Decan-20180619-1753 - TreePlan Decision Tree Excel Add-in
Decision TreesUsing TreePlan1616.1 TREEPLAN OVERVIEWTreePlan is a decision tree add-in for Microsoft Excel 2007 & 2010 & 2013 & 2016 (Windows)and Microsoft Excel 2011 & 2016 (Macintosh).TreePlan helps you build a decision tree diagram in an Excel worksheet using dialog boxes.Decision trees are useful for analyzing sequential decision problems under uncertainty. Yourdecision tree model may include various controllable alternatives (e.g., whether to introduce a newproduct, whether to bid on a new project) and uncontrollable uncertainties (e.g., possible demandfor a product, whether you're awarded a contract), arranged in chronological order. TreePlanautomatically includes formulas for summing cash flows to obtain outcome values and forcalculating rollback values for determining the optimal strategy.To use TreePlan, you(1) open a new worksheet,(2) press Ctrl Shift T (or Option Command t) to build a new decision tree diagram,(3) select a node to change the structure of your decision tree,(4) enter branch names, cash flows, and probabilities, and(5) determine the optimal strategy from TreePlan's results.All of TreePlan’s functionality, including its built-in help, is a part of the TreePlan XLAM file.There is no separate setup file or help file. When you use TreePlan on a Windows computer,TreePlan does not create any Windows Registry entries (although Excel may use such entries tokeep track of its add-ins).16.2 BUILDING A DECISION TREE IN TREEPLANWith Windows Excel 2007 & 2010 & 2013 & 2016, you can start TreePlan either by choosingAdd-ins TreePlan Decision Tree or by pressing Ctrl Shift T (hold down the Ctrl and Shiftkeys and press T).With Mac Excel 2011, you can start TreePlan either by choosing Tools TreePlan DecisionTree from the menu or by pressing Option Cmd t (hold down the Option and Command keysand press t).With Mac Excel 2016, you can start TreePlan by pressing Option Cmd t.If the worksheet doesn't have a decision tree, TreePlan prompts you with a dialog box with threeoptions; choose New Tree to begin a new tree. TreePlan draws a default initial decision tree with
2000Chapter 166 Decision Trees Using TreePlanitss upper left corrner at the selected cell. For example,ethe fiigure below shows the initial tree whenceell C3 is selecteed before creatting the new treee. (Note that TTreePlan writees over existingg values inthhe spreadsheet: begin your treee to the right ofo the area wheere your data iss stored, and ddo notsuubsequently addd or delete rowws or columns in the tree-diagagram area.)Figure 16.1 TreeePlan Initial DefaultDDecisioon Treeb adding or modifyingmbrancches or nodes iin the default trree. To changee the branchBuild up a tree bybilities, click onn the cell contaaining the labell or probabilityy and type the nnew labellaabels or probaborr probability. ToT modify the structuresof thee tree (e.g., addd or delete brannches or nodes in thetree), select the nodenor the celll containing thhe node in the ttree to modify,, and press Ctrrl Shift T(oor Option Cmmd t). TreePlann will then pressent a dialog bbox showing thhe available commmands.Foor example, to add an event nodento the top branch of the tree shown aboove, select celll H5 orseelect the triangle shape, and presspCtrl Shift T (or Optioon Cmd t). TTreePlan then ppresentsthhis dialog box.Figure 16.2 TreeePlan Terminaal Node dialog boxnge the selectedd terminal nodee to an event nnode byTo add an eventt node to the brranch, we change to event nodde in the dialogg box, selectinng the number oof branches (heere two),seelecting Changannd pressing OKK. TreePlan theen redraws the tree with a chaance node in pplace of the termminal node.
