Example 2.19: Activity Splitting

The CPM Procedure

Example 2.19: Activity Splitting

This example illustrates the use of activity splitting to help reduce project duration. By default, PROC CPM assumes that an activity cannot be interrupted once it is started (except for holidays and weekends). During resource-constrained scheduling, it is possible for a noncritical activity to be scheduled first, and at a later time a critical activity may be held waiting for a resource to be freed by this less critical activity. In such situations, you way want to allow noncritical activities to be preempted by critical ones. PROC CPM enables you to specify, selectively, the activities that can be split into segments, the minimum length of each segment, and the maximum number of segments per activity.

The data set WIDGR19, displayed in Output 2.19.1, contains the widget network in AON format with two resources: prodman and hrdware. Suppose the production manager is required to oversee certain activities, as indicated by a `1' in the prodman column. hrdware denotes some piece of equipment that is required by the activity `Drawings' (perhaps a plotter to produce the engineering drawings). The variable minseg denotes the minimum length of the split segments for each activity. Missing values for this variable are set to default values (one-fifth of the activity's duration). The Resource data set WIDGRIN, displayed in Output 2.19.2, indicates that both resources are replenishable, there is one production manager available from December 2, and the hardware is unavailable on the 11th and 12th of December (perhaps it is scheduled for maintenance or has been reserved for some other project).

Output 2.19.1: Activity Splitting: Activity Data Set

Activity Splitting

Project Data

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

Output 2.19.2: Activity Splitting: Resource Availability Data Set

Activity Splitting

Resource Availability Data Set

Obs	per	otype	prodman	hrdware
1	.	restype	1	1
2	02DEC91	reslevel	1	1
3	11DEC91	reslevel	.	0
4	13DEC91	reslevel	.	1

The project is first scheduled without allowing any of the activities to be split. The Schedule data set SCHED, displayed in Output 2.19.3, indicates that the project has been delayed by one week (five working days, since maximum S_FINISH = `18MAR9'1 while maximum E_FINISH = `11MAR92'). Note that the activity `Drawings' has been postponed to start after the equipment has been serviced (or used by the other project), and the activity `Prototype' (which is actually a critical activity) cannot start on schedule because the production manager is tied up with the noncritical activity `Mkt. Strat.'.

   proc cpm date='02dec91'd
            data=widgr19 resin=widgrin
            holidata=holdata
            out=sched resout=rout
            interval=weekday collapse;
      activity task;
      duration days;
      successor succ;
      holiday hol;
      resource prodman hrdware / period=per obstype=otype
                                 t_float f_float rcs avl;
      run;

Output 2.19.3: Project Schedule: Splitting Not Allowed

Activity Splitting

Project Schedule: Splitting not Allowed

Obs	task	succ	days	prodman	hrdware	S_START	S_FINISH	E_START	E_FINISH	L_START	L_FINISH	T_FLOAT	F_FLOAT
1	Approve Plan	Drawings	5	1	.	02DEC91	06DEC91	02DEC91	06DEC91	02DEC91	06DEC91	0	0
2	Drawings	Prototype	10	.	1	13DEC91	27DEC91	09DEC91	20DEC91	09DEC91	20DEC91	0	0
3	Anal. Market	Mkt. Strat.	5	.	.	09DEC91	13DEC91	09DEC91	13DEC91	22JAN92	28JAN92	30	0
4	Write Specs	Prototype	5	.	.	09DEC91	13DEC91	09DEC91	13DEC91	16DEC91	20DEC91	5	5
5	Prototype	Materials	15	1	.	31DEC91	21JAN92	23DEC91	14JAN92	23DEC91	14JAN92	0	0
6	Mkt. Strat.	Test Market	10	1	.	16DEC91	30DEC91	16DEC91	30DEC91	29JAN92	11FEB92	30	30
7	Materials	Init. Prod.	10	.	.	22JAN92	04FEB92	15JAN92	28JAN92	15JAN92	28JAN92	0	0
8	Facility	Init. Prod.	10	.	.	22JAN92	04FEB92	15JAN92	28JAN92	15JAN92	28JAN92	0	0
9	Init. Prod.	Test Market	10	1	.	05FEB92	18FEB92	29JAN92	11FEB92	29JAN92	11FEB92	0	0
10	Evaluate	Changes	10	1	.	19FEB92	03MAR92	12FEB92	25FEB92	19FEB92	03MAR92	5	5
11	Test Market	Changes	15	.	.	19FEB92	10MAR92	12FEB92	03MAR92	12FEB92	03MAR92	0	0
12	Changes	Production	5	.	.	11MAR92	17MAR92	04MAR92	10MAR92	04MAR92	10MAR92	0	0
13	Production		0	1	.	18MAR92	18MAR92	11MAR92	11MAR92	11MAR92	11MAR92	0	0
14	Marketing		0	.	.	19FEB92	19FEB92	12FEB92	12FEB92	11MAR92	11MAR92	20	20

