Linear programming components

1. Linear programming components • LP is composed of the following: 1- decision variables- vars whose values are unknown and / or searched for. 2- objective functions: math functions that do the following: a- relates decision vars to goals. b- measure goal attainment to be optimized.

2. 3- objective function coefficient: unit profit or cost coefficient indicating the contribution to the objective of one unit of decision variable. 4- constraints: expressed in the form of linear inequalities or equalities that limit resources and/or requirements. 5-capacities describe upper and lower limits on constraint variables.

3. 6- input-output coefficient-technology which indicate resource utilization for decision variables. Do the homework handed in class for linear programming implentation.

4. Multiple Goals • Analysis of management decision aims at evaluating how far each alternative brings management toward achieving its goals. • Most management decisions have multiple goals. • Different management have different goals • To achieve multiple goals, we need to analyze each alternative in light of achievement of the proposed goal.

5. Goals my complement each other or conflict each other. • Difficulties of analyzing multiple goals: 1- it is hard for organizations to clearly state their goals. 2-DM may change the importance assigned to goals overtime or for different situation – situation change.

6. 3- goals and sub goals are viewed differently at various levels of organization and within different departments. • 4-if organization changes or the environment changes goals also change. • 5-difficult to quantify relations between alternatives and their role in goal determination.

7. 6-Each DM has different goals regarding a complex problem and he participate to solve it. 7-particpant in problem solving assess the priorities of various goals differently.

8. Method to handle Multiple Goals 1- utility theory 2- goal programming 3- expression of goals and constraints using LP. 4- a point system

9. Sensitivity Analysis • Attempts to assess the impact of change in the input data or parameters on the proposed solution- the result variables. • Allows flexibility and adaptation to changing conditions and to the requirements of different decision-making situation. • Provide better understanding of the model and the decision making situation it attempts to describe.

10. Permits managers to input data so that confidence in the model increases. • Tests relationships such as: 1- impact of change in external variables (uncontrolled) and on outcome variables. 2-Impact of changes in decision variables on outcome vars. 3- effect of uncertainly in estimating external vars.

11. 4-Effects of different dependent interactions among vars. 5-Robustness of decision under changing conditions

12. Uses of sensitivity analysis Sensitivity analysis can be used for: 1- revising models to eliminate large sensitivities. 2-adding details about sensitive vars or scenarios. 3-obtaining better estimates of sensitive external vars. 4-altering the real-world system to reduce actual sensitivity.

13. 5- accepting and using the sensitive real world, leading to continuous and close monitoring of actual results.

14. Types of sensitivity A- automatic sensitivity analysis • Reports the range within which a certain input var (unit cost) can vary without affecting the proposed solution. • Usually limited to one change at a time, only for certain vars.

15. B- Trail and Error: • Impact of change in any var or several vars, can be determined through trail and error approach. • You can change some input and solve problem again. The more vars change the more solutions you discover. This can be done through either what-if or goal seeking.

16. What-if : structured as what will happen to the solution if an input var or an assumption or value is changed? • Goal-seeking: calculates values of the input necessary to achieve a desired level of an output (goal). It represent a backward solution approach. Ex: how many tellers needed to reduce waiting time in a bank?

17. Problem-solving search methods • When problem solving, Choice phase involves a search for an appropriate course of action that can solve the problem. • For normative models such as math programming based ones, either an analytical approach is used OR a complete, exhaustive calculations are applied (comparing outcomes of all alternatives).

18. For descriptive models, comparison of limited number of alternatives is used. • Analytical techniques: • Use math formulas to derive an optimal solution directly or predict a certain result. • Used for solving structured problems of operational nature such as resource allocation or inventory managment

19. Algorithms: • Used by analytical technique to increase efficiency of search. • It is step by step search process for getting an optimal solution. • Solutions are generated and tested for improvements, and tested again , this repeats until no further improvements is possible.

20. Simulation • To assume the appearance of the characteristics of reality. It is a technique for conducting experiments (what-if analysis) with computer on a model of a management system. • Most common method for handling semi structured and unstructured situation. • It is a well established, useful method for gaining insights into complex MSS situation.

21. Simulation characteristics • It imitates a model. • It conducting experiments, it involves testing specific values of decision or uncontrolled vars and observing the impact on output vars. • It is descriptive, describes or predict the characteristics of a system under different situation.

22. Repeats an experiment many times to obtain an estimate of the overall effect of certain actions. • Used when a problem is too complex to be treated by numerical optimization techniques. Complexity means: 1- problem can not be formulated for optimization ( assumption do not hold)

23. 2- formulation is too large 3-too many interactions among variables. 4-The problem exhibits some Risk and uncertainty.

24. Simulation advantages • It allows managers to pose what-if questions, use trail and error approach which is considered cheaper, faster, more accurate and less risks. • Managers can experiment to determine which decision vars and part of environment that are important with different alternatives.

25. Provide more understanding of the problem. • Built for specific problem, no generalization is required • Can include the real complexities of the problem, simplification are not necessary, handles unstructured problems.

26. Simulation Disadvantages • Optimal solutions can not be guaranteed, good ( satisfying) is found. • Construction of simulation models could be slow and costly. • Solutions are not transferable to other problem. • Simulation SW need special skills. Not easy to use.

27. Building simulation modle • Building a simulation model consists of the following steps: 1- problem definition: - real-world problem is examined and classified. -here we specify why simulation is appropriate. -define system boundaries, environment.

28. 2- construction of simulation model: - determine vars and relationships among them. -data are gathered, flowcharts are drawn and computer programs are written. 3-testing and validating the model: Making sure that the model represent the system under study properly- testing and validation.

29. 4- design the experiment -determine how long to run the simulation. - consider two conflicting objectives (accuracy and cost) which are identified by three scenarios : a- typical  mean and median cases for random vars b-best-case (low-cost, high revenues) c- worst-case (high-cost, low revenues)

30. 5-Conducting experiment: -range from random-number generation to presenting results. 6- evaluation of results: results must be interpreted, use sensitivity analysis. 7- implementation: Chances of success are high because managers are involved in the process of simulation model development.

31. Simulation types