Operations Research 2 (0365.3531)

uriy@post.tau.ac.il

Office Hours:    Wednesday 16:00 - 17:00 (and by appointment),   Schreiber 326

Class Hours:

Spring semester 2005

Sunday 13:15 - 14:30 and 14:45 - 16:00, Dan David 204    

Prerequisites

Probability Theory, Operations Research 1.

Course Content:

The course concentrates on Stochastic models in Operations Research (OR) and it complements the Operations Research 1 course in which the main discussion involves Deterministic OR models (i.e. Linear Programming, Transportation models, Flows in Networks, etc). Since many real-life systems contain stochastic elements, the aim of the course is to present and study OR methods that can be applied to analyse and solve such problems. Examples of stochastic systems include all sorts of Queueing and Communication networks in which random arriving jobs request random processing times from a limited number of 'servers'; Inventory systems where demand is random; Reliability models where life times of the components of systems are stochastic, and alike.

The course is directed to 3rd year Undergraduate students with solid background in Probability Theory and with basic knowledge of Deterministic OR models.

Topics:

1. Markovian queueing models.

1.1. Schematic description of queueing systems; Examples; Classification of queues; The Poisson process; Exponential and Erlang (Gamma) probability distribution functions; The M/M/1 queue: time-dependent differential equations, steady state, balance equations, the traffic intensity, mean queue size, waiting and sojourn times; General Birth-and-Death processes; M/M/1/N-1 model and the Parking-Lot problem; The M/M/c queue; Trancated models; Erlang's loss formula.

1.2. Jackson Networks.

2. Inventory models.

The EOQ formula; Backlogs; The Newsboy problem; Stochastic multi-period models.

3. Reliability models.
4. Introduction to Markov chains (MCs), Examples.

One-step transition probabilities, Stationary distributions, Embedded MCs.

5. Markov Decision Processes.

Sequential decision processes; State space; Action space; One-step expected costs; Howards algorithm; Formulation by Linear Programming; Existance of pure stationary policies; Examples.

Helpful Reference Books

• Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research (5th or higher Edition), McGraw-Hill.
• Winston, W.L., Operations Research (3rd or higher Edition), Duxbury Press.