Methods of Operations Research
by
P.M. Morse and G.E. Kimball
Operations Research is a scientific method of providing
executive departments with a quantitative basis for decisions
regarding the operations under their control.
· developed in response to military needs in World War II
· applicable to industry and government as well
Definition of Operations Research
Operations Research is a scientific method of providing
executive departments with a quantitative basis for decisions
regarding the operations under their control.
Scientific Method -- an organized activity amenable to a variety of problems and capable of being taught.
Executive -- an applied (not theoretical) science, used as a tool to solve a specific problem: providing a basis for executive decisions.
Quantitative -- focuses on aspects of an operation that can be measured and compared.
Decisions -- science as an aid to decision-making, not just as a descriptive tool; OR worker as advisor and consultant, but not the decision-maker; need to report results of analysis to executive clearly, in a manner that will aid the latter to make decisions.
Operations -- a repetition of an action, therefore amenable to scientific analysis.
Control -- OR group must report to the executive who is in control of the operation; staff (advisory) function, personal contact with executive is important.
Early Development: Why did it take a war to give birth to OR?
· lives and national freedom at stake
· scientists of high ability could be enlisted to help
· during peacetime such scientists are likely to be engaged in pure research
Value of Operations Research
“The complexity of modern warfare…demands exacting analysis of the
measures and countermeasures introduced at every stage…
Scientific research can not only speed the invention and production
of weapons, but also assist in insuring their correct use…
Operations research, bringing scientists in to analyze the technical
import of the fluctuations between measure and countermeasure,
made it possible to speed up our reaction time in several critical cases.”
¨ Admiral E.J. King
Examples
· Re-arrangement of use of equipment
· Changes in setting, rearrangement of unit size
¨ depth setting of anti-submarine depth charge
¨ size of convoys
These examples illustrate importance of choice of proper measure of effectiveness: e.g., no. of ships lost per no. crossing the ocean, not no. lost per convoy.
· Dependence on operational parameters: OR as an experimental science
· Problem of defining the problem (example: anti-aircraft guns on ships)
· Finding the sensitive parameters: goal is to predict the future
· Mathematical analysis: often simple arithmetic is enough
Methods of Operations Research
· Statistical methods: limited in usefulness to problems that are repetive (e.g., bombing operations on a target of a given type)
· Field assignments, collection of data: assign scientist as close to operation as possible
· Limitations of operational data: only marginal changes in operations can be evaluated from data
· Limitations of expert opinion
· Operational experiments: vary the parameters
· Analytical methods: can work only with simplified special cases (models)
Summary of OR Approach
· Collect data
· Find dependence of results on different parameters (build a model)
· Devise measures of effectiveness to assess desirability of outcomes (objectives)
· Preliminary predictions
· Refine the model, until “dependence of results on operational parameters can be explained in terms of elements involved” (?)
· Check against new operational experiments, if possible
· Choice of optimum operation depends on which (of many possible) measures of effectiveness is used
· Report must therefore examine several alternatives
· Results must be understood by the executive
· Report should not contain recommendations
Comments
· OR worker is not a “gadgeteer”: concerned with operations -- the use of equipment, not its design and manufacture
· Choice of personnel: best minds come from physics and biology (?)
· Importance of mutual understanding between scientist and executive
“The operations research worker must work out those aspects of the problem
that are amenable to quantitative analysis and report the findings to
the executive …[who] must then combine these findings with the
qualitative aspects … to form the basis for the final decision.”
-- P. 10b