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Operations Research

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Operations Research (MTH601)
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Table 71
Destination
Origin
1
2
3
4
1
-5
-19
2
54
67
3
50
17
(ui + vj) for unalloted cells
Table 72
Destination
Origin
1
2
3
4
1
61
67
2
28
14
3
49
54
Cell evaluation
In table 72 (matrix of cell evaluation) there is no negative entry indicating that the solution found in
table 66 is optimal.
The optimum cost = Rs. 6698
REVIEW QUESTIONS
1.
What do you understand by degeneracy in a transportation problem?
2.
What is degeneracy?
3.
Write a short note on degeneracy in a transportation problem.
4.
Explain how degeneracy in a transportation problem may be resolved.
5.
How the problem of degeneracy arises in a transportation problem?
6.
A company has three plants at locations A, B and C which supply to warehouses located at D, E, F, G
and H. Monthly plant capacities are 800, 500 and 900 units respectively. Monthly warehouse
requirements are 400, 400, 500, 400 and 800 units respectively. Unit transportation costs (in Rupees)
are given below.
To
D
E
F
G
H
A
5
8
6
6
3
B
4
7
7
6
5
C
8
4
6
6
4
Determine an optimum distribution for the company in order to minimize the total transportation cost.
199
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Operations Research (MTH601)
200
7.
A company has four manufacturing plants and five warehouses. Each plant manufactures the same
product, which is sold at different prices at each warehouse area. The cost of manufacturing and cost of
raw materials are different in each plant due to various factors. The capacities of the plants are also
different. These data are given in the following table:
Item/Plants
1
2
3
4
Manufacturing
Cost (Rs.) per
12
10
8
7
unit
Raw material
Cost (Rs.) per
8
7
7
5
unit
Capacity  per
unit time
100
200
120
80
The company has five warehouses. The sale prices, transportation costs and demands are
given in the following table:
Transportation Cost (Rs.)
Sale Price
Warehouse
per unit
(Rs.) Per
Demand
Plants
Unit
1
2
3
4
80
30
A
4
7
4
3
120
32
B
8
9
7
8
150
28
C
2
7
6
10
70
34
D
10
7
5
8
90
30
E
2
5
8
9
(i) Formulate this into a transportation problem to maximize profit.
(ii) Find the solution using VAM method.
(iii) Test for optimality and find the optimal solution.
200
Table of Contents:
  1. Introduction:OR APPROACH TO PROBLEM SOLVING, Observation
  2. Introduction:Model Solution, Implementation of Results
  3. Introduction:USES OF OPERATIONS RESEARCH, Marketing, Personnel
  4. PERT / CPM:CONCEPT OF NETWORK, RULES FOR CONSTRUCTION OF NETWORK
  5. PERT / CPM:DUMMY ACTIVITIES, TO FIND THE CRITICAL PATH
  6. PERT / CPM:ALGORITHM FOR CRITICAL PATH, Free Slack
  7. PERT / CPM:Expected length of a critical path, Expected time and Critical path
  8. PERT / CPM:Expected time and Critical path
  9. PERT / CPM:RESOURCE SCHEDULING IN NETWORK
  10. PERT / CPM:Exercises
  11. Inventory Control:INVENTORY COSTS, INVENTORY MODELS (E.O.Q. MODELS)
  12. Inventory Control:Purchasing model with shortages
  13. Inventory Control:Manufacturing model with no shortages
  14. Inventory Control:Manufacturing model with shortages
  15. Inventory Control:ORDER QUANTITY WITH PRICE-BREAK
  16. Inventory Control:SOME DEFINITIONS, Computation of Safety Stock
  17. Linear Programming:Formulation of the Linear Programming Problem
  18. Linear Programming:Formulation of the Linear Programming Problem, Decision Variables
  19. Linear Programming:Model Constraints, Ingredients Mixing
  20. Linear Programming:VITAMIN CONTRIBUTION, Decision Variables
  21. Linear Programming:LINEAR PROGRAMMING PROBLEM
  22. Linear Programming:LIMITATIONS OF LINEAR PROGRAMMING
  23. Linear Programming:SOLUTION TO LINEAR PROGRAMMING PROBLEMS
  24. Linear Programming:SIMPLEX METHOD, Simplex Procedure
  25. Linear Programming:PRESENTATION IN TABULAR FORM - (SIMPLEX TABLE)
  26. Linear Programming:ARTIFICIAL VARIABLE TECHNIQUE
  27. Linear Programming:The Two Phase Method, First Iteration
  28. Linear Programming:VARIANTS OF THE SIMPLEX METHOD
  29. Linear Programming:Tie for the Leaving Basic Variable (Degeneracy)
  30. Linear Programming:Multiple or Alternative optimal Solutions
  31. Transportation Problems:TRANSPORTATION MODEL, Distribution centers
  32. Transportation Problems:FINDING AN INITIAL BASIC FEASIBLE SOLUTION
  33. Transportation Problems:MOVING TOWARDS OPTIMALITY
  34. Transportation Problems:DEGENERACY, Destination
  35. Transportation Problems:REVIEW QUESTIONS
  36. Assignment Problems:MATHEMATICAL FORMULATION OF THE PROBLEM
  37. Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM
  38. Queuing Theory:DEFINITION OF TERMS IN QUEUEING MODEL
  39. Queuing Theory:SINGLE-CHANNEL INFINITE-POPULATION MODEL
  40. Replacement Models:REPLACEMENT OF ITEMS WITH GRADUAL DETERIORATION
  41. Replacement Models:ITEMS DETERIORATING WITH TIME VALUE OF MONEY
  42. Dynamic Programming:FEATURES CHARECTERIZING DYNAMIC PROGRAMMING PROBLEMS
  43. Dynamic Programming:Analysis of the Result, One Stage Problem
  44. Miscellaneous:SEQUENCING, PROCESSING n JOBS THROUGH TWO MACHINES
  45. Miscellaneous:METHODS OF INTEGER PROGRAMMING SOLUTION