The CPM Procedure

Example 4.12 Activity Time Constraints

Often, in addition to a project start date or a project finish date, there may be other time constraints imposed selectively on the activities in the project. The ALIGNDATE and ALIGNTYPE statements enable you to add various types of time constraints on the activities. In this example, the data set WIDGET12 displayed in Output 4.12.1 contains two variables, adate and atype, which enable you to specify these restrictions. For example, the activity 'Drawings' has an 'feq' (Finish Equals) constraint, requiring it to finish on the 15th of December. The activity 'Test Market' has a mandatory start date imposed on it.

Output 4.12.1: Activity Data Set WIDGET12

Activity Time Constraints

Activity data set

Obs	task	days	succ1	succ2	succ3	adate	atype
1	Approve Plan	5	Drawings	Study Market	Write Specs	.
2	Drawings	10	Prototype			15DEC03	feq
3	Study Market	5	Mkt. Strat.			.
4	Write Specs	5	Prototype			15DEC03	sge
5	Prototype	15	Materials	Facility		.
6	Mkt. Strat.	10	Test Market	Marketing		.
7	Materials	10	Init. Prod.			.
8	Facility	10	Init. Prod.			.
9	Init. Prod.	10	Test Market	Marketing	Evaluate	.
10	Evaluate	10	Changes			27FEB04	fle
11	Test Market	15	Changes			16FEB04	ms
12	Changes	5	Production			.
13	Production	0				.
14	Marketing	0				.

The following statements are needed to schedule the project subject to these restrictions. The option XFERVARS in the PROC CPM statement causes CPM to transfer all variables that were used in the analysis to the Schedule data set. Output 4.12.2 shows the resulting schedule.

proc cpm data=widget12 date='1dec03'd
     xfervars interval=weekday;
   activity task;
   successor succ1 succ2 succ3;
   duration days;
   aligndate adate;
   aligntype atype;
   run;


title 'Activity Time Constraints';
title2 'Aligned Schedule';
proc print;
   id task;
   var adate atype e_: l_: t_float f_float;
   run;

Output 4.12.2: Aligned Schedule

Activity Time Constraints

Aligned Schedule

task	adate	atype	E_START	E_FINISH	L_START	L_FINISH	T_FLOAT	F_FLOAT
Approve Plan	.		01DEC03	05DEC03	25NOV03	01DEC03	-4	-4
Drawings	15DEC03	feq	08DEC03	19DEC03	02DEC03	15DEC03	-4	-4
Study Market	.		08DEC03	12DEC03	26JAN04	30JAN04	35	0
Write Specs	15DEC03	sge	15DEC03	19DEC03	22DEC03	26DEC03	5	0
Prototype	.		22DEC03	09JAN04	29DEC03	16JAN04	5	0
Mkt. Strat.	.		15DEC03	26DEC03	02FEB04	13FEB04	35	30
Materials	.		12JAN04	23JAN04	19JAN04	30JAN04	5	0
Facility	.		12JAN04	23JAN04	19JAN04	30JAN04	5	0
Init. Prod.	.		26JAN04	06FEB04	02FEB04	13FEB04	5	0
Evaluate	27FEB04	fle	09FEB04	20FEB04	16FEB04	27FEB04	5	5
Test Market	16FEB04	ms	16FEB04	05MAR04	16FEB04	05MAR04	0	0
Changes	.		08MAR04	12MAR04	08MAR04	12MAR04	0	0
Production	.		15MAR04	15MAR04	15MAR04	15MAR04	0	0
Marketing	.		09FEB04	09FEB04	15MAR04	15MAR04	25	25

Note that the MS and MF constraints are mandatory and override any precedence constraints; thus, both the late start and early start times for the activity 'Test Market' coincide with February 16, 2004. However, the other types of constraints are not mandatory; they are superseded by any constraints imposed by the precedence relationships. In other words, neither the early start nor the late start schedule violate precedence constraints. Thus, even though the activity 'Drawings' is required to finish on the 15th of December (by the 'feq' constraint), the early start schedule causes it to finish on the 19th of December because of its predecessor’s schedule. This type of inconsistency is indicated by the presence of negative floats for some of the activities alerting you to the fact that if some of these deadlines are to be met, these activities must start earlier than the early start schedule. Such activities are called supercritical.