The CLP Procedure

This example illustrates the use of the cumulative constraint to solve a resource-constrained project scheduling problem that has nonstandard temporal constraints.

For more information about this example, see the same example in SAS/OR User's Guide: Constraint Programming, which illustrates the capabilities of the scheduling solver.

Output 4.10.1: The Bridge Problem

The project consists of 44 tasks and a set of constraints that relate these tasks. Table 11 displays the activity information, standard precedence constraints, and resource constraints. The sharing of a unary resource by multiple activities results in the resource constraints being disjunctive in nature.

The following constraints are added to the standard precedence constraints:

For convenience, the activity name is used to represent the start time variable of the activity. Each temporal constraint is represented by a linear constraint in the Constraint data table. An additional observation is added to the Constraint data table to define the objective of minimizing the makespan, which in this case is the milestone , indicating the end of the project. The CLP procedure is invoked with the WDEG variable selection strategy along with seven cumulative constraints, one corresponding to each of the resources: Excavator, Pile Driver, Carpentry, Concrete Mixer, Bricklaying, Crane, and Caterpillar.

proc clp condata=mylib.condata varselect=wdeg out=mylib.out usecondatavars=1;
   obj lb=0 ub=2000;
   cumulative (start=( m1-m6 ) dur=( 16 8 8 8 8 20 ))
              (start=( s1-s6 ) dur=( 8 4 4 4 4 10 ))
              (start=( v1 v2 ) dur=( 15 10 ))
              (start=( b1-b6 ) dur=( 1 1 1 1 1 1))
              (start=( l t1-t5 ) dur=( 2 12 12 12 12 12 ))
              (start=( a1-a6 ) dur=( 4 2 2 2 2 5))
              (start=( p1 p2 ) dur=( 20 13 ));
run;

The solution summary shown in Output 4.10.2 reports an optimal objective value of 104 days.

The solution data table shown in Output 4.10.3 displays the corresponding start times for all the tasks.

A Gantt chart of the resulting schedule, zoned by resource, is shown in Output 4.10.4.

Output 4.10.4: Bridge Construction Schedule