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Excel Tools: Solver and Goal Seek A Brown Bag discussion for N-81 26 Sept 2012 THIS PRESENTATION IS UNCLASSIFIED

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Purpose This Talk promises to: – (re)introduce some powerful tools in Excel Optimization – centric functions Goal seek Solver – To show practical examples of how they may be used This Talk will not: – Be a course in Linear Optimization

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References Albright, S. C. (2007) VBA for modelers Thompson – Brookstone. Walkenbach, J Microsoft Excel 2010 Bible Wiley. Ragsdale, C. Decision Analysis with Spreadsheets Balakrishnan, N. Managerial Decision Modeling with Spreadsheets Frontline Systems: www.solver.comwww.solver.com

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Block 0: Goal Seek Goal Seek: A Line Search algorithm that iteratively seeks to find the (User set) goal value. – Goods: Robust, fast, and easy to use. Can work on non-linear problems – Bads: Goal Seek is not an optimization algorithm, but rather a regulated form of iterated guessing. Sometimes doesn’t work. Can miss multiple/optimal solutions – Others: Will only take literals as the goal value. – For Nerds: Is it Binary or Golden Section? Microsoft doesn’t specify in documentation

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The important thing to know about Goal Seek: G/S simply automates the ‘trial – and – error’ approach to problem solving. In strict terms, Goal Seek is Guessing.

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Invoking Goal Seek Data -> What If Analysis -> Goal Seek Set Cell: The ‘target’ The desired value of the Set Cell. Must be a ‘literal’. “By Changing”

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Goal Seek Example Given a maintenance department with two ‘shops’, if aircraft break at a rate of 1 per day, at what rate does each shop need to fix planes in order to have 80% chance that at any given moment there are no down planes? This is a queuing problem

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Solving The hard way: Break out your stochs textbook, and try to formulate this as a Markov Chain The Easy way: Q.xls and Goal Seek!

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Goal Seek Example

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Goal Seek Example II: Military Application Recall Lanchester’s Aimed Fire model of combat from our last lunchtime series: Given, find the value of that results in 70 blue survivors when the Red side is eliminated.

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Approach 1 TOO EASY! Just solve:

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Approach II Use Goal Seek!

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Summary Goal seek is ideal in situations where you want answers, not proofs! DISCLAIMERS: – You will not know if there are multiple solutions – You will not get any sensitivity analysis

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SOME USEFUL EXCEL FUNCTIONS

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Named Cells Sometimes, you want to use cells, but D$3$ can become cumbersome to type. Also, you might want to be able to understand the formulae without an interpreter. Naming Cells is very handy for this! How to? – Use the Name box!

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Naming Cells Name Box

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Which is easier to understand?

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Formula Auditing Sometimes, you want to know what the ‘goezintas’ for a particular answer are. There’s a great function for this: Formula Auditing – Formulas -> Formula Auditing

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Example I cannot overstress how useful this is for reviewing someone else’s spreadsheet!

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SUMPRODUCT() Sometimes you have data in two columns, and you wish to find the total the product of the two sides. – Such as finding the expectation and variance of a discrete variable manually – Tallying up costs by aircraft type Excel has a special function for this: SUMPRODUCT()

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SUMPRODUCT() II Takes two arrays, X and Y as inputs – Must be equally sized Returns a single number, which is: In English: Multiply all these by all those and add up Very useful for the objective function of a LP.

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SUMXMY2() Sometimes you want to find the squared Euclidian distance between two points or sets of points. – Such as distance between ships in the example we will work later – Or OLS (Ordinary Least Squares) SUMXMY2: – Why did they name it that? I don’t know! – SUM of X Minus Y Squared (2)

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SUMXMY2() II Takes two arrays, X and Y and returns the sum of square differences (i.e. squared Euclidian measure)

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Block 1: Solver What is it: an optimization package. Can handle LP, MIP, NLP. It’s not anyone’s favorite package, but it’s the one we have. Goods: Graphical interface with spreadsheets can make formulation more visually appealing Bads: There are some problems where it fails to converge. Limits on number of variables, and number of Integer/Binary variables Others: Some important things ‘under the hood’ that should be considered (upcoming slides) For Nerds: I’ve never used Evolutionary Solver mode.

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Invoking Solver To use Solver, it must be installed – Why? Because Bill Gates Hates you, that’s why! To use Solver in VBA, it must be installed there as well – Why? See above!

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Installing Solver – Main Body

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Installing Solver- VBA

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Block II: How to use Solver

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Solver Differences - 2010 Excel 2010 has a different (and not better) interface. Report options are now available after the solution is complete – Used to be an option in the dialog box Report Options

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A Toy Force Structure Problem You need to put together a force that is able to carry 15 helicopters, using a mix of ships at a minimum cost. Data Given: Use at least 1 LHA, 2 LCS, and no more than 4 of any type of ship.

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Switch to Spreadsheet

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Some Pointers I like to use color: – Objective function GREEN – Constraints RED – Variables BLUE This makes it easy to see ‘what’s what

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Sensitivity Report

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Okay, well, that answer was great… (but what does.5 ships mean?) In order to go forward, we need to solve as a Mixed Integer Program. In Excel, we add another constraint… … and a whole universe of complexity WARNING! It is NOT GENERALLY true that the solution to a problem with Integer constraints is ‘close’ to the associated Linear Program!

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Solver – Pro Tips Frontline solvers claims that the limit on variables is 200, – But it might crash much, much sooner! Solutions: – A. Upgrade solver – B. Use MATLAB solver – C. Ask us (NPS) for help.

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Solver: what can go wrong Here’s something that can go wrong: – Max X^2, unconstrained, with an incumbent solution of zero.

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Practical Example: Optimum placement of Ships http://puzzlor.editme.com/Relief-Mission

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Problem Description Given the map shown and the ability to place two ships, what is the optimum placement to minimize the maximum distance to a target? Real-world applications: – Ballistic Missile Defense – Medical Facility Placement – Logistics Hubs – Others?

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First, an easier Problem What if there was only one ship to be placed?

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Now, the Placement Problem This is actually two problems – If we knew which ship was associated with each Target, this would be easy – If we knew where the two ships were stationed, it would be easy to know which Target to associate with them We have to figure both out, simultaneously This is a hard problem – but one that is probably worth the effort

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Formulation

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Why does this work? Because for at one and only one of the constraints, the RHS is negative, and therefore irrelevant. – Here we’re using constraints to shape the objective function! While combining the constraints into an expression like looks good, it is highly non-linear and may cause solver to crash

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Summary Today we talked about: – Excel Practice, generally – Goal Seek: A useful way for getting answers but Proofs – Excel Functions: Named cells are infinitely better than R$2$:D$2$, etc. SUMPRODUCT() SUMXMY2() – Solver – Practical Applications.

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Final Note: Presentation Don’ts BEWARE what MS office does when you copy and paste! – If you copy and paste a graph from a spreadsheet, you might be pasting the entire spreadsheet. This may be handing someone else your entire analysis. – Solution: Be sure to paste graphs as pictures BEWARE what MS office does when you use track changes. – You might leave them in. – Solution: Copy your text, paste to clipboard, then copy and paste back to word Solution to both problems: convert to.pdf before distribution

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Point of Contact CDR Harrison Schramm hcschram@nps.edu schrammhc@nps.navy.smil.mil 831.656.2358 After April, 2013 – BE922

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Graphical Solutions Plot all constraints including nonnegativity ones

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