Example 2.11: Nonstandard Relationships

The CPM Procedure

Example 2.11: Nonstandard Relationships

This example shows the use of LAG variables to describe nonstandard relationships. Consider the project network in AON format. Output 2.11.1 shows the data set WIDGLAG, which contains the required project information; here the data set contains only one successor variable, requiring multiple observations for activities that have more than one immediate successor. In addition, the data set contains two new variables, lagdur and lagdurc, which are used to convey nonstandard relationships that exist between some of the activities. In the first part of the example, lagdur specifies a lag type and lag duration between activities; in the second part, the variable lagdurc specifies a lag calendar in addition to the lag type and lag duration. Note that when multiple successor variables are used, you can specify multiple lag variables and the lag values specified are matched one-for-one with the corresponding successor variables.

Output 2.11.1: Network Data

Non-Standard Relationships

Activity Data Set WIDGLAG

Obs	task	days	succ	lagdur	lagdurc
1	Approve Plan	5	Drawings
2	Approve Plan	5	Anal. Market
3	Approve Plan	5	Write Specs
4	Drawings	10	Prototype
5	Anal. Market	5	Mkt. Strat.
6	Write Specs	5	Prototype
7	Prototype	15	Materials	ss_9	ss_9
8	Prototype	15	Facility	ss_9	ss_9
9	Mkt. Strat.	10	Test Market
10	Mkt. Strat.	10	Marketing
11	Materials	10	Init. Prod.
12	Facility	10	Init. Prod.	fs_2	fs_2_SEVENDAY
13	Init. Prod.	10	Test Market
14	Init. Prod.	10	Marketing
15	Init. Prod.	10	Evaluate
16	Evaluate	10	Changes
17	Test Market	15	Changes
18	Changes	5	Production
19	Production	0
20	Marketing	0

Suppose that the project calendar follows a five-day work week. Recall from Example 2.6 that the project finishes on March 9, 1992. The data set, WIDGLAG, specifies that there is a `ss_9' lag between the activities `Prototype' and `Materials', which means that you can start acquiring raw materials nine days after the start of the activity `Prototype' instead of waiting until its finish time. Likewise, there is an `ss_9' lag between `Prototype' and `Facility'. The `fs_2' lag between `Facility' and `Init. Prod' indicates that you should wait two days after the completion of the `Facility' task before starting the initial production. To convey the lag information to PROC CPM, use the LAG= specification in the SUCCESSOR statement. The program and the resulting output (Output 2.11.2) follow:

   proc cpm data=widglag date='2dec91'd
            interval=weekday collapse out=lagsched;
      activity task;
      succ     succ / lag = (lagdur);
      duration days;
      run;

Output 2.11.2: Project Schedule: Default LAG Calendar

Non-Standard Relationships

Lag Type and Duration: Default LAG Calendar

task	E_START	E_FINISH	L_START	L_FINISH	T_FLOAT	F_FLOAT
Approve Plan	02DEC91	06DEC91	02DEC91	06DEC91	0	0
Drawings	09DEC91	20DEC91	09DEC91	20DEC91	0	0
Anal. Market	09DEC91	13DEC91	14JAN92	20JAN92	26	0
Write Specs	09DEC91	13DEC91	16DEC91	20DEC91	5	5
Prototype	23DEC91	10JAN92	23DEC91	10JAN92	0	0
Mkt. Strat.	16DEC91	27DEC91	21JAN92	03FEB92	26	26
Materials	03JAN92	16JAN92	07JAN92	20JAN92	2	2
Facility	03JAN92	16JAN92	03JAN92	16JAN92	0	0
Init. Prod.	21JAN92	03FEB92	21JAN92	03FEB92	0	0
Evaluate	04FEB92	17FEB92	11FEB92	24FEB92	5	5
Test Market	04FEB92	24FEB92	04FEB92	24FEB92	0	0
Changes	25FEB92	02MAR92	25FEB92	02MAR92	0	0
Production	03MAR92	03MAR92	03MAR92	03MAR92	0	0
Marketing	04FEB92	04FEB92	03MAR92	03MAR92	20	20

Note that due to the change in the type of precedence constraint, the project finishes earlier, on March 3, 1992, instead of on March 9, 1992 (compare with Output 2.6.1).

