PPT on Operations research introduction- DOM 208, Slides of Operational Research

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Research

: Theory

and

Applicati

on

By, Prof. Utsav Pandey

Course

Outline

Introduction Modelling Linear Programming problems Solving OR models: Theory of Simplex method Applications Heuristic Programming & Simulation

 Define OR Models Agenda

 (^) Model Building  (^) Art of Modeling Students should learn

A brief

History

 (^) Got its name from military operations.  (^) https://www.youtube.com/watch?v=IL WbaWrjgU  (^) After WW2, OR has been applied in various real-time problems.  (^) Charles Babbage-Father of Computational Maths/Analytical Engine.  (^) G. Dantzig, G. Hadley.  (^) Indian Context: Regional Research Lab (Hyderabad, 1949); O.R. unit (ISI, Kol, 1953).  (^) N. Karmarkar: LP problems solved in polynomial time (1984).

Algebraic Problems Vs. Decision Problems  (^) Virat spent $100 for his shoes. This was 10 less than twice what he spent for his helmet. What is the price of his helmet?

• (^) Pat and Anjali can produce two types of soaps. One block of the first soap requires a total of 6 machine-hours and 1 man-hour. The corresponding figures for the second soap are 4 and 2, respectively. The machines can run 24X7, but there is only one labor who works for 6 hours. The maximum daily demand of the second soap is 2 blocks. Due to the marketing strategies of the firm, the production of the second soap cannot exceed that of the first soap by more than one. If one block of the first and second soaps are priced at $5 and $4, what is the maximum revenue Pat and Anjali can generate on a daily basis? (Ans. 3, 1.5)

An initial solution technique

• (^) Determine the feasible solution.
  • Treat the inequalities as equations and identify the feasible region ( HOW? ).
• (^) Search for the point(s) where the objective attains the maximum value.
  • Derive the objective function.
  • (^) Identify the direction of increment (in case of maximization).
  • Find out the point where the objective function leaves the feasible region.

Production Planning and Inventory Control Times per unit (in Hrs) Dept. Sports Flip-Flops Boot Sandals Capacity Cutting .3 .3 .25 .15 1000 Insulating .25 .35 .30 .10 1000 Sewing .45 .50 .40 .22 1000 Packaging .15 .15 .1 .05 1000 Demand 800 750 600 500 Profit (000) 3 4 2 1 Penalty (000) 1.5 2 1.  (^) Four types of footwears are produced in a factory that has four departments. It is charged with a penalty amount from the wholesellers for every undelivered items.  (^) How to capture the lost-sale values (i.e., the penalty)?  (^) Which products are more likely to face lost-sales than the rest?  (^) X1=  (^) X2=  (^) X3=387.  (^) X4=  (^) Issue with the solution?

Multi-period inventory model  (^) A real estate firm has contracts to deliver 100, 250, 190, 140, 220 and 110 residential flats in the next 6 months, respectively. The cost (in 000) of finishing the current flats over the 6 months vary: 50,45,55,48,52,50. To take advantage of lower cost in some months it can finish more flats in those months. But a finished flat needs to be maintained that costs 8k per month. Determine the best possible plan for the builder to finish the required flats in the given time. x I x I x I x I x I x I

Electric-bus scheduling for demand matching  (^) Newtown, a smart city, was developed to strengthen the IT infrastructure of WB. To promote sustainability in this project, transport dept. plans to schedule electric buses plying inside the area only. The Demand of its service varies with the time of the day (office hours see more demand). However, It is assumed to remain constant over a four-hour window. Based on that, the window-wise demands are given. If a bus can ply 8 hours per day, then what would be the minimum no. of buses required to meet the demand? 2 6 10 8 1212 2 00:00 (^) 04:00 08:00 12:00 (^) 16:00 20:00 24:

Results

•  X1=
•  X2=
•  X3=
•  X4=
•  X5=
•  X6=
  •  X1=
  •  X2=
  •  X3=
  •  X4=
  •  X5=
  •  X6=
    •  Total number of Bus:
    •  Previous solution (3 shifts with no overlap) :

Chemical flow in a production factory (Exercise)  (^) Crude oil is converted into three different varieties of gasoline denoted by ON number.  (^) A distillation unit (DU) produces feedstock (ON-82) from crude oil in 5:1 input to output ration.  (^) A cracker (CK) unit produces gasoline (ON=98) from a portion of the feedstock (FS) generated by DU in 2:1 ratio (i.e., 2 barrels of input (FS) is converted into 1 barrel of output (gasoline)).  (^) A blender unit blends the gasoline and FS (generated by DU) in 1:1 ratio. Distillation Unit (5:1) Cracker (2:1) Blender (1.1) Crude ON= FS FS ON= ON= Gasoline ON=87; D=50K P=6. ON=89; D=30K P=7. ON=92; D=40K P=8.