STOCHASTIC MODELS IN MANAGEMENT
2012/2013, Semester 1
School of Business (Analytics & Operations)
Modular Credits: 4
Stochastic Models in Management makes use of analytical methods (in particular, probabilistic method) to distil intelligence for business leaders' decision-making. Thus, this module is concerned with modelling, analyzing and solving quantitative problems in management, and shall find applications in fields like finance, economics, marketing science, operations management, logistics, and engineering.
As an introductory module, we strive for breadth, giving an overview of several practical approaches, as well as sufficient depth, so as to provide a substantial feel for the discipline and a good foundation for further studies. Topics will include discrete-time Markov chains, continuous-time Markov chains, the Poisson process, the renewal theory, Markov decision processes, queueing models, stochastic inventory model, reliability models, production models, customer brand-switching models, insurance contract models, and the Markowitz investment portfolio selection models.
Although there are no formal prerequisites, this module assumes prior knowledge of
, and the following probability concepts:
Expected value, variance, conditional probability, Bayes’s Rule, Normal distribution, and the Poisson distribution
There are no formal computer programming requirements.
Weekly 3 hour sessions (combination of lectures and tutorials).
All lecture notes will be posted in IVLE-DSC3215 at least 2 days before the lectures.
All assignments will be posted in IVLE-DSC3215 at least 1 week before the tutorials.
1.Modelling business problems;
2.Discrete-time Markov Chains. Markov property, transition probabilities, state classifications, and stationary distribution;
3.Continuous-time Markov Chains. Markov property, transition probabilities, birth-death process, stationary distribution;
4.The Poisson Process and Renewal Reward Processes;
5.Markov Decision Processes. The optimality equation, the method to solve the finite-state models;
6.Queueing Models. M/M/1, M/M/c, M/G/1, G/M/1, open Jackson network, closed Jackson network;
7.Stochastic Inventory Models. The single-period inventory model, the multiperiod inventory models;
8.Production Models. Serial production system, selecting distributions, and line balancing;
9.Stochastic Models in Marketing Science. New product diffusion model, and the consumer behaviour models;
10.Insurance Contract Models;
11. The Markowitz Investment Portfolio Selection Models.
Assessment will be given by
Class Participation 10%
Mid-Term Test 30%
Final Exam 60%
Workload Components : A-B-C-D-E
A: no. of lecture hours per week
B: no. of tutorial hours per week
C: no. of lab hours per week
D: no. of hours for projects, assignments, fieldwork etc per week
E: no. of hours for preparatory work by a student per week