Cheat Sheet MGMT 306
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This 6 page Test Prep (MCAT, SAT...) was uploaded by YanRou Ng on Monday October 12, 2015. The Test Prep (MCAT, SAT...) belongs to MGMT 306 at Purdue University taught by F Cauley in Spring 2015. Since its upload, it has received 231 views. For similar materials see Management Science in Business, management at Purdue University.
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Date Created: 10/12/15
MGMT 306 EXAM 1 Cheat Sheet Components of mathematical model for decisionmaking decision variables objective functions and constraints input parameters If a LP has an optimal solution then the feasible region cannot be empty In order to obtain a feasible solution to an otherwise infeasible problem some of the constraints must be changed or removed Changing objective function will never make an infeasible problem feasible Why conduct sensitivity analysis Some input parameters may not have been known with certainty estimationapproximation Model represents a dynamic environment in which some of the parameters are subject to change by time Given an optimal solution to a LP There is always some amount by which the RHS value of a non binding constraint can be changed without affecting the optimal solution If a shadow price of a constraint is negative a unit decreases in the RHS value of the constraint within feasible range results in an increase in the optimal objective function value Objective Function An equation to be maximized or minimized representing the goal of a mathematical model Optimal Solution The set of values for the decision variables that yield the best value for the objective function 4 types of LP Unique optimal solution alternate optimal solution when obj function parallel to a boundary constraint in the direction of optimization all points on the line are optimal solutions in nite infeasible no point satis es all the constraints 0 optimal solution unbounded optimal solution feasible region unbounded value can always be improved Sensitivity Report Determine how the optimal solution and the optimal objective value are affected by changes in model input data Investigate objective function coefficient and RHS constraints Shadow Price Change of the optimal objective value due to a unit increase to the RHS RatioUnit Price Change of the optimal objective value shadow price X change of RHS Binding Solution makes inequality function equal MGMT 306 EXAM 1 Cheat Sheet Slack Difference between LHS and RHS call slack Don t forget NONNEGATIVITY constraints Nonlinear Optimization Models NLP Xn NONNEGATIVITY CONSTRAINT Eg Diminishing return on Advertising Pricing Portfolio Optimization Model Sometimes obtains a suboptimal solution in solver worst than optimal solution Local optimal solution better than nearby points Global optimal solution best point in the entire feasible region NLP solver can solve certain types of NLPs globally some cant be solve O Convex slope of the region is always increasing or no line segment connecting two points on the curve goes below the function Minimization problem ConvexConstraints are linear O Concave slope of the region is always deceasing or no line segment connecting two points on the curve goes above the function Maximization problem concaveconstraints are linear EaX i bY aEX i bEY VaraX i bY o pm 0 IoE SUMPRODUCTMMULT0 p R I p 0 Std of return pPortfolio RCorelation a2 b2 c2 SQRTXX12 YY12 Don t forget to X2 if return Expectation is Linear Distance Integer Programming Models IPILP INT BIN OR NONNEGATIVITY CONSTRAINT Ask solver to take only integer values because variable represents quantities that are naturally integral and model special requirements 01 variables binary capital budgeting fixed cost vehicle routing applications YES1 No0 All the variables are restricted in IP some of the variables are restricted in MIPMILP mixed integer programming LP Relaxation of IP is a LP obtained from the integer program without forcing integer requirements LP relaxation of IP is at least as good as the optimal objective value of IP LP has more feasible region than IP Max obj value of LP gt Max obj value of IP Min obj value of LPlt min obj value of IP Logical constraints 0 If A then B A lt B 0 If A then not B A lt lB or ABlt1 at most one of A or B 0 IonrBthenC AltCandBltC O IfAthenBandC AltBandAltC 0 If A and B then C AB1 lt C 0 If A then B or C A lt BC O A happens only if B happens A B O A happens if and only if B does not happens AB 1 0 At least one of A and B happens AB gt 1 0 If AampB then CampD AB1 ltC AB1ltD 0 If A or B then CampD AltC AltD BltC BltD 0 IfA or not B then C or D Linking constraints 0 If the company rents dress machine it produce no more than 40 min of other constraints dresses if the company doesn t rent dress machine it produces no more than 0 dress I Quantity variable D lt 40upper bound RD Binary variable Other constraint 0 If shorts machinery is rented then at least 40 shorts should be produced 39 Sgt40Rs01RS 0 If pants machinery is rented then at most 30 dresses should be produced AltCD 1BltCD I If Rp 1 then D lt 30 if Rp 0 then D lt40 I D lt 30Rp 401Rp Spreadsheet Simulation Modeling with Risk 0 Triangle Risk RoundRiskTriangmin most likely max0 0 DiscreteRisk xy RoundRiskDiscrete Probability of 0 0 BinomialRisllt RoundRiskBinomialnp0 0 Normal Risk Roundrisknormalmean std0 0 OutPut Risk RiskOutput 0 A lot of output to test RiskSimTable enter of output you want to test for simulation if you want to test 5 output enter 5 then risk will run each of the five numbers 500 times 0 Random Number Excel RAND 0 Random between RANDBetweenab 0 Normal NORMINVRANDmean std 0 Revenue