BDC5101 Deterministic Operations Research

“Operations Research is the scientific approach to decision-making. By the use of mathematical models, the science of Operations Research seeks to design, improve and operate complex systems in the best possible way. Mathematical models are either deterministic or stochastic, depending on the nature and requirements of the system under study. This course is an introduction to deterministic modeling and optimisation. The goal is to learn methods of formulating a wide variety of engineering problems and understanding solution strategies. These strategies are used today by hundreds of companies successfully.” – cited from the Syllabus of ISyE6669, GIT.

The course takes a unified view of models in operations research and covers their main areas of applications and some main algorithms. It includes the following topics:

  • Linear Optimisation
  • Network Flows
  • Discrete Optimisation
  • Nonlinear Optimisation

BDC6111 Foundation of Optimisation

The course takes a unified view of optimisation models in operations research and covers the main areas of application and the main optimisation algorithms. It includes the following topics:

  • Linear Optimisation
  • Robust Optimisation
  • Network Flows
  • Discrete Optimisation
  • Nonlinear Optimisation

BDC6112 Stochastic Processes

This course will cover important topics in Applied Probability, Operations Research and Stochastic Optimisation. It will focus on methodology, modelling techniques and mathematical insights. The aim is to train students to a level of technical competency to appreciate and understand current literatures. This is a core module for PhD students in the Decision Science department

This is a lecture-based course. However, students are expected to read the course materials before the class and participate the class discussion. 

BDC6113 Foundation of Inventory Management 

This course will first provide an in-depth study of a variety of production and inventory control planning problems, the development of mathematical models corresponding to these problems, approaches to characterise solutions, and algorithm designs for finding solutions. We will cover both classical deterministic and stochastic inventory models.  Although many of the topics we will cover are of great interest to managers, our focus will be not on practice but on theory. In particular, we concentrate on the following:

  1. Deterministic Inventory Theory
    • The Economic Order Quantity (EOQ) Model
    • Quantity Discount Model
    • The Economic Lot Scheduling Model
    • Wagner-Whitin Model
    • Power-of-Two Lot Sizing
  2. Stochastic Inventory Theory
    • Newsvendor Model
    • Dynamic Models with No Setup Cost
    • (R,Q) Model  (Hadley-Whitin)
    • (s,S) Model
    • Series Inventory Systems
    • Assembly Inventory Systems
    • Distribution Inventory Systems
    • Lost Sales Inventory Systems
    • Empirical Bayesian Inventory Systems
    • Time-dependent Demand Inventory Systems

The goals of  the course are to familiarise the students with i) a thorough knowledge of classical inventory models like the EOQ model, news vendor model, (R,Q)-model, (s, S)-model, and base-stock model (finite-horizon and infinite horizon); ii) a good understanding of the relationship among these models; iii) approaches and techniques used in studying these models.

BDC6114 Logistics and Supply Chain

The objective of this course is to expose students to the issues that need to be considered in designing and operating supply chains.

We will start with an introduction to supply chain management including definition of supply chain management, key supply chain costs and metrics, and fundamental issues and trade-offs in supply chain management.

We will then discuss the interactions between stages in a supply chain, double marginalisation and contracts for supply chain coordination, strategic alliances and incentive alignment, channels of distribution, coordinating distribution strategies, pricing/promotions. We will also introduce and discuss supply chain planning and differentiated service problems, approximation algorithms for stochastic inventory control models with remanufacturing, L-natural convexity (multi-modularity) and its applications, product assortment. We will discuss how to explore good flexibility structure and the impact of flexibility and postponement in operations and supply chain management.

BDC6115 Stochastic Modelling and Optimisation 

Stochastic models are used extensively to analyse and optimise in a wide variety of applications including business operations, economic systems, finance and engineering. This module provides the core knowledge for graduate students specialising in operation research, operation management, management science, and industrial engineering. Topic covered includes renewal processes, stochastic dynamic programming, stochastic ordering and their applications. In particular,

  1. Renewal Processes
    • Definition, properties, and limit behaviours
    • Wald’s equation, elementary renewal theorem, key limit theorem
    • Delay, stationary and alternative renewal processes
    • Renewal reward process
    •  Application in inventory models, queueing problems and reliability theory
  2. Stochastic Dynamic Programming
    • Finite horizon Markov decision processes
    • Discounted dynamic programming
    • Minimising Costs
    • Maximising costs
    • Average reward criterion
    • Applications in inventory models, scheduling problem and equipment maintenance
  3. Stochastic Comparison
    • Definitions and properties
    •  Applications in inventory models and queueing problems.

It is indispensable for PhD students in the areas of operations management, operations research and management sciences to have good knowledge of stochastic processes and their applications. This course is the follow- up of BDC 6112 Stochastic Process.

BDC6228 Seminars in Stochastic Processes

Stochastic models and optimisation techniques to analyse complex systems that encompass all walks of life and involve queues, congestion, and interaction in networks.  Queues and congestion arise in service systems, transportation, health care, manufacturing, computing, and information networks.  They are characterised by variability as well as rates, and are controlled by protocols, admissions, and schedules and routing.  Such systems are modelled as stochastic networks of queues and controlled through Markov decision methods. 

 

The objective of this course is to INTRODUCE and INTEGRATE knowledge in this area with applications in manufacturing, supply chains, health systems and computer networks. It will introduce students to advanced topics in stochastic processes, queues, control, scheduling and optimisation, and prepare them for further research in these areas.