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Example 2.2: Activity-on-Arc Representation

Figure 2.7: Network Showing Task Relationships in Activity-on-Arc Format

The problem discussed in Example 2.1 can also be described in an AOA format. The network is illustrated in Figure 2.7. The network has an arc labeled 'Dummy', which is required to accurately capture all the precedence relationships. Dummy arcs are often needed when representing scheduling problems in AOA format.

The following DATA step saves the network description in a SAS data set, WIDGAOA. The data set contains the minimum amount of information required by PROC CPM for an activity network in AOA format, namely, the TAILNODE and HEADNODE variables, which indicate the direction of each arc in the network and the DURATION variable which gives the length of each task. In addition, the data set also contains a variable identifying the name of the task associated with each arc. This variable, task, can be identified to PROC CPM using the ACTIVITY statement. PROC CPM treats each observation in the data set as a new task, thus enabling you to specify multiple arcs between a pair of nodes. In this example, for instance, both the tasks 'Drawings' and 'Write Specs' connect the nodes 2 and 3; likewise, both the tasks 'Materials' and 'Facility' connect the nodes 5 and 7. If multiple arcs are not allowed, you would need more dummy arcs in this example. However, the dummy arc between nodes 8 and 6 is essential to the structure of the network and cannot be eliminated.

As in Example 2.1, the data set DETAILS containing additional activity information, can be merged with the Activity data set and used as input to PROC CPM to determine the project schedule. For purposes of display (in Gantt charts, and so on) the dummy activity has been given a label, 'Production Milestone'. Output 2.2.1 displays the project schedule.

  
  /* Activity-on-Arc representation of the project */ 
    data widgaoa; 
       format task $12. ; 
       input task & days tail head; 
       datalines; 
    Approve Plan   5   1   2 
    Drawings      10   2   3 
    Anal. Market   5   2   4 
    Write Specs    5   2   3 
    Prototype     15   3   5 
    Mkt. Strat.   10   4   6 
    Materials     10   5   7 
    Facility      10   5   7 
    Init. Prod.   10   7   8 
    Evaluate      10   8   9 
    Test Market   15   6   9 
    Changes        5   9  10 
    Production     0  10  11 
    Marketing      0   6  12 
    Dummy          0   8   6 
    ;
 

  
    data details; 
       format task $12. dept $13. descrpt $30.; 
       input task & dept $ descrpt & ; 
       label dept = "Department" 
             descrpt = "Activity Description"; 
       datalines; 
    Approve Plan  Planning       Finalize and Approve Plan 
    Drawings      Engineering    Prepare Drawings 
    Anal. Market  Marketing      Analyze Potential Markets 
    Write Specs   Engineering    Write Specifications 
    Prototype     Engineering    Build Prototype 
    Mkt. Strat.   Marketing      Develop Marketing Concept 
    Materials     Manufacturing  Procure Raw Materials 
    Facility      Manufacturing  Prepare Manufacturing Facility 
    Init. Prod.   Manufacturing  Initial Production Run 
    Evaluate      Testing        Evaluate Product In-House 
    Test Market   Testing        Mail Product to Sample Market 
    Changes       Engineering    Engineering Changes 
    Production    Manufacturing  Begin Full Scale Production 
    Marketing     Marketing      Begin Full Scale Marketing 
    Dummy         .              Production Milestone 
    ; 
  
    data widgeta; 
       merge widgaoa details; 
       run; 
  
    /* The project is scheduled using PROC CPM */ 
    /* The network information is conveyed using the TAILNODE */ 
    /* and HEADNODE statements. The ID statement is used to   */ 
    /* transfer project information to the output data set    */ 
    proc cpm data=widgeta date='1dec03'd out=save; 
       tailnode tail; 
       headnode head; 
       duration days; 
       activity task; 
       id dept descrpt; 
       run; 
  
    proc sort; 
       by e_start; 
       run; 
  
    options ls=90; 
  
    title 'Widget Manufacture: Activity-On-Arc Format'; 
    title2 'Project Schedule'; 
    proc print; 
       id descrpt; 
       var dept e_: l_: t_float f_float; 
       run;