Example 2.2: Activity-on-Arc Representation

The CPM Procedure

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. Note that the network has an arc labeled `Dummy', which is required to capture accurately 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. Note that 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;
      input task $ 1-12 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;
      input task $ 1-12 dept $ 15-27 descrpt $ 30-59;
      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='2dec91'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;

Output 2.2.1: Critical Path: Activity-on-Arc Format

Widget Manufacture: Activity-On-Arc Format

Project Schedule

descrpt	dept	E_START	E_FINISH	L_START	L_FINISH	T_FLOAT	F_FLOAT
Finalize and Approve Plan	Planning	02DEC91	06DEC91	02DEC91	06DEC91	0	0
Prepare Drawings	Engineering	07DEC91	16DEC91	07DEC91	16DEC91	0	0
Analyze Potential Markets	Marketing	07DEC91	11DEC91	06JAN92	10JAN92	30	0
Write Specifications	Engineering	07DEC91	11DEC91	12DEC91	16DEC91	5	5
Develop Marketing Concept	Marketing	12DEC91	21DEC91	11JAN92	20JAN92	30	30
Build Prototype	Engineering	17DEC91	31DEC91	17DEC91	31DEC91	0	0
Procure Raw Materials	Manufacturing	01JAN92	10JAN92	01JAN92	10JAN92	0	0
Prepare Manufacturing Facility	Manufacturing	01JAN92	10JAN92	01JAN92	10JAN92	0	0
Initial Production Run	Manufacturing	11JAN92	20JAN92	11JAN92	20JAN92	0	0
Evaluate Product In-House	Testing	21JAN92	30JAN92	26JAN92	04FEB92	5	5
Mail Product to Sample Market	Testing	21JAN92	04FEB92	21JAN92	04FEB92	0	0
Begin Full Scale Marketing	Marketing	21JAN92	21JAN92	10FEB92	10FEB92	20	20
Production Milestone		21JAN92	21JAN92	21JAN92	21JAN92	0	0
Engineering Changes	Engineering	05FEB92	09FEB92	05FEB92	09FEB92	0	0
Begin Full Scale Production	Manufacturing	10FEB92	10FEB92	10FEB92	10FEB92	0	0

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