16.22 Building a Decicision Tree in TreeePlan201Figure 16.3 Inittial Decision TreeT Diagramhe dialog boxees presented byy TreePlan varyy depending onn what you havve selected wheen youThprress Ctrl Shifft T (or Option Cmd t). WithW an event noode selected, thhe dialog box sshownbeelow is presentted when you presspCtrl Shiift T (or Optioon Cmd t); a similar dialogg box isprresented when you select a deecision node. If you want to aadd a branch too the selected nnode,chhoose Add braanch and presss OK. If you wantw to insert a decision or eveent node beforre theseelected node, choose Insert decisiondor Inssert event and press OK. To get a description of theavvailable commands, click on the Help buttoon.Fiigure 16.4 TreeePlan Event Diialog BoxThhe Copy subtrree command isi particularly usefuluwhen buuilding large trrees. If two or mmore partsoff the tree are siimilar, you cann copy and pastte "subtrees" raather than buildding up each ppartseeparately. To copy a subtree, select the nodee at the root off the subtree annd choose Copyy subtree.Thhis tells TreePlan to copy thee selected nodee and everythinng to the right oof it in the tree. To pastethhis subtree, seleect a terminal nodenand choosse Paste subtrree. TreePlan thhen duplicates thesppecified subtreee at the selecteed terminal nodde.Siince TreePlan decision trees area built directtly in Excel, yoou can use Exccel's commandss to formatyoour tree. For exxample, you caan use bold or italicifonts for branch labels: select the cells you wanttoo format and chhange them usiing Excel's formmatting commaands. To help yyou, TreePlan provides a
2002Chapter 166 Decision Trees Using TreePlanSeelect dialog boox that appears when you presss Ctrl Shift T (or Option Cmd t) withhout a nodeseelected. You caan also bring upp this dialog boox by pressingg the Select buttton on the Nodde dialogboox. From here, you can selectt all items of a particular typee in the tree. Foor example, if you chooseProbabilities annd press OK, TreePlanTselectts all cells conttaining probabiilities in the treee. You canthhen format all ofo the probabiliities simultaneously using Exxcel's formattinng commands. (Becauseoff limitations inn Excel, the Sellect dialog boxx may not be avvailable when wworking with vvery largetrees.)16.3 ANATTOMY OFF A TREEEPLAN DEECISION TREEAnA example of a TreePlan deccision tree is shhown below. Inn the example, a firm must deecide (1)whetherwto prepaare a proposal for a possible contractcand (22) which methood to use to sattisfy thecoontract. The treee consists of decisiondnodes,, event nodes aand terminal noodes connectedd bybrranches. Each branchbis surroounded by cellss containing foormulas, cell reeferences, or lababelspeertaining to thaat branch. You may edit the laabels, probabillities, and partiial cash flows aassociatedwithw each branchh. The partial cashcflows are the amount thee firm "gets paaid" to go downn thatbrranch. For the scenario with terminaltvalue 30,000, the fifirm pays 50,0000 if it decidees toprrepare the propposal, receives 250,000 up frontfrif awardedd the contract, spends 50,0000 to try theellectronic methood, and spends 120,000 on thet mechanicall method if the electronic metthod fails.Figure 16.5 Noddes, Labels, Caash Flows, andd Probabilitieshe trees are "soolved" using foormulas embeddded in the spreeadsheet. The tterminal valuees sum allThthhe partial cash flowsfalong thee path leading to that terminaal node. The treee is then "rollled back"byy computing exxpected valuess at event nodess and by maximmizing at decission nodes; thee rollbackEVs appear nextt to each node anda show the expectedevaluee at that point inn the tree. The numbers inthhe decision noddes indicate whhich alternativee is optimal forr that decision. In the examplle, the "1"inn the first decission node indiccates that it is optimaloto prep are the proposal, and the "2" in theseecond decision node indicatess the firm shouuld try the electtronic method because that allternativeleeads to a higherr expected valuue, 90,000, thhan the mechannical method, 80,000.
