1. Operational Research I By Dr. SW Poon

2. Definitions O. R. Society of Great Britain “OR is the application of the methods of science to complex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government and defence” O. R. Society of America “OR is concerned with scientifically deciding how to best design and operate man-machine systems, usually requiring the allocation of scarce resources”

3. Models in O.R. When does a problem exist? Daellenbach and George: There must be a decision-maker who must have an objective The decision-maker must have at least two alternative courses of action available There must be some degree of doubt as to which course of action best achieves the objective There must be an environment to which the problem pertains (firm, economy)

4. Models in O.R. (Cont’) A mathematical model consists of decision variables linked by constraining relationships ad entering into an objective function. In the model, there will be certain fixed factors (constants, parameters, coefficients) which are data. There may be uncontrollable factors such as random variables Yet, the model is UNREALISTIC as it fails to reflect the important factors and relationships in a situation. The purpose of building a model is: To identify the best values of the decision variables To study the system so as to find ways to improve its performance

5. Steps in an operational research project

6. Network Diagrams The traditional method Network diagrams Producing an Activity List Drawing the Network Diagrams Dummy Activities

7. Six steps in the Critical Path Method Step 1: Identification of project activities Step 2: Network formulation Step 3: Duration estimation Step 4: Forward pass computation Step 5: Backward pass computation Step 6: Tracing the critical path

8. The float of an activity Float = latest finish time of an activity – earliest finish time of the activity Independent float: the time by which an activity can expand without affecting any other activity, either previous or subsequent Free float: the time by which an activity can expand without affecting subsequent activities. If it is absorbed at the planning stage the float in earlier activities will be reduced. Once a project is under way, the free float in an activity can be used once the tail event is reached without affecting any other activity in the network

9. The float of an activity (Cont’) Total float: the time by which an activity can expand. When total float is absorbed at the planning stage, the floats in both previous and subsequent activities may be reduced. Interfering float: the difference between total and free float (The use of this float reduces float available to subsequent activities. If INTF is fully used then subsequent activities become critical.

13. What is PERT? PERT (Programme Evaluation and Review Technique) uses three quantities in estimating the duration of a single activity. They are: The optimistic time The pessimistic time The most likely time

14. The Probability Concept of PERT

15. The Probability Concept of PERT (Cont’)

16. Preference Network Diagram No dummy activity is necessary in a precedence network A precedence network is usually simpler than an AOA network for the same number of activities, because there are no dummies; In a precedence network, each activity can be assigned a single unique number to represent it; but in an AOA network, an activity has to be represented by two numbers, i and j. Hence, the creation and modification of a precedence network diagram is easier; and Less arithmetic will be involved in the forward pass and backward pass in a precedence network since there are no dummies

17. Introduction to transportation problem The general form of a transportation problem A special algorithm Example 1: Transportation problem with Demand equal to supply

18. Example 1 (Cont’)

23. Example 2: Transportation problem with demand not equal to supply

29. The MODI method: despatching cost and receiving cost

34. The general form of an assignment problem

36. Using the MODI method to solve an assignment problem