Operation Research
Teacher
Dr. Mohammed Siddique
Category
Domain Courses
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Course Name : Operation Research
Code(Credit) : CUNT2483 (3-0-1)
Objectives
- To introduce a brief understanding of Linear Programming
- To cater to the characteristics of Linear Programming Problems and its
- To demonstrate the utilization of Linear Programming Problems in industry and business.
Course Outcomes
| COs | Course outcomes | Mapping Cos with POs (High-3, Medium-2, Low-1) |
| CO1 | Can formulate the necessary and sufficient optimality conditions for linear programming and demonstrate the geometrical interpretation of these conditions. | PO1(3), PO9(3) |
| CO3 | Can use various techniques inventory and queuing theory to solve real-life application problems. | PO4(3), PO2(2), |
| CO5 | Can use the mathematical foundations learned in this course to formulate new applications as optimal decision problems and seek appropriate solutions algorithms. | PO5(2), PO9(2) |
Course Syllabus
Module-I:
Linear programming problem & Simplex method: Introduction to linear programming problem,
Formulation of linear programming problem, Graphical solution of linear programming problem, Solution of linear programming problem using simplex method, Artificial variables, Solution of linear programming problem using Big-M and two-phase method
Module -II:
Duality in Linear Programming: Introduction, General primal-dual pair, formulating primal-dual problem, Duality in simplex method, Dual simplex method.
Module – III:
Inventory Controls: Introduction, Inventory decision, Cost associate with inventories, Factor affecting inventory control, Economic order quantity (EOQ).
Module - IV:
Deterministic inventory problem with no shortages, Deterministic inventory problem with shortages, Economic order quantity (EOQ) problem with price breaks.
Module – V:
Elementary queuing theory: Introduction, Queuing system, Elements of queuing system, Operating characteristics of queuing system.
Module – VI:
Probability distribution in queuing systems, Classification of queuing models, Definition of transient and steady state.
Module – VII:
Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.
Projects:
- Project on Inventory management system
- Project on queuing theory
Text Books:
- KantiSwarup, P.K. Gupta and Man Mohan-Operations Research, S. Chand and Co. Pvt.Ltd.
- Engineering Optimization Theory and Practice by Singiresu S. Rao, JOHN WILEY & SONS, INC., Fourth Edition
Reference Book:
Mathematical Programming by N. S. Kambo, East West Press.
Session Plan
Session-1:
Introduction to linear programming problem
Session-2:
Formulation of linear programming problem
Session-3:
Graphical solution of linear programming problem
Session-4:
Solution of linear programming problem using simplex method
https://www.youtube.com/watch?v=H2Ji-Q4MfqU&list=PLU6SqdYcYsfIaokdZTmptaf-PK7s-B0ju&index=4
Session-5:
Artificial variables, Solution of linear programming problem using Big-M and two-phase method
https://www.youtube.com/watch?v=L0zWnBrjhng
Session-6:
Introduction to Duality in Linear Programming
https://www.youtube.com/watch?v=Ag8XJuskG78&list=PLRNL7AjA6rjxW80He0tS0Xv1l2PEvAQNZ
Session-7:
General primal-dual pair
https://www.youtube.com/watch?v=z0Ry_3_qhDw
Session-8:
Formulating primal-dual problem
https://www.youtube.com/watch?v=4kDScWSaEWs
Session-9:
Duality in simplex method
https://www.youtube.com/watch?v=Za1YxRJL-SA&list=PLwJRxp3blEvZBAn3bwAAtdJqotRPBWBlP
Session-10:
Dual simplex method
https://www.youtube.com/watch?v=pJh1oZ401NI
Session-11:
Introduction to Inventory Controls
https://www.youtube.com/watch?v=9vwucf8RZH0
Session-12:
Introduction to Inventory decision
https://www.youtube.com/watch?v=Cq9Jr6v8p0M
Session-13:
Cost associate with inventories
https://www.youtube.com/watch?v=E-S-E6HsR_k
Session-14:
Factor affecting inventory control
https://www.youtube.com/watch?v=HdUul6xIocg
Session-15:
Introduction to Economic order quantity (EOQ)
https://www.youtube.com/watch?v=y5nxiL6civU
Session-16:
Deterministic inventory problem with no shortages
https://www.youtube.com/watch?v=UwzuJW4P2Jw
Session-17:
Problems of deterministic inventory problem with no shortages
https://www.youtube.com/watch?v=8e0zaHhTHyY
Session-18:
Deterministic inventory problem with shortages
https://www.youtube.com/watch?v=lzGKRSvs5HM
Session-19:
Problems of deterministic inventory problem with shortages
https://www.youtube.com/watch?v=dQNpSa-bq4M
Session-20:
Economic order quantity (EOQ) problem with price breaks.
https://www.youtube.com/watch?v=zAULhNrnuL4
Session-21:
Introduction to elementary queuing theory
https://www.youtube.com/watch?v=UVvuwv-ne1I
Session-22:
Introduction to Queuing system
https://www.youtube.com/watch?v=0WY9WYZGl9c
Session-23:
Elements of queuing system
https://www.youtube.com/watch?v=nkTZ7XdIp-A
Session-24:
Problems on Elements of queuing system
https://www.youtube.com/watch?v=2J8pVynRZ8A
Session-25:
Operating characteristics of queuing system
https://www.youtube.com/watch?v=HIiBoL-z0cU&list=PLHRHy1-UoGh2pdh2hqTAUKtb0bCjttby8
Session-26:
Probability distribution in queuing systems
https://www.youtube.com/watch?v=0l3tzQI_ApM
Session-27:
Problems of probability distribution in queuing systems
https://www.youtube.com/watch?v=F5DhWBsp8J4
Session-28:
Classification of queuing models
https://www.youtube.com/watch?v=osgqQy9Hr8s
Session-29:
Problems of queuing models
https://www.youtube.com/watch?v=2EjGJXzsC2U
Session-30:
Definition of transient and steady state.
https://www.youtube.com/watch?v=3MnVCX94jJM
Session-31:
Steady-state solutions of Markovian queuing model: M/M/1
https://www.youtube.com/watch?v=KLAEwukvuZs
Session-32:
Steady-state solutions of Markovian queuing model: M/M/1 with limited waiting space
https://www.youtube.com/watch?v=O5TjsbZBs2E
Session-33:
Steady-state solutions of Markovian queuing model: M/M/C
https://www.youtube.com/watch?v=O5TjsbZBs2E
Session-34:
Steady-state solutions of Markovian queuing model: M/M/C with limited waiting space
https://www.youtube.com/watch?v=O5TjsbZBs2E
Session-35:
Steady-state solutions of Markovian queuing model: M/G/1.
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Our Main Teachers
Dr. Mohammed Siddique, received Ph. D in Mathematics in the area of Optimization Techniques and Machine Learning from KIIT, Deemed to be University, Bhubaneswar and completed his M.Sc in Mathematics and M.Tech in Computer Science from Utkal University, Bhubaneswar. He is having more than 16 years of teaching experience. He is having more than 50 […]