16.3 Anatomy of a TrreePlan Decisionn Tree203Figure 16.6 Terrminal Values, Rollback EVss, and Choice Inndicatorsf options thaat control the wayw calculationns are done in tthe tree. To sellect theseTrreePlan has a fewopptions, press thhe Options buttton in any of TreePlan'sTdialoog boxes. The first choice is whether toUseU Expected ValuesVor Use ExponentialEUtilityUFunctioon for computinng certain equiivalents.Thhe default is too rollback the trree using expected values. Iff you choose too use exponentiial utilities,TrreePlan will coompute utilitiess of endpoint cashcflows at thhe terminal noddes and compuute expecteduttilities instead of expected vaalues at event nodes.nExpectedd utilities are ccalculated in thhe cellbeelow the certain equivalents. You may also choose to Maxximize (profitts) or Minimizze (costs) atdeecision nodes; the default is tot maximize prrofits. If you chhoose to minimmize costs insteead, thecaash flows are innterpreted as costs, and decissions are made by choosing thhe minimum exxpectedvaalue or certain equivalent rathher than the maaximum. See thhe Help file foor details on theese options.
204Chapter 16 Decision Trees Using TreePlan16.4 TREEPLAN INPUTS AND FORMULASFigure 16.7 Influence Chart of TreePlan Inputs and FormulasBranch InputsCash FlowCell FormulasDefined NameTerminal NodeEndpoint ValueOptionalEvent NodeRollback ValueProbabilityOptionalRT (Risk Tolerance)Decision NodeRollback ValueDecision NodeChoice IndicatorFigure 16.8 Explanation of FormulasLocationEndpoint Valueat Terminal NodeRollback Valueat Event NodeFormulaSUM of branch cash flowsIF probabilities SUM toapproximately one, then SUM theproducts of probabilities timessubsequent rollback valuesRollback Valueat Decision NodeMAX or MIN of subsequent rollbackvaluesChoice Indicatorat Decision NodeNested IF functions16.5 STEP-BY-STEP TREEPLAN TUTORIALA decision tree can be used as a model for a sequential decision problems under uncertainty. Adecision tree describes graphically the decisions to be made, the events that may occur, and theoutcomes associated with combinations of decisions and events. Probabilities are assigned to theevents, and values are determined for each outcome. A major goal of the analysis is to determinethe best decisions.Decision tree models include such concepts as nodes, branches, terminal values, strategy, payoffdistribution, certain equivalent, and the rollback method. The following problem illustrates thebasic concepts.
16.5 Step-by-Step TreePlan Tutorial205DriveTek ProblemDriveTek Research Institute discovers that a computer company wants a new storage device for aproposed new computer system. Since the computer company does not have research peopleavailable to develop the new storage device, it will subcontract the development to an independentresearch firm. The computer company has offered a fee of 250,000 for the best proposal fordeveloping the new storage device. The contract will go to the firm with the best technical planand the highest reputation for technical competence.DriveTek Research Institute wants to enter the competition. Management estimates a cost of 50,000 to prepare a proposal with a fifty-fifty chance of winning the contract.However, DriveTek's engineers are not sure about how they will develop the storage device if theyare awarded the contract. Three alternative approaches can be tried. The first approach is amechanical method with a cost of 120,000, and the engineers are certain they can develop asuccessful model with this approach. A second approach involves electronic components. Theengineers estimate that the electronic approach will cost only 50,000 to develop a model of thestorage device, but with only a 50 percent chance of satisfactory results. A third approach usesmagnetic components; this costs 80,000, with a 70 percent chance of success.DriveTek Research can work on only one approach at a time and has time to try only twoapproaches. If it tries either the magnetic or electronic method and the attempt fails, the secondchoice must be the mechanical method to guarantee a successful model.The management of DriveTek Research needs help in incorporating this information into adecision to proceed or not.[Source: The storage device example is adapted from Spurr and Bonini, Statistical Analysis forBusiness Decisions, Irwin.]Nodes and BranchesDecision trees have three kinds of nodes and two kinds of branches. A decision node is a pointwhere a choice must be made; it is shown as a square. The branches extending from a decisionnode are decision branches, each branch representing one of the possible alternatives or courses ofaction available at that point. The set of alternatives must be mutually exclusive (if one is chosen,the others cannot be chosen) and collectively exhaustive (all possible alternatives must be includedin the set).There are two major decisions in the DriveTek problem. First, the company must decide whetheror not to prepare a proposal. Second, if it prepares a proposal and is awarded the contract, it mustdecide which of the three approaches to try to satisfy the contract.An event node is a point where uncertainty is resolved (a point where the decision maker learnsabout the occurrence of an event). An event node, sometimes called a "chance node," is shown asa circle. The event set consists of the event branches extending from an event node, each branchrepresenting one of the possible events that may occur at that point. The set of events must bemutually exclusive (if one occurs, the others cannot occur) and collectively exhaustive (allpossible events must be included in the set). Each event is assigned a subjective probability; thesum of probabilities for the events in a set must equal one.The three sources of uncertainty in the DriveTek problem are: whether it is awarded the contractor not, whether the electronic approach succeeds or fails, and whether the magnetic approachsucceeds or fails.
