Timo Leipälä

Optimization of the movements of a component placement machine

Abstract The efficient operation of an automatic electronic component placement machine ( Panasert RH) is considered. The machine inserts electronic components into predefined places on a printed circuit board. The components are supplied from a set of feeders each containing a sequence of identical components. We treat the problem as two different sequencing problems. The optimal insertion sequence for a fixed feeder setting is obtained by considering the problem as a three-dimensional asymmetric traveling salesman problem. The optimal permutation of the components in the feeders for a fixed insertion sequence can be formