1 Operations Research Operations Research (OR) is the field of how to form mathematical models of complex management decision problems and how to analyze the models to gain insight about possible solutions.

2 History of OR operational use of military resources Although scientists had (plainly) been involved in the hardware side of warfare (designing better planes, bombs, tanks, etc) scientific analysis of the operational use of military resources had never taken place in a systematic fashion before the Second World War. Military personnel, often by no means stupid, were simply not trained to undertake such analysis. J E Beasley, Imperial College, London

3 History of OR "scientifically trained" minds, used to querying assumptions, logic, exploring hypotheses, devising experiments, collecting data, analysing numbers, etc. These early OR workers came from many different disciplines, one group consisted of a physicist, two physiologists, two mathematical physicists and a surveyor. What such people brought to their work were "scientifically trained" minds, used to querying assumptions, logic, exploring hypotheses, devising experiments, collecting data, analysing numbers, etc. Many too were of high intellectual calibre (at least four wartime OR personnel were later to win Nobel prizes when they returned to their peacetime disciplines). J E Beasley, Imperial College, London

4 History of OR Following the end of the war OR took a different course in the UK as opposed to in the USA. In the UK (as mentioned above) many of the distinguished OR workers returned to their original peacetime disciplines. As such OR did not spread particularly well, except for a few isolated industries (iron/steel and coal). In the USA OR spread to the universities so that systematic training in OR began. J E Beasley, Imperial College, London

5 History of OR OR started just before World War II in Britain with the establishment of teams of scientists to study the strategic and tactical problems involved in military operations. The objective was to find the most effective utilisation of limited military resources by the use of quantitative techniques. J E Beasley, Imperial College, London

6 History of OR growth of OR the result of the increasing power and widespread availability of computers You should be clear that the growth of OR since it began (and especially in the last 30 years) is, to a large extent, the result of the increasing power and widespread availability of computers. Most (though not all) OR involves carrying out a large number of numeric calculations. Without computers this would simply not be possible. J E Beasley, Imperial College, London

7 History of OR Manufacturers used operations research to make products more efficiently, schedule equipment maintenance, and control inventory and distribution. And success in these areas led to expansion into strategic and financial planning … and into such diverse areas as criminal justice, education, meteorology, and communications. J E Beasley, Imperial College, London

8 Future of OR A number of major social and economic trends are increasing the need for operations researchers. In today’s global marketplace, enterprizes must compete more effectively for their share of profits than ever before. And public and non-profit agencies must compete for ever-scarcer funding dollars. J E Beasley, Imperial College, London

9 Future of OR This means that all of us must become more productive. Volume must be increased. Consumers’ demands for better products and services must be met. Manufacturing and distribution must be faster. Products and people must be available just in time. J E Beasley, Imperial College, London

10 Terminology OROperations Research Operational Research MSManagement Science OMOperations Management DSDecision Science

11 Planning, Strategic Decision-Making Production Distribution, Logistics, Transportation Supply Chain Management Marketing Engineering Financial Engineering Applications grouped by function

12 Build Your Knowledge to increase your success in practice Linear Programming Non-linear Programming Dynamic Programming Markov Decision Processes Multiple Criteria Decision Making Queuing Models General Simulation

13 OR Journals Operations Research Management Science MS/OR Today (Management Science/Operations Res.) European Journal of Operational Research Journal of the Operational Research Society Mathematical Programming Journal of Optimization Theory and Applications Interfaces OR - Spektrum International Transactions in Operational Research Annals of Operations Research Central European Journal of Operations Research

14 Build Your Knowledge to increase your success in practice OR in SpreadsheetsOR in Spreadsheets Modeling LanguagesModeling Languages Decision support systems Genetic Algorithms, Neural Networks Fuzzy Logic Simulated Annealing General AI

15 Build Your Knowledge to increase your success in practice Regression and Econometrics Forecasting Models Data Envelopment Analysis General Measurement of Effectiveness Cost Benefit Analysis (Reliability,Maintainability) Data Mining Methods Applied Stochastic Processes

16 Production system

17 Operations Research Operations Research deals with decision problems by formulating and analyzing mathematical models – mathematical representations of pertinent problem features.

