IBM ILOG Scheduler User's Manual > Advanced Concepts > Scheduling with Unary Resources: the Bridge Problem > Describing the Problem

The problem is to schedule the construction of a five-segment bridge. To our knowledge, this problem was first published in Germany in a Ph.D. thesis at the University of Passau, and it is very commonly used as a benchmark in the constraint programming community. In this chapter, we offer a simple, efficient program for solving the problem.

The bridge is made of five segments. Five preformed bearers (or horizontal beams) must be placed on top of six vertical pillars: one bearer between any two successive pillars. In the notation generally used for this problem, the activity which consists of putting bearer number k on top of pillars number k and k+1 is denoted Tk, and we'll follow the same convention, respecting the usual naming conventions in this widely used benchmark.

Constructing each pillar means that four activities must be completed: excavation (denoted Ak for pillar number k), formwork (Sk), concrete foundation (Bk), and masonry (Mk). In addition:

The following table lists the activities to be scheduled, the duration in days for each, and the unary resource to be used (if any is necessary).

Name  
Activity Description  
Duration  
Resource  
A1  
Excavation  
4  
Excavator 
A2  
Excavation  
2  
Excavator 
A3  
Excavation  
2  
Excavator 
A4  
Excavation  
2  
Excavator  
A5  
Excavation  
2  
Excavator 
A6  
Excavation  
5  
Excavator 
P1  
Foundation piles  
20  
Pile driver 
P2  
Foundation piles  
13  
Pile driver 
S1  
Formwork  
8  
Carpentry 
S2  
Formwork  
4  
Carpentry 
S3  
Formwork  
4  
Carpentry 
S4  
Formwork  
4  
Carpentry 
S5  
Formwork  
4  
Carpentry 
S6  
Formwork  
10  
Carpentry 
B1  
Concrete foundation  
1  
Concrete mixer 
B2  
Concrete foundation  
1  
Concrete mixer 
B3  
Concrete foundation  
1  
Concrete mixer 
B4  
Concrete foundation  
1  
Concrete mixer 
B5  
Concrete foundation  
1  
Concrete mixer 
B6  
Concrete foundation  
1  
Concrete mixer 
AB1  
Concrete setting time  
1  

 
AB2  
Concrete setting time  
1  

 
AB3  
Concrete setting time  
1  

 
AB4  
Concrete setting time  
1  

 
AB5  
Concrete setting time  
1  

 
AB6  
Concrete setting time  
1  

 
M1  
Masonry work  
16  
Bricklaying 
M2  
Masonry work  
8  
Bricklaying 
M3  
Masonry work  
8  
Bricklaying 
M4  
Masonry work  
8  
Bricklaying 
M5  
Masonry work  
8  
Bricklaying 
M6  
Masonry work  
20  
Bricklaying 
T1  
Positioning  
12  
Crane 
T2  
Positioning  
12  
Crane 
T3  
Positioning  
12  
Crane 
T4  
Positioning  
12  
Crane  
T5  
Positioning  
12  
Crane 
V1  
Filling  
15  
Caterpillar 
V2  
Filling  
10  
Caterpillar 
L  
Delivery of the preformed bearers  
2  

 
UE  
Erection of the temporary housing  
10  

 
UA  
Removal of the temporary housing  
10  

 
PE  
End of project  
0