The CPM Procedure

Example 4.2 Activity-on-Arc Representation

Output 4.2.1: Network Showing Task Relationships in Activity-on-Arc Format

Network Showing Task Relationships in Activity-on-Arc Format

The problem discussed in Example 4.1 can also be described in an AOA format. The network is illustrated in Output 4.2.1. 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 4.1, 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 4.2.2 displays the project schedule.

/* Activity-on-Arc representation of the project */
data widgaoa;
   format task $12. ;
   input task & days tail head;
Approve Plan   5   1   2
Drawings      10   2   3
Study 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";
Approve Plan  Planning       Finalize and Approve Plan
Drawings      Engineering    Prepare Drawings
Study 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;

/* 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;

proc sort;
   by e_start;

title 'Widget Manufacture: Activity-On-Arc Format';
title2 'Project Schedule';
proc print;
   id descrpt;
   var dept e_: l_: t_float f_float;

Output 4.2.2: Critical Path: Activity-on-Arc Format

Widget Manufacture: Activity-On-Arc Format
Project Schedule

Finalize and Approve Plan Planning 01DEC03 05DEC03 01DEC03 05DEC03 0 0
Prepare Drawings Engineering 06DEC03 15DEC03 06DEC03 15DEC03 0 0
Analyze Potential Markets Marketing 06DEC03 10DEC03 05JAN04 09JAN04 30 0
Write Specifications Engineering 06DEC03 10DEC03 11DEC03 15DEC03 5 5
Develop Marketing Concept Marketing 11DEC03 20DEC03 10JAN04 19JAN04 30 30
Build Prototype Engineering 16DEC03 30DEC03 16DEC03 30DEC03 0 0
Procure Raw Materials Manufacturing 31DEC03 09JAN04 31DEC03 09JAN04 0 0
Prepare Manufacturing Facility Manufacturing 31DEC03 09JAN04 31DEC03 09JAN04 0 0
Initial Production Run Manufacturing 10JAN04 19JAN04 10JAN04 19JAN04 0 0
Evaluate Product In-House Testing 20JAN04 29JAN04 25JAN04 03FEB04 5 5
Mail Product to Sample Market Testing 20JAN04 03FEB04 20JAN04 03FEB04 0 0
Begin Full Scale Marketing Marketing 20JAN04 20JAN04 09FEB04 09FEB04 20 20
Production Milestone   20JAN04 20JAN04 20JAN04 20JAN04 0 0
Engineering Changes Engineering 04FEB04 08FEB04 04FEB04 08FEB04 0 0
Begin Full Scale Production Manufacturing 09FEB04 09FEB04 09FEB04 09FEB04 0 0