18 Operations Research The model-based OR approach to problem solving works best on problems important enough to warrant the time and resources for a careful study.

19 OR Process Model solution Real world problem Model Real world solution Analysis Abstraction Interpretation Assessment

20 Math Modeling is Only One Part of Problem Solving Define an Opportunity or Problem Formulate a Mathematical Model Acquire Input Information and Data Validate (Calibrate) Model and Data Solve and Analyze Solution’s Sensitivity Implement Solution Monitor and Follow-Up

21 OR models The three fundamental concerns of forming operations research models are decisions open to decision makers, the constraints limiting decision choices, and the objectives making some decisions preferred to others.

22 Mathematical Programs Optimzation models (also called mathematical programs) represent choices as decision variables and seek values that maximize or minimize objective functions of the decisions variables subject to constraints on variable values expressing the limits on possible decision choices.

23 Feasible - Optimal A feasible solution is a choice of values for the decision variables that satisfies all constraints. Optimal solutions are feasible solutions that achieve objective functions value(s) as good as those of any other feasible solutions.

24 Parameters – Output Variables Parameters – quantities taken as given –Weekly demand, fixed cost of replenishment, cost for holding inventory, cost per carat lost sales, lead time, minimum order size. Parameters and decision variables determine results measured as output variables –c(r,q ; d,f,h,s,l,m)

25 Closed-form solution Closed-form (analytic) solutions represent the ultimate in analysis of mathematical models because they provide both immediate results and rich sensitivity analysis.

26 Sensitivity Analysis Sensitivity Analysis is an exploration of results from mathematical models to evaluate how they depend on the values chosen for parameters.

27 Tractability-Validity Tractability in modeling means the degree to which the model admits convenient analysis. The validity of a model is the degree to which inferences drawn from the model hold for the underlying real world problem. Tradeoff between validity of models and their tractability to analysis.

28 Simulation A simulation model is a computer program that simply steps through the behavior of a system of interest and reports experience. Simulation models often possess high validity because they track true system behavior fairly accurately.

29 Simulation Descriptive models (simulation) Prescriptive optimization models (mathematical programming) Descriptive models yield fewer analytic inferences (conclusions) than prescriptive optimization models because they take both input parameters and decision as fixed.

30 Numerical Search Numerical search is a process of systematically trying different choices for the decision variables, keeping track of the feasible one with the best objective function value found so far. Deals with specific values of the variables - Not with symbolic quantities!

31 MM Numerical Part Conclusions from numerical search are limited to the specific points explored unless mathematical structure in the model support further deduction.

32 Exact - Approximate An exact optimal solution is a feasible solution to an optimization model that is provably as good as any other in objective function value. A approximate optimal solution is a feasible solution derived from prescriptive analysis that is not guaranteed to yield an exact optimum.

33 Exact - Approximate Losses from settling for approximate instead of exact optimal solutions are often dwarfed by variations associated with questionable model assumption and doubtful data. Exact optima add a satisfying degree of certainty.

34 Deterministic - Stochastic A mathematical model is termed deterministic if all parameter values are assumed to be known with certainty. A mathematical model is termed probabilistic or stochastic if it involves quantities known only in probability.

35 Deterministic - Stochastic

36 Deterministic - Stochastic

37 MM Stochastic Simulation Besides providing only descriptive analysis, stochastic simulation models impose the extra analytic burden of having to estimate results statistically from a sample of system realizations.

38 Deterministic - Stochastic The power and generality of available mathematical tools for analysis of stochastic models does not nearly match that available for deterministic models. Most optimization models are deterministic – not because all problem parameters are known with certainty, but because useful prescriptive results can often be obtained only if stochastic variation is ignored.