. A failing grade in either
component results in an overall failing grade.
In the second session, the written examination is retaken; the mark obtained for the case
study is carried over unless the student explicitly asks to submit a new one.
Use of generative AI must be explicitly declared in the case study report, and the student
remains fully responsible for the correctness of every model, computation and claim
submitted.
verbally described decision problem as an integer program, deriving and comparing bounds,
reasoning on the structure of a formulation, and interpreting the properties of the
models seen in class. Closed book.
Case study (indicatively 35%, but this percentage can change from year to year in function of the complexity of the case chosen). Students formulate and solve a network design or location problem
related to the topics of the course, on real or realistic data, individually or in small
groups. The deliverable must include the mathematical model, its implementation with a
solver, an analysis of computational behaviour, an interpretation of the results, and a
justification of the resulting decisions.
The final grade is the weighted sum of the two components. A failing grade in either
component results in an overall failing grade.
In the second session, the written examination is retaken; the mark obtained for the case
study is carried over unless the student explicitly asks to submit a new one.
Use of generative AI must be explicitly declared in the case study report, and the student
remains fully responsible for the correctness of every model, computation and claim
submitted.
Other information
Students are expected to be comfortable with:
- Linear algebra: vector spaces, matrices, rank, systems of linear equations.
- Elementary graph theory: graphs, trees, paths, cuts and flows.
- Descriptive statistics and linear regression.
- Programming in Python, and the ability to implement, run and debug an optimisation model
through a solver interface. The course uses FICO Xpress, via the Mosel language and the
Python API; no prior knowledge of either is assumed.
- Linear programming: geometry of the feasible region, duality, and the ability to read and
write a linear model.
- Basic notation, hulls, independence, dimension; elements of graph theory: paths, cuts,
trees and spanning structures.
- Systems of linear Diophantine equations and inequalities, with and without nonnegativity
constraints; Farkas' lemma.
- Optimising over Diophantine inequalities: modelling with integer and binary variables —
knapsack, bin packing, packing/covering/partitioning, stable set and clique, colouring,
crew scheduling, assignment, generalised and quadratic assignment, travelling salesman,
vehicle routing, minimum-cost network flow, shortest path, minimum spanning tree.
- Optimality, relaxations and bounds: primal and dual bounds; continuous, combinatorial,
surrogate and Lagrangian relaxations; relaxation by decomposition; relationships among
them.
- A general solution approach: branch-and-bound and pruning rules; the efficient
optimisation property and the limits of greedy characterisations.
- Linear algebra: vector spaces, matrices, rank, systems of linear equations.
- Elementary graph theory: graphs, trees, paths, cuts and flows.
- Descriptive statistics and linear regression.
- Programming in Python, and the ability to implement, run and debug an optimisation model
through a solver interface. The course uses FICO Xpress, via the Mosel language and the
Python API; no prior knowledge of either is assumed.
- Linear programming: geometry of the feasible region, duality, and the ability to read and
write a linear model.
- Basic notation, hulls, independence, dimension; elements of graph theory: paths, cuts,
trees and spanning structures.
- Systems of linear Diophantine equations and inequalities, with and without nonnegativity
constraints; Farkas' lemma.
- Optimising over Diophantine inequalities: modelling with integer and binary variables —
knapsack, bin packing, packing/covering/partitioning, stable set and clique, colouring,
crew scheduling, assignment, generalised and quadratic assignment, travelling salesman,
vehicle routing, minimum-cost network flow, shortest path, minimum spanning tree.
- Optimality, relaxations and bounds: primal and dual bounds; continuous, combinatorial,
surrogate and Lagrangian relaxations; relaxation by decomposition; relationships among
them.
- A general solution approach: branch-and-bound and pruning rules; the efficient
optimisation property and the limits of greedy characterisations.
Online resources
All the course material is availabe in the Teams channel of the course.
Bibliography
Useful references:
- Chopra, S. and P. Meindl, Supply Chain Management: Strategy, Planning and Operation, Prentice Hall
- M. Christopher, Logistics and Supply Chain Management, FT Prentice Hall.
Faculty or entity