206Chapter 16 Decision Trees Using TreePlanIn general, decision nodes and branches represent the controllable factors in a decision problem;event nodes and branches represent uncontrollable factors.Decision nodes and event nodes are arranged in order of subjective chronology. For example, theposition of an event node corresponds to the time when the decision maker learns the outcome ofthe event (not necessarily when the event occurs).The third kind of node is a terminal node, representing the final result of a combination ofdecisions and events. Terminal nodes are the endpoints of a decision tree, shown as the end of abranch on hand-drawn diagrams and as a triangle on computer-generated diagrams.The following table shows the three kinds of nodes and two kinds of branches used to represent adecision tree.Figure 16.9 Nodes and SymbolsType of NodeWritten puter Symbolsquarecircletriangle or barNode Successordecision branchesevent branchesterminal valueTerminal ValuesEach terminal node has an associated terminal value, sometimes called a payoff value, outcomevalue, or endpoint value. Each terminal value measures the result of a scenario: the sequence ofdecisions and events on a unique path leading from the initial decision node to a specific terminalnode.To determine the terminal value, one approach assigns a cash flow value to each decision branchand event branch and then sum the cash flow values on the branches leading to a terminal node todetermine the terminal value. In the DriveTek problem, there are distinct cash flows associatedwith many of the decision and event branches. Some problems require a more elaborate valuemodel to determine the terminal values.The following diagram shows the arrangement of branch names, probabilities, and cash flowvalues on an unsolved tree.
16.5 Step-by-SStep TreePlan TuTutorial207Figure 16.10 DrriveTek Decisiion Tree DiagrramUse mechanical method 80,00050.5Eleectronic success 150,0000.5Awarded contractTry electronicc method0.55Eleectronic failure 30,0000.77Maagnetic successPrepare propoosal 120,000Try magneticc method0.33Maagnetic failure 00.5Nott awarded contract- 50,000Don't prepare proposal 0To build the deccision tree, youu use TreePlan’’s dialog boxess to develop the structure. Yoou enter abrranch name, brranch cash floww, and branch probabilityp(forr an event) in tthe cells abovee and belowthhe left side of eachebranch. Ass you build thee tree diagram, TreePlan enteers formulas in other cells.BuildingBthee Tree Diaggram1.Start withw a new workksheet. (If no workbookwis oppen, choose Fille New. If a wworkbookis openn, choose Insertt Worksheet.)2.Select cellc A1. In Exccel 2007 & 20110 & 2013 & 22016, choose AAdd-ins TreePPlanDecisioon Tree; in Maac Excel 2011, choose Tools TreePlan Deecision Tree. Or, in anyWindowws version, preess Ctrl Shift T. In Mac Exccel 2011 & 20116, press Optioon Cmd t.Subseqquent instructioons refer only tot the Window s shortcut key. In the TreePlaan NewTree diialog box, clickk the New Treee button. A deccision node witth two branchees appears.Figure 16.11 TrreePlan New TreeT Dialog Box
