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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Risk and Logistics (MATH11190)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryAlthough risk and uncertainty affect our everyday life, both are very vague concepts. As a result, there does not exist a concise definition for them that holds in general. Different public and industrial sectors will assess and manage risk in very different ways, depending on whether past observations are available, how severe outcomes can be, whether it affects only few or many, etc. Therefore, after a general introduction, specific examples from various sectors are discussed to illustrate how differing the approaches to assess and manage risk can be in practice.
Starting in the 1950s, optimization and OR techniques have been developed and used to optimize logistics activities, with an ever increasing importance, role and proliferation since then. For example, in 2012 the total expenditure for logistics activities in Europe was 1,726 billion Euros. Thus, even small improvements may result in considerable monetary gains. Uncertainty and risk are inherent in logistics: Customer demand can never be forecasted exactly, travel times will never be certain, and machines or vehicles may break down, severely affecting and impairing logistics operations.
Course description The core of risk analysis deals with questions like: What is risk? How to measure it? And what to do about it? The answers to those questions will vary from sector to sector. The course will start with introducing basic concepts of risk analysis, focusing especially on decision trees, expected utility theory and decision making under complete uncertainty. Afterwards, examples from different application areas will be discussed and it will be show how to apply these (and other) concepts to tackle the corresponding problems.
Logistics focuses on moving objects, e.g. goods, in space and time such that the right object is in the right quantity at the right time at the right place. Classical logistics activities are the transportation and distribution of raw materials, subassemblies, and finished products between suppliers, factories, warehouses, and retailers, and their storage, handling, processing, and packaging. Typical goals are to maximize customer satisfaction (expressed through service levels, product quality, responsiveness, etc.) and to minimize total costs, environmental impact, and tied-up equity. Logistics planners face many challenges, ranging from conflicting goals, over supply uncertainties, uncertain customer demands and the lack of information, to the inherent difficulties of having to organize logistics activities across borders and cultures in multi-national companies.
This course will focus on OR techniques to optimize the structure of the logistics network and to efficiently transport, store, and distribute goods. For each of those problems, a brief introduction and a characterization of the different types of sub-problems will be given. Afterwards, mathematical models and algorithms to solve classical problems will be discussed, each accompanied by small case studies.
The overall course outline is as follows
Part I: Risk Analysis
1. Decision Making under Uncertainty
- Introduction
- Expected Utility
- Having (no) Clues About the Future
- (Personal) Financial Risk
- Optimization under Uncertainty

Part II: Logistics
3. Facility Location and Network Design
- The Warehouse Location Problem
- Stochastic Location Problems
- A Strategic Network Design Model
4. Inventory Management
- Deterministic Inventory Systems
- Stochastic Inventory Systems
5. Distribution Planning
- Vehicle Routing Problems
- Arc Routing Problems
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Methodology, Modelling and Consulting Skills (MATH11007) OR Linear Programming, Modelling and Solution (MATH10073)
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 20, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 66 )
Assessment (Further Info) Written Exam 50 %, Coursework 50 %, Practical Exam 0 %
Additional Information (Assessment) Coursework: 50%
Exam: 50%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. characterize the type(s) of risk for a problem involving uncertainty, identify appropriate ways of measuring and assessing risk, and formulate suitable approaches to manage and mitigate it
  2. identify logistics activities and apply existing mathematical models and algorithms to solve standard problems
  3. implement exact as well as heuristic methods and understand the trade-offs between them
  4. modify existing or derive new mathematical models to solve non-standard logistics problems
  5. transfer their skills to model and efficiently solve a logistics problem that was not discussed in the lecture and is new to them
Reading List
G. Gigerenzer, Reckoning with Risk: Learning to Live with Uncertainty, Penguin, 2003
D. Simchi-Levi, P. Kaminski, E. Simchi-Levi, Designing and Managing the Supply Chain: Concepts, Strategies, and Cases, McGraw-Hill Education, 3rd Edition, 2007
G. Ghiani, G. Laporte, R. Musmanno, Introduction to Logistics Systems Management, Wiley, 2nd Edition, 2013
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Joerg Kalcsics
Tel: (0131 6)50 5953
Course secretaryMiss Gemma Aitchison
Tel: (0131 6)50 9268
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