Unit Pricemindemandorder quanitity 0 Refund Unit Refund maxorder quantity demand 0 0 Leftover maxorder quantitydemand 0 0 Profit revenuecostrefund 0 Use max to get positive number round to round to whole number 0 Simulation model is a computer model that imitates a reallife situation Contains Parametersuncontrollable input decision variablescontrollable input and outputobj It incorporates uncertainty in one or more parameters 0 Simulation Settings simulation segment of the Risk menu bar shows we are set to do 500 iteration on 1 simulation but we may click on simulation settings button to open and change it through simulation setting dialogue box 0 Browse Result button generate an interactive histogram for any risk inputoutput in spreadsheet model the slider at the top of the chart can be moved to see various probabilities and corresponding values 0 Expected Profit mean of profit 0 Simulation detailed Statistic open a window displaying detailed summary statistic 0 Simulation data button display all the inputsoutputs in the simulation model 0 Tornado Graph shows graphically and numerically how each of the random input affects the profit output Higher coefficient implies stronger relationship between the input and the profit The coefficient is the number of std deviation by which the output increases if the input increases by one standard deviation assume all other are constant Decision Analysis 0 Used to determine a strategy when a decision maker is faced with several decision alternatives and uncertainty Eg new product development bidding for a contract 0 Payoff Measurement of the outcome that results from a specific decision alternative and the occurrence of a particular state of nature Profits cost time distance 0 Decision making situation 0 Certainty State of nature is known when decision is made Optimal decision is to pick highest payoff O Uncertainty Doesn t know which state of nature will be occurring Decision made using chosen criteria 3 approach I Optimistic Choose largest possible ngoff if cost choose lowest I Conservative Choose largest minimum possible payoff max of the min if cost choose smallest maximum possible payoff I Minimax regret Construct Egret table or an onnortunitv loss tabi Regret table 1 Calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature 2 List the maximum regret for each possible decision 3 Choose minimum of the maximum regrets 0 Decisionmaking with probability If probability stated use the expected value EV approach 0 Calculate Expected value by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring choose the best expected return 0 Expected value of perfect information EVPI the increase in the expected profit that would result if one knew with certainty which state of nature will occur 1 Find expected value with perfect information EVwPI multiply the max payoff for each state by the corresponding probability and sup up these value 2 Subtract the EV of the optimal decision from EVwPI I EVPI EVWPI EV 0 Decision tree Chronological representation of a decision problem 0 Round nodes states of nature chances 0 Square nodes decision alternatives 0 Different states of nature may happen after making different decision 0 Outcomes attained at the end of each limb of a tree 0 Precision tree 0 Start by clicking the Decision Tree button in a blank cell A dialog box appear can enter the tree name If want to get minimum outcome manipulate it by clicking calculation tab At the end of branch is a blue triangle click to add node Node setting dialogue box appear click on green square to denote decision give the node a name and click the branch tab to define the node given two can click add to add more if you have more decision Name each branch and add its value normally the cost of the decision 0 Click the blue triangle at the end of the decision to enter chance red circle Similar with decision but have to key in the probability and value here Can copy the entire subtree and paste just don t forget to edit the value 0 Reports help understand the optimal strategy and the risk and return that can result from following that strategy From menu select I Policy Suggestion display optimal strategy in tree form only show the chosen part I Risk Pro le display distribution of payoffs for decision alternatives color bar and values associated with the distribution in the chart table below color bar I Multiple stage decision tree similar with decision tree difference is that there are decisions have to made after the first decision or first outcome Multiple Criteria Decisions In multiobjective problems there are no optimal solutions there are usually many ef cient solutions Efficient Solution 0 Feasible solution B dominates Feasible solution A if I B is not worse than A in every objectives and I B is strictly better than A in at least one objective 0 Solution A is called ef cient if no other feasible solution dominates A Efficient Frontier 0 Decision maker have to limit choices to only efficient solutions 0 When only two objective exist if we graph the objective values for the efficient solutions we obtain a tradeoff curve also called ef cient frontier Goal Programming Used to solve linear program with multiple objectives each objectives view as a goal Goal added to the constraint set indicating the targeted amount overachievement and underachievement amounts Satisfy goals in a priority sequence Goals have preemptive priorities when the decision maker is not willing to sacrifice any goal Goal equations are called soft constraint 0 Deviation variable the difference between the target value for the goal and the level achieved
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