2008Chapter 166 Decision Trees Using TreePlanFigure 16.12 Innitial Decision TreeT DiagramA123456789B CDEFGAlternative 100010Alternative 2003.0Select cellc D2, and ennter Prepare proposal.pSelecct cell D4, and enter –50000. Select cellD7, andd enter Don't prepareppropoosal.a Cash FlowFigure 16.13 Brranch Names andA123456789B CDEFGPrepare propossal-500000-50000-5000020Don't prepare proposalp004.0Select cellc F3. Press Ctrl Shift T.CInI the TreePlann Terminal Node dialog box, selectChangee To Event Node, select Twoo Branches, andd click OK. Thhe tree is redrawwn.Figure 16.14 TrreePlan Terminnal Node Dialoog Box
16.5 Step-by-Step TreePlan Tutorial209Figure 16.15 Initial Event BranchesA1234567891011121314B CDEF GH0.5Outcome 3IJK-50000Prepare proposal0-500000.5Outcome 4-50000-50000-5000020-500000Don't prepare proposal005.0Select cell H2, and enter Awarded contract. Select cell H4, and enter 250000. Select cellH7, and enter Not awarded contract.Figure 16.16 Event Branches With Names and Cash FlowA1234567891011121314B CDEF GHI0.5Awarded contractJK200000Prepare proposal250000-500000.5Not awarded contract75000200000-5000010-5000075000Don't prepare proposal006.0Select cell J3. Press Ctrl Shift T. In the TreePlan Terminal Node dialog box, selectChange To Decision Node, select Three Branches, and click OK. The tree is redrawn.
210Chapter 16 Decision Trees Using TreePlanFigure 16.17 Subsequent Decision BranchesA123456789101112131415161718192021222324B CDEF GHIJKLMNOAlternative 520000000.5Awarded contract200000Alternative 612500002000002000000200000Prepare proposalAlternative 7-500000200000750002000000.5Not awarded contract1-50000750000-50000Don't prepare proposal007.0Select cell L2, and enter Use mechanical method. Select cell L4, and enter –120000.Select cell L7, and enter Try electronic method. Select cell L9, and enter –50000. Selectcell L12, and enter Try magnetic method. Select cell L14, and enter –80000.Figure 16.18 Subsequent Decision Branches With Names and Cash FlowsA123456789101112131415161718192021222324B CDEF GHIJKLMNOUse mechanical method80000-1200000.5Awarded contract80000Try electronic method2250000150000150000-50000150000Prepare proposalTry magnetic method-50000-80000120000500001200000.5Not awarded contract1-50000500000-50000Don't prepare proposal008.0Select cell N8. Press Ctrl Shift T. In the TreePlan Terminal Node dialog box, selectChange To Event Node, select Two Branches, and click OK. The tree is redrawn.
21116.5 Step-by-Step TreePlan TutorialFigure 16.19 Branches for Electronic Method 42526272829B CDEF GHIJKLMN OPQRSUse mechanical method80000-120000800000.5Outcome 80.5Awarded contract150000Try electronic method0150000-500000.5Outcome 922500001500001500001500000150000Prepare proposal-5000050000Try magnetic method120000-800001200000.5Not awarded contract150000-500000-50000Don't prepare proposal009.0Select cell P7, and enter Electronic success. Select cell P12, and enter Electronicfailure. Select cell P14, and enter –120000.Figure 16.20 Branch Names and Cash Flows for Electronic Method 4252627282910.B CDEF GHIJKLMN OPQRSUse mechanical method80000-120000800000.5Electronic success0.5Awarded contract150000Try electronic method0150000-500000.5Electronic failure32500001200009000030000-12000030000Prepare proposal-5000035000Try magnetic method120000-800001200000.5Not awarded contract135000-500000-50000Don't prepare proposal000Select cell N18. Press Ctrl Shift T. In the TreePlan Terminal Node dialog box, selectChange To Event Node, select Two Branches, and click OK. The tree is redrawn.