In the second invocation of PROC CPM, the MINSEGMTDUR= option is used in the RESOURCE statement to identify the variable minseg to the procedure. This allows the algorithm to split the `Drawings' activity so that some of it is done before December 11, 1991, and the rest is scheduled to start on December 13, 1991. Likewise, the production manager is allocated to the activity `Mkt. Strat.' on December 16, 1991. On the 26th of December the activity `Prototype' demands the production manager, and since preemption is allowed, the earlier activity `Mkt. Strat.', which is less critical than `Prototype', is temporarily halted and is resumed on the 17th of January after the completion of `Prototype' on the 16th of January. The Schedule data set, displayed in Output 2.19.4, contains separate observations for each segment of the split activities as indicated by the variable SEGMT_NO. Note that the project duration has been reduced by three working days, by allowing appropriate activities to be split.

   proc cpm date='02dec91'd
            data=widgr19
            holidata=holdata resin=widgrin
            out=spltschd resout=spltrout
            interval=weekday collapse;
      activity task;
      duration days;
      successor succ;
      holiday hol;
      resource prodman hrdware / period=per obstype=otype
                                 minsegmtdur=minseg
                                 rcs avl;
      id task;
      run;

Output 2.19.4: Project Schedule: Splitting Allowed

Activity Splitting

Project Schedule: Splitting Allowed

Obs	task	succ	SEGMT_NO	days	prodman	hrdware	S_START	S_FINISH	E_START	E_FINISH	L_START	L_FINISH
1	Approve Plan	Drawings	.	5	1	.	02DEC91	06DEC91	02DEC91	06DEC91	02DEC91	06DEC91
2	Drawings	Prototype	.	10	.	1	09DEC91	24DEC91	09DEC91	20DEC91	09DEC91	20DEC91
3	Drawings	Prototype	1	2	.	1	09DEC91	10DEC91	09DEC91	20DEC91	09DEC91	20DEC91
4	Drawings	Prototype	2	8	.	1	13DEC91	24DEC91	09DEC91	20DEC91	09DEC91	20DEC91
5	Anal. Market	Mkt. Strat.	.	5	.	.	09DEC91	13DEC91	09DEC91	13DEC91	22JAN92	28JAN92
6	Write Specs	Prototype	.	5	.	.	09DEC91	13DEC91	09DEC91	13DEC91	16DEC91	20DEC91
7	Prototype	Materials	.	15	1	.	26DEC91	16JAN92	23DEC91	14JAN92	23DEC91	14JAN92
8	Mkt. Strat.	Test Market	.	10	1	.	16DEC91	21JAN92	16DEC91	30DEC91	29JAN92	11FEB92
9	Mkt. Strat.	Test Market	1	7	1	.	16DEC91	24DEC91	16DEC91	30DEC91	29JAN92	11FEB92
10	Mkt. Strat.	Test Market	2	3	1	.	17JAN92	21JAN92	16DEC91	30DEC91	29JAN92	11FEB92
11	Materials	Init. Prod.	.	10	.	.	17JAN92	30JAN92	15JAN92	28JAN92	15JAN92	28JAN92
12	Facility	Init. Prod.	.	10	.	.	17JAN92	30JAN92	15JAN92	28JAN92	15JAN92	28JAN92
13	Init. Prod.	Test Market	.	10	1	.	31JAN92	13FEB92	29JAN92	11FEB92	29JAN92	11FEB92
14	Evaluate	Changes	.	10	1	.	14FEB92	27FEB92	12FEB92	25FEB92	19FEB92	03MAR92
15	Test Market	Changes	.	15	.	.	14FEB92	05MAR92	12FEB92	03MAR92	12FEB92	03MAR92
16	Changes	Production	.	5	.	.	06MAR92	12MAR92	04MAR92	10MAR92	04MAR92	10MAR92
17	Production		.	0	1	.	13MAR92	13MAR92	11MAR92	11MAR92	11MAR92	11MAR92
18	Marketing		.	0	.	.	14FEB92	14FEB92	12FEB92	12FEB92	11MAR92	11MAR92

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