By default, all the lags are assumed to follow the default calendar for the project. In this case, the default project calendar has five workdays (since INTERVAL=WEEKDAY). Suppose now that the `fs_2' lag between `Facility' and `Init. Prod.' really indicates two calendar days and not two workdays. (Perhaps you want to allow two days for the paint to dry or the building to be ventilated.) The variable lagdurc in the WIDGLAG data set indicates the calendar for this lag by specifying the lag to be `fs_2_sevenday' where `sevenday' is the name of the seven-day calendar defined in the Calendar data set, CALENDAR, displayed in Output 2.11.3. PROC CPM is invoked with LAG=lagdurc and Output 2.11.4 displays the resulting schedule. Note that the project now finishes on March 2, 1992.

   proc cpm data=widglag date='2dec91'd calendar=calendar
            interval=weekday collapse out=lagsched;
      activity task;
      succ     succ / lag = (lagdurc);
      duration days;
      run;

Output 2.11.3: Calendar Data Set

Non-Standard Relationships

Calendar Data Set

Obs	_cal_	_sun_	_mon_	_tue_	_wed_	_thu_	_fri_	_sat_
1	SEVENDAY	workday	workday	workday	workday	workday	workday	workday

Output 2.11.4: Project Schedule: Lag Type, Duration, and Calendar

Non-Standard Relationships

Lag Type, Duration, and Calendar

task	E_START	E_FINISH	L_START	L_FINISH	T_FLOAT	F_FLOAT
Approve Plan	02DEC91	06DEC91	03DEC91	09DEC91	1	0
Drawings	09DEC91	20DEC91	10DEC91	23DEC91	1	0
Anal. Market	09DEC91	13DEC91	13JAN92	17JAN92	25	0
Write Specs	09DEC91	13DEC91	17DEC91	23DEC91	6	5
Prototype	23DEC91	10JAN92	24DEC91	13JAN92	1	0
Mkt. Strat.	16DEC91	27DEC91	20JAN92	31JAN92	25	25
Materials	03JAN92	16JAN92	06JAN92	17JAN92	1	1
Facility	03JAN92	16JAN92	06JAN92	17JAN92	1	1
Init. Prod.	20JAN92	31JAN92	20JAN92	31JAN92	0	0
Evaluate	03FEB92	14FEB92	10FEB92	21FEB92	5	5
Test Market	03FEB92	21FEB92	03FEB92	21FEB92	0	0
Changes	24FEB92	28FEB92	24FEB92	28FEB92	0	0
Production	02MAR92	02MAR92	02MAR92	02MAR92	0	0
Marketing	03FEB92	03FEB92	02MAR92	02MAR92	20	20

In fact, you can specify an alternate calendar for all the lag durations by using the ALAGCAL= or NLAGCAL= option in the SUCCESOR statement. The next invocation of the CPM procedure illustrates this feature by specifying ALAGCAL=SEVENDAY in the SUCCESSOR statement. Thus, all the lag durations now follow the seven-day calendar instead of the five-day calendar, which is the default calendar for this project. Output 2.11.5 shows the resulting schedule. Note that now the project finishes on February 28, 1992. Output 2.11.6 displays a precedence Gantt chart of the project. Note how the nonstandard precedence constraints are displayed.

   proc cpm data=widglag date='2dec91'd calendar=calendar
            interval=weekday collapse out=lagsched;
      activity task;
      succ     succ / lag = (lagdur) alagcal=sevenday;
      duration days;
      run;

   goptions hpos=100 vpos=60;
   title  c=black f=swiss h=2.5 'Non-Standard Relationships';
   title2 c=black f=swiss h=2   'Precedence Gantt Chart';
   title3 ' ';
   proc gantt graphics data=lagsched logic=widglag;
      chart / compress act=task succ=(succ) dur=days
              font=swiss 
              cprec=black cmile=blue
              caxis=black cfram=cyan
              height=1.5 skip=2 nojobnum
              dur=days increment=7 lag=(lagdur);
      id task;
      run;

Output 2.11.5: Project Schedule: LAG Calendar = SEVENDAY

Non-Standard Relationships

Lag Type and Duration: LAG Calendar = SEVENDAY

task	E_START	E_FINISH	L_START	L_FINISH	T_FLOAT	F_FLOAT
Approve Plan	02DEC91	06DEC91	02DEC91	06DEC91	0	0
Drawings	09DEC91	20DEC91	09DEC91	20DEC91	0	0
Anal. Market	09DEC91	13DEC91	10JAN92	16JAN92	24	0
Write Specs	09DEC91	13DEC91	16DEC91	20DEC91	5	5
Prototype	23DEC91	10JAN92	23DEC91	10JAN92	0	0
Mkt. Strat.	16DEC91	27DEC91	17JAN92	30JAN92	24	24
Materials	01JAN92	14JAN92	03JAN92	16JAN92	2	2
Facility	01JAN92	14JAN92	01JAN92	14JAN92	0	0
Init. Prod.	17JAN92	30JAN92	17JAN92	30JAN92	0	0
Evaluate	31JAN92	13FEB92	07FEB92	20FEB92	5	5
Test Market	31JAN92	20FEB92	31JAN92	20FEB92	0	0
Changes	21FEB92	27FEB92	21FEB92	27FEB92	0	0
Production	28FEB92	28FEB92	28FEB92	28FEB92	0	0
Marketing	31JAN92	31JAN92	28FEB92	28FEB92	20	20

Output 2.11.6: Precedence Gantt Chart

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