212Chapter 16 Decision Trees Using TreePlanFigure 16.21 Branches for Magnetic Method 42526272829303132333411.B CDEF GHIJKLMN OPQRSUse mechanical method80000-120000800000.5Electronic success1500000.5Awarded contract3250000Try electronic method0-500000.5Electronic e 10Prepare proposal-50000120000Try magnetic method0-800000.5Outcome 1112000035000120000120000011200000.5Not awarded contract35000-500000-50000Don't prepare proposal000Select cell P16, and enter .7. Select cell P17, and enter Magnetic success. Select cellP21, and enter .3. Select cell P22, and enter Magnetic failure. Select cell P24, and enter–120000.
21316.5 Step-by-Step TreePlan TutorialFigure 16.22 Complete Diagram Before 25262728293031323334B CDEF GHIJKLMN OPQRSUse mechanical method80000-120000800000.5Electronic success1500000.5Awarded contract2250000Try electronic method0-500000.5Electronic c successPrepare proposal-50000120000Try magnetic method0120000-800000.3Magnetic failure20000840000-120000100.5Not awarded contract20000-500000-50000Don't prepare proposal0012.0Double-click the sheet tab (or right-click the sheet tab and choose Rename from theshortcut menu), and enter Original. Save the workbook.Interpreting the ResultsThe 30,000 terminal value on the far right of the diagram in cell S13 is associated with thefollowing scenario:Figure 16.23 Evaluation of a ScenarioBranch TypeDecisionEventDecisionEventBranch NamePrepare proposalAwarded contractTry electronic methodElectronic failure (Use mechanical method)Cash Flow– 50,000 250,000– 50,000– 120,000Terminal value 30,000TreePlan put the formula SUM(P14,L11,H12,D20) into cell S13 for determining the terminalvalue.Other formulas, called rollback formulas, are in cells below and to the left of each node. Theseformulas are used to determine the optimal choice at each decision node.In cell B26, a formula displays 1, indicating that the first branch is the optimal choice. Thus, theinitial choice is to prepare the proposal. In cell J11, a formula displays 2, indicating that the
2114Chapter 166 Decision Trees Using TreePlanseecond branch (nnumbered 1, 2, and 3, from toop to bottom) iis the optimal cchoice. If awarrded thecoontract, DriveTTek should try the electronic method.mA subbsequent chapteer provides moore detailsabbout interpretattion.FormattingFthe Tree DiagramDThhe following stteps show howw to use TreePlan and Excel ffeatures to formmat the tree diaagram. Youmaym choose to useu other formaats for your owwn tree diagramms.13.From thhe Edit menu, choose Move oro Copy Sheet (or right-clickk the sheet tab aand chooseMove OrO Copy from the shortcut menu).mIn the lowwer left cornerr of the Move OOr Copydialog box,b check thee Create A Coppy box, and clicck OK.14.On sheeet Original (2), if the probabiilities are not leeft-aligned, sellect cell H9. PrressCtrl Shhift T. In the TreePlanTSelecct dialog box, vverify that the ooption button ffor Cellswith Prrobabilities is selected,sand cllick OK. With all probabilityy cells selected,, click theAlign LeftL button.Figure 16.24 TrreePlan Select Dialog Box15.Select cellc H12. Presss Ctrl Shift T. In the TreePllan Select dialoog box, verify tthat theoption button for Cellls with Partial Cash Flows is selected, and cclick OK. Withh all partialcash floow cells selected, if the cash flows are not lleft-aligned, cliick the Align LLeft button.With thhose cells still selected, choosse Home Forrmat Format Cells. In the FFormatCells dialogdbox, click the Number tab. In the Cattegory list box,, choose Currenncy; type 0(zero) forf Decimal Pllaces; select ini the Symbol llist box; selectt - 1,234 for NNegativeNumbeers. Click OK.
16.5 Step-by-SStep TreePlan TuTutorial215Figure 16.25 Exxcel Format Ceells Dialog Boxx16.Select cellc I12. Press Ctrl Shift T. In the TreePlaan Select dialogg box, verify thhat theoption button for Cellls with Rollbacck EVs/CEs is selected, and cclick OK. Withh allrollback cells selectedd, choose Formmat Cells. Reepeat the Curreency formattingg of step 16above.17.Select cellc S3. Press Ctrl Shift T.CInI the TreePlann Select dialogg box, verify thhat theoption button for Cellls with Terminnal Values is seelected, and cliick OK. With aall terminalvalue cellscselected, choosecFormat Cells. Repeaat the Currencyy formatting off step 16above.
216Chapter 16 Decision Trees Using TreePlanFigure 16.26 Complete DriveTek Decision 28293031323334B CDEF GHIJKLMN OPQRSUse mechanical method 80,000- 120,000 80,0000.5Electronic success 150,0000.5Awarded contract2 250,000Try electronic method 0- 50,0000.5Electronic failure 90,000 90,000 150,000 30,000- 120,000 30,0000.7Magnetic successPrepare proposal- 50,000 120,000Try magnetic method 0 120,000- 80,0000.3Magnetic failure 20,000 84,000 0- 120,00010.5Not awarded contract 20,00018. 0- 50,000 0- 50,000Don't prepare proposal 0 0 0Double-click the Original (2) sheet tab (or right-click the sheet tab and choose Renamefrom the shortcut menu), and enter Formatted. Save the workbook.Displaying Model InputsWhen you build a decision tree model, you may want to discuss the model and its assumptionswith co-workers or a client. For such communication it may be preferable to hide the results offormulas that show rollback values and decision node choices. The following steps show how todisplay only the model inputs.19.From the Edit menu, choose Move or Copy Sheet (or right-click the sheet tab and chooseMove Or Copy from the shortcut menu). In the lower left corner of the Move Or Copydialog box, check the Create A Copy box, and click OK.20.On sheet Formatted (2), select cell B1. Press Ctrl Shift T. In the TreePlan Select dialogbox, verify that the option button for Columns with Nodes is selected, and click OK.With all node columns selected, choose Format Cells Number or Home Format Format Cells Number. In the Category list box, select Custom. Select the entry in theType edit box, and type ;;; (three semicolons). Click OK.
16.5 Step-by-SStep TreePlan TuTutorial217Figure 16.27 Exxcel Format Ceells Dialog BoxxExplanation: A custom numbeer format has foour sections off format codes. The sections aareseeparated by semmicolons, and theytdefine thee formats for poositive numberrs, negative nummbers, zerovaalues, and text,, in that order. When you speecify three semmicolons withouut format codess, Exceldooes not displayy positive numbbers, negative numbers,nzero values, or textt. The formula remains inthhe cell, but its resultris not dissplayed. Later, if you want too display the reesult, you can cchange thefoormat without havinghto enterr the formula again. Editing aan existing formmat does not deelete it. Allfoormats are saveed with the worrkbook unless you explicitly delete a formaat.21.Select cellc A27. Presss Ctrl Shift T. In the TreePllan Select dialoog box, verify tthat theoption button for Cellls with Rollbacck EVs/CEs is selected, and cclick OK. Withh allrollback values selectted, choose Forrmat Cells Number or Hoome Format FormatCells Number. In thhe Category lisst box, select CCustom. Scroll to the bottom oof the Typelist boxx, and select the three-semicoolon entry. Clicck OK.22.Doublee-click the Formmatted (2) sheeet tab (or right--click the sheett tab and choosse Renamefrom thhe shortcut mennu), and enter ModelMInputs . Save the worrkbook.PrintingPthee Tree Diaggram23.In the NameNBox list box, select TreeeDiagram (or select cells A11:S34).24.To prinnt the tree diagrram from Exceel, with the treee diagram rangge selected, in EExcel 2007& 20100 & 2013 & 20016, choose Pagge Layout Prrint Area Sett Print Area. Thhen chooseOffice Button or File Print Preview Page Setuup. In the Page Setup dialog bbox, clickthe Pagge tab; for Orieentation click thhe option buttoon for Landscaape, and for Scaaling clickthe option button for Fit To 1 Page WideW By 1 Pagge Tall. Click tthe Header/Foooter tab; inthe Heaader list box seelect None, andd in the Footer list box select None (or selecct otherappropriate headers anda footers). Cllick the Sheet ttab; clear the ccheck box for GGridlines,
218Chapter 16 Decision Trees Using TreePlanand clear the check box for Row And Column Headings. Click OK. Choose File Printand click OK.25.To print the tree diagram from Word, clear the check boxes for Gridlines and for RowAnd Column Headings on Excel’s Page Setup dialog box Sheet tab. Select the treediagram range. In Excel 2007 & 2010 & 2013 & 2016, choose Home Paste AsPicture Copy as Picture. In the Copy Picture dialog box, click the option button AsShown When Printed, and click OK. In Word select the location where you want to pastethe tree diagram and choose Edit Paste.Figure 16.28 DriveTek Without Rollback ValuesUse mechanical method 80,000- 120,0000.5Electronic success 150,0000.5Awarded contractTry electronic method 0- 50,0000.5Electronic failure 250,000 30,000- 120,0000.7Magnetic successPrepare proposal 120,000Try magnetic method 0- 80,0000.3Magnetic failure- 50,000 0- 120,0000.5Not awarded contract- 50,000 0Don't prepare proposal 0 0Alternative ModelIf you want to emphasize that the time constraint forces DriveTek to use the mechanical approachif they try either
TreePlan is a decision tree add-in for Microsoft Excel 2007 & 2010 & 2013 & 2016 (Windows) and Microsoft Excel 2011 & 2016 (Macintosh). TreePlan helps you build a decision tree diagram in an Excel worksheet using dialog boxes. Decision trees are useful for analyzing sequential decision problems under uncertainty. Your
TM 9-6625-1753-14 C3 TECHNICAL MANUAL HEADQUARTERS DEPARTMENT OF THE ARMY No. 9-6625-1753-14 WASHINGTON, D. C., 4 April 1968 Operator, Organizational, DS, And GS
SPIETH Gymnastics GmbH In den Weiden 13 73776 Altbach el.: T 49 (0) 1753 / 503 28 - 00 Fax: 49 (0) 1753 / 503 28 - 11 . In a shopping center in Almaty a kids gym with a combination between standard SPIETH gymnastics apparatuses and SPIETH Gym&Fun equipment was created. That proves - space for sports is everywhere!
product, whether to bid on a new project) and uncontrollable uncertainties (e.g., possible demand . select a node to change the structure of your decision tree, (4) enter branch names, cash flows, and probabilities, and (5
1754 Matern Child Health J (2016) 20:1753–1758 123. . law enforcement, social services and health—around a Fig. 1 A framework for health equity Matern Child Health J (2016) 20:1753–1758 1755 . Land Use Work Group is advancing multiple effo
Perquimans County . Guardians’ Records, 1753-1948 (Archibald – Zimmerman) 29 Fibredex Boxes . C.R.077.510.5- C.R.077.510.33 . Perquimans County guardians’ have .
2015 John Crane Revised 10/15 www.johncrane.com TD-1648/2648/3648 North America United States of America Tel: 1-847-967-2400 Fax: 1-847-967-3915 Europe United Kingdom Tel: 44-1753-224000 Fax: 44-1753-224224 Latin America Brazil Tel: 55-11-3371-2500 Fax: 55-11-3371-2599 Middle East & Africa .
1. What is decision theory?.5 1.1 The decision disciplines 5 1.2 Decision processes 7 1.3 Decision matrices 11 1.4 Classification of decision theories 13 1.4.1 Normative and descriptive theories 14 1.4.2 Individual and collective decision-making 15 1.4.3 Degrees of knowledge 16 2.
Astrology People believed that astrology (the alignment of the stars and planets) also had an influence on disease. During diagnosis, physicians would consider star charts, when a patient was born, and when they fell ill. The Church traditionally disliked the use of astrology, but began to accept it more after the
