| IBM ILOG Scheduler User's Manual > Advanced Concepts > Scheduling with Unary Resources: the Bridge Problem > Describing the Problem |
Describing the Problem |
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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:
P1 and P2 must occur between the excavations of the central pillars A3 and A4 and the corresponding formwork S3 and S4.
ABk, is required between the concrete foundation Bk and the corresponding masonry work Mk.
Sk precedes Bk, Bk precedes ABk, ABk precedes Mk, and both Mk and M(k+1) precede Tk.
Sk and the completion of the corresponding concrete foundation Bk is at most 4 days.
L) occurs exactly 30 days after the beginning of the construction project; it lasts two days. Positioning activities Tk cannot start before the end of the delivery activity L.
V1 and V2 are required so that the bridge can be properly connected to the road.
UE) and later disassembling (an activity denoted UA) temporary housing.
UA can start at most two days before the end of the last masonry work Mk.
PE, is an activity of null duration, which "executes" when the positioning activities Tk, the filling activities Vk, and the disassembling activity UA are completed.
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).
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