1. Network Planning

A telephone network is given with specified flows between each pair of nodes. The problem is to efficiently cover the network by a set of rings with specific properties, so that all flows are transferred through the rings without exceeding their capacities. Criteria for efficiency are: equipment cost and flexibility, namely the maximal ratio of the flow in a ring and its capacity. A planning tool was constructed which allows the user to define and edit a network with its pertinent data and obtain efficient sets of rings and optimal sets of paths and flows.

#### 2. Edge Detection of body parts

The problem consists in detecting a segment of a border of a part.  In some cases it is a difficult problem due to light effects.  The suggested algorithm first searches for (within a pre-specified region of interests) an initial point belonging to the considered edge and then proceeds along the margin.  The algorithm finds the next point maximizing the suggested threshold criterion within the square with the center at the previous found point.  To retain the found points near the border the algorithm adaptively determines upper bounds of gray level in the considered rectangles. Another algorithm based on a special gradient procedure was used for exact detect of the edges.  The algorithm uses very small sliding window and provides for sub-pixellian accuracy of edge detection in the case of a clear edge. The sub-pixellian detector is based on very specific technique originating from the control theory and real-time robust differentiators.

The Israeli railroads company needs a planning tool to schedule the transportation of empty freight cars so as to enable the daily realization of freight transportation plans. Three problems have been investigated: (1) an algorithm to select which transportation orders to satisfy from among the incoming stream considering the expected revenue and some administrative constraints; (2) application of the transportation problem with restrictions to determine the number of cars to be transported from points where they are found in the evening to points where they are needed next morning; (3) a combination of optimization and heuristic methods to plan the transportation by existing trains. An appropriate scheme for data collection and instruction distribution has been designed.

4. Image Understanding

An image of an area is given, and it is required to define the locations of the area and of the photographing camera within some pre-defined scene, as well as the camera parameters. The method of solution is as follows: details of the scene are extracted from a sequence of its images and fed into a database. The recognition system tries to identify the details in the image and to obtain equations comprising parameters of the camera and of the found details. The solution of the equations provides the required data. The problem is generalized for sequences of images.

5. Defect recognition on cutting tool surface

The problem is to recognize surface defects of a cutting tool in order to perform an automatic selection of damaged tools.  The known methods of pattern recognition do not solve the problem because they find numerous objects not being defects.  A new algorithm was suggested taking into account the specific essential features of the considered defects.  The suggested algorithm is applicable for various types of cutting tools (including carbide inserts) and many examples confirm it.

It is necessary to emphasize that all gradient-based ideas do not work here, for the gradients at the points of the defect boundary are much smaller than at the points of most other “natural” edges.  Contour tracing algorithms cannot be applied as well, for they find domains that are more color-saturated than the considered defects.

6.  Fault Management System

The Fault Management System receives signals about faults found in the managed network. These alarm signals are analyzed in order to pinpoint the fault that has caused the alarm and the eliminate it. Since the flow of signals can contain hundreds and even thousands  of practically simultaneous events, advanced methods    of analysis are required to decode the signals and in particular to reveal correlation among them. The purpose of establishing the correlation is to concentrate on the leading, determinant events, but not on their corollaries, and thereby identify the most probable root causes of the faults even in caseswhen no signal is received directly from the root of the problem.  The decision on the Alarm Correlation Problem  is based on the search for such propagation of faults and alarms which will most probably result in a pattern   of alarms identical or close to that which was actually received at the given moment of time.

7. optimAL tank farms for a pipeline

The Eilat-Ashqelon pipeline serves to transport crude oil on land from the port of Eilat to the Ashqelon terminal, thereby overcoming the difficulties caused by the inability of large tankers to use the Suez Canal. The pipeline system handles many types of  fuel and is subject to constraints on allowed mixing procedures. As the arrival times of tankers at the terminals exhibit considerable uncertainty, tank farms are needed at both ends of the pipeline to provide temporary storage. The volume needed for storage fluctuates quite significantly due to variations in arrival times and also weather conditions which eventually disturb loading and unloading of oil. It is also expected that the need for storage would increase as the expected annual flow increases. Since the construction of new storage facilities is extremely expensive, a thorough analysis of the system was needed to determine the optimal policy as to when and where new tanks should be constructed.

In the course of the work on this subject a measure of performance for the system had to be selected, and after analyzing the operational features it was taken to be the average length of the queue of tankers that might form at both terminals. The length of the queue directly affects the total expenses on the operation of the entire system. The queue length is affected by a diversity of factors some of which are uncontrollable, such as conditions at sea, and some that result from human decisions, such as the order in which different types of oil are pumped through the pipeline. Planning and designing the infrastructure of the system depends significantly on its highly random operational behavior.

The tool constructed to attack this problem not only reveals undesirable developments resulting from inadequacies of the tank farms, but also produces recommendations as to where and when additional tanks are expedient for different annual flow rates. The tool also permits to ascertain the measure in which the entire quality of operations is affected by various decisions, therefore it can be used for improving the operational policy. The tool is realized in friendly and convenient  software.

8. Planning device for Wafer Fabrication

The problem may be described as follows. N (~4000) lots are given and each lot kÎN has its own sequence of technological stages Sk={sk1, …, skm}, where m (~300) is the number of stages for the individual lot k. Stage skl can be processed on the determined set of machines P(skl), and on machine jÎ P(skl) the processing time is tj(skl). Each lot k is to be completed before the due date dk.

We need to obtain a work plan, that is, for each lot to determine the machine for stage skl and the time for the beginning of this stage. The plan is more detailed for the next shift and less detailed for several subsequent shifts. The quality of the plan is estimated by several optimization criteria.