Source document. This page reproduces the syllabus this course was written to, as published — its semesters, credits and paper numbers are that document’s, not this site’s. The course itself is studied on its own, in any order.

Course Information

Title	Operations Research
Theory Credits	3 (3 hrs/week)
Practical Credits	1 (2 hrs/week)

Course Outcomes

1. Know the scope and applications of Operations Research.
2. Link OR techniques with business environment and life sciences.
3. Convert real-life problems into mathematical models.
4. Find a solution to the problem in different cases.
5. Inculcate logical thinking to find a solution to optimisation problems.

Theory — Five Units

Unit 1: Introduction & LPP Formulation

Introduction of OR — origin and development; nature and features of OR; scientific method in OR; modelling in OR; advantages and limitations of models; general solution methods of OR models; applications of OR. Linear Programming Problem (LPP) — mathematical formulation, illustrative examples.

Open Unit 1 →

Unit 2: Graphical Method

Graphical solution of LPPs with maximising and minimising objective functions up to 3 variables. Finding convex hull and non-convex hull of LPP. Exceptional cases — alternative solutions, unbounded solutions, non-existing feasible solutions by graphical method.

Open Unit 2 →

Unit 3: Simplex Method

General LPP — definition and matrix form; slack, surplus, unrestricted variables; standard and canonical forms of LPP. Solution, basic solution, degenerate solution, basic feasible solution, optimum BFS. Simplex method — computational procedure; solving LPP by simplex (max and min, up to three variables).

Open Unit 3 →

Unit 4: Big-M & Two-Phase Methods

Artificial variable technique — Big-M method and Two-Phase simplex; degeneracy in LPP and methods to resolve degeneracy. Alternative, unbounded, non-existing feasible solutions and solution of simultaneous equations by simplex.

Open Unit 4 →

Unit 5: Duality & Dual Simplex

Duality in Linear Programming — concept of duality; definition of primal and dual; general rules for converting any primal into its dual; relation between primal and dual (statements only). Using duality to solve primal. Dual Simplex method.

Open Unit 5 →

Practical — List of Experiments (7)

1. Solution of LPP by Graphical method.
2. Solution of LPP by Simplex method.
3. Problem solving using Big-M method.
4. Problem solving using Two-Phase method.
5. Solution of special cases in LPP using simplex method — (i) unbounded, (ii) alternative.
6. Problems based on the Principle of Duality.
7. Problems based on the Dual Simplex method.

Open practical course material →

Text Books / References

1. S. D. Sharma — Operations Research, Kedar Nath Ram Nath & Co., Meerut.
2. Kanti Swarup, P. K. Gupta & Manmohan — Operations Research, Sultan Chand and Sons.
3. J. K. Sharma — Operations Research and Application, Macmillan, New Delhi.
4. S. I. Gass — Linear Programming, McGraw Hill.
5. G. Hadly — Linear Programming, Addison-Wesley.
6. H. A. Taha — Operations Research: An Introduction, Macmillan.

Suggested Co-Curricular Activities

1. Training of students by related industrial experts.
2. Assignments including technical assignments, if any.
3. Seminars, group discussions, quiz, debates etc. on related topics.
4. Preparation of audio and videos on tools of diagrammatic and graphical representations.
5. Collection of material / figures / photos of related topics.
6. Invited lectures and presentations of stalwarts on those topics.
7. Visits / field trips of firms, research organizations etc.

Exam Blueprint (recommended)

Unit	Topic	Approx. Weightage
1	Introduction & LPP Formulation	15 %
2	Graphical Method	20 %
3	Simplex Method	25 %
4	Big-M & Two-Phase	20 %
5	Duality & Dual Simplex	20 %

Quick Reference — Key Formulas & Procedures

Concept	Formula / Rule
LPP general form	Max/Min Z = cᵀx; Ax ≤/=/≥ b; x ≥ 0
Slack (≤)	aᵢx + sᵢ = bᵢ, sᵢ ≥ 0
Surplus (≥)	aᵢx − sᵢ = bᵢ, sᵢ ≥ 0
Big-M objective	Min Z + M·ΣAᵢ (Max: Z − M·ΣAᵢ)
Simplex optimality (Max)	All cⱼ − zⱼ ≤ 0
Simplex optimality (Min)	All cⱼ − zⱼ ≥ 0
Entering variable (Max)	Largest cⱼ − zⱼ > 0
Leaving variable	Smallest non-negative bᵢ / aᵢⱼ
Strong duality	Z* (primal) = W* (dual)
Complementary slackness	(bᵢ − aᵢx) yᵢ = 0; (Aᵀy − c)ⱼ xⱼ = 0