Operations Research I Phases of operations research Ing

Operations Research I Phases of operations research Ing. Lenka Skanderová, Ph. D.

Phases of operations research 1/2 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR 1. Problem definition (relevant data gathering) 2. Formulation of the mathematical model representing the problem 3. Development of the computer-based procedure to derive the solutions of the problem based on the model 4. Test of the model (refine the model if needed) 5. Preparation of the outgoing application of the model 6. Implementation [1] Operations research I 2/19

Examples of using OR in real life Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • San Francisco Police Department developed the computerized system for optimally scheduling and deploying police patrol officers. • The Health Department of New Haven, Connecticut used OR team to design an effective needle Exchange program to combat the spread of the HIV. • Citgo Petroleum Corporation – optimization of refinery operations and the suply, distribution, and marketing of its product. [1] Operations research I 3/19

How to create a model 1/3 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR Model is an idealized representation of the reality • We meet models every day: • models of cars, airplanes, globes • some physical laws • graphs • flowcharts • models of DNA, atoms and molecules Operations research I 4/19

How to create a model 2/3 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR „The mathematical model of a business problem is the system of equations and related mathematical expressions describing the essence of the problem. “ [1] Operations research I 5/19

How to create a model 3/3 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Real problems usually do not have just a single „right“ model • Iterative proces of model creation: • Begin with very simple version of the model • Model will be evolving toward more elaborate model taking into consideration the complexity of the real problem • Ciritical step: • Objective function formulation • „If there are multiple objectives, their respective measures commonly are then transformed and combined into a composite measure – overal measure of performance. “ [1] Operations research I 6/19

Example: Optimization of production operations in chemical plants 1/4 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR An OR study done for Monsanto Corp. 1 was concerned with optimizing production operations in Monsanto’s chemical plants to minimize the cost of meeting the target for the amount of a certain chemical product (maleic anhydride) to be produced in a given month. The decisions to be made are the dial setting for each of the catalytic reactors used to produce this product, where the setting determines both the amount produced and the cost of operating the reactor. [1] Operations research I 7/19

Example: Optimization of production operations in chemical plants 2/4 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR [1] Operations research I 8/19

Example: Optimization of production operations in chemical plants 3/4 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR production target otherwise [1] Operations research I 9/19

Example: Optimization of production operations in chemical plants 4/4 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR objective function parameters constraints [1] Operations research I 10/19

Example: Reassigning crews to flights in Continental Airlines Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Reassigning crews to flights as soon as the emergencies arise • Many thousands of crews and dailz flights • The model has millions of decision variables and many thousands of constraints • In its first year of use (2001) the model was applied four times: • 2 snowstorms • flood • 11 th September 2001 • Saving approximately $40 million [1] Operations research I 11/19

Satisfactory + optimizing = satisficing Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Nobel Laureate Herbert Simon: Satisficing is much more prevalent than optimizing. • Satisficing: • combination of satisfactory and optimizing • tendency of managers to seek a solution that is „good enough“ for the problem • „…rather than trying to develop an overal measure of performance to optimally reconcile conflicts between various desirable objectives, the goals may be set to establish minimum satisfactory levels of performance in various areas. When a solution is found that enables all these goals to be met, the research is finished. “ [1] Operations research I 12/19

Methods used by OR teams Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Heuristic procedures are used occasionally to find a suboptimal solution • Metaheuristics – provide a general structure and strategy guidelines for designing a specific heuristic procedure to fit a particular kind of problém • Mathematical methods [1] Operations research I 13/19

Postoptimality analysis Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Postoptimality analysis (what-if analysis) – analysis done after finding an optimal solution … what would happen to the optimal solution if different assumptions are made about future conditions • Spreadsheed software • Sensitivity analysis – which parameters of the model are most critical in determining the solution Sensitive parameter: „For a mathematical model with specified values for all its parameters, the model’s sensitive parameters are the parameters whose value cannot be changed without changing the optimal solution. “ • When the sensitive parameter is identified, the solution that remains a particularly good one for all the various combinations of likely values of the sensitive parameters is seeking. Operations research I [1] 14/19

Testing the model 1/2 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR „It is easy to lose the forest for the trees. “ • When the details (trees) of the initial version of the model are completed, it is necesarry to look at the overall model (forest). • This work should be done by the team member who was not participating on the model development (fresh look). • Make sure that all the mathematical expressions are dimensionally consistent in the units used. [1] Operations research I 15/19

Testing the model 2/2 Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Retrospective test: • using historical data to reconstruct the past and then determine how well the model would performed if it had been applied • Determines whether the model tends to yield a significant improvement over current practice • Can identify the bottlenecks of the model • Disadvantage: Using the same data in testing as well as in model development. „Is the past truly representative of the future? “ [1] Operations research I 16/19

Preparing to apply the model Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • Creating system including the model, solution procedure (including postoptimality analysis), and operating procedures for implementation • Computer-based system + decision support system (helps to managers to use data and models to support their decision making) • System for maintaining [1] Operations research I 17/19

Implementation Phases of OR Examples of using OR in real life How to create model Examples Next phases of OR • The implementation should be documented very clearly and accurately → the work is reproducible • Replicability should be involved in the ethical code of all operations researchers [1] Operations research I 18/19

Literature [1] Hillier and Lieberman: Introduction to Operations Research, 8 th edition, 2005 Operations research I 19/19