MCA-251
Operational Research
Optimising decisions with mathematics — linear programming and duality, transportation and assignment, queuing and project networks, game theory and simulation.
- Semester
- Semester 3
- Credits
- 3
- Scheme
- 3 lectures a week
- Contact hours
- 40 across four units
- Category
- Open Elective - II
What the paper is
Operational Research is the most computational of the open electives and one of the most self-contained papers in the degree. Every unit is a family of problems with a standard algorithm, and almost every exam question is an instance of one of them.
The simplex method in Unit I is the foundation; the transportation and assignment problems in Unit II are special cases solved more cheaply because of their structure. Recognising that relationship is worth more than memorising the three procedures separately.
Unit III pairs queuing theory with PERT and CPM — the same project scheduling material that appears in Software Project Management, from the mathematical side. Unit IV then closes with game theory, replacement models and simulation.
What to concentrate on
- The simplex method, including Big-M and two-phase for artificial variables, is the highest-yield topic. Practise until you can set up the tableau and iterate without hesitation, and know how to read an unbounded or infeasible outcome off it.
- The transportation problem is asked as a sequence: find an initial solution by north-west corner, least cost and Vogel's method, then optimise with MODI. Know all four and the degeneracy special case.
- The Hungarian method for assignment is short, mechanical and near-certain to appear. So is the M/M/1 queue — know its standard results rather than deriving them in the exam.
Syllabus, unit by unit
Summarised from the approved scheme. Hours are the contact hours the scheme allots, which is a fair guide to where the marks sit.
Unit I · Introduction and linear programming
10 hours- Historical background, operations research and decision making, scope and applications, features
- Phases of operations research, types of model, methodology, techniques and tools
- Structure of the mathematical model and the limitations of operations research
- Linear programming: assumptions, mathematical formulation, graphical methods and their special cases
- The simplex method, standard form, minimisation, special cases, Big-M and two-phase methods
- Duality and the economic interpretation of the dual; sensitivity analysis; solving with software
Unit II · Transportation and assignment problems
10 hours- Formulation of the transportation problem; initial basic feasible solution by north-west corner, least cost and Vogel's approximation methods
- Optimality by the MODI method; unbalanced problems, maximisation, special cases and degeneracy
- The assignment problem: mathematical formulation and the Hungarian method
- Unbalanced assignment, maximisation, special cases, the travelling salesperson problem
Unit III · Queuing theory and project scheduling
10 hours- Queuing theory: operating characteristics, constituents of a queuing system, service facility, queue discipline
- Mathematical analysis of the queuing process, properties, notation, service systems
- Single-channel and multiple-service-channel models, the Erlang family of service time distributions
- Applications and limitations of queuing theory
- Network analysis: the difference between PERT and CPM, network components and precedence relationships, PERT time-cost trade-off
Unit IV · Game theory, replacement and simulation
10 hours- Game theory: competitive situations and their characteristics, the maximin-minimax principle, dominance, mixed strategy
- Replacement of items that deteriorate with maintenance costs increasing over time
- Replacement of items that fail suddenly: individual and group replacement policies
- Simulation: methodology, basic concepts, procedure and applications
How it is examined
- Question 1 is compulsory, covers the whole syllabus, and is made of objective or short-answer questions. It carries 12 marks.
- The rest of the paper is four units matching the four above. Each unit sets two questions and you attempt one, so there are four more answers at 12 marks each.
- Examiners are asked to map every question to a course outcome using Bloom's taxonomy, which is why questions are phrased as “apply”, “analyse” or “evaluate” rather than only “explain”.
The pass mark is 40 out of 100 in every paper.
Learning objectives
- Formulating real-life problems as operations research models and studying methods to solve them
- Linear programming, transportation and assignment problems, and methods for optimum solutions
- The theory of duality and sensitivity analysis in linear programming
- Project management techniques and their solution
- Queuing models and their applications
Assumed beforehand
- Basic knowledge of mathematics, statistics, information technology and economics
Books it is taught from
- TB1J. K. Sharma, “Mathematical Models in Operations Research”, TMH, 1st edition, 1989
- TB2V. K. Kapoor, “Operations Research: Quantitative Techniques for Management”, Sultan Chand & Sons, 1st edition, 2013
- TB3N. D. Vohra, “Quantitative Techniques in Management”, Tata McGraw-Hill, 3rd edition, 2007
Notes for MCA-251
Lecture notes, question papers and assignments filed against MCA-251 are in the library. Everything there has been checked by a moderator before it appears, and an account is free — new ones are approved by hand, which is what keeps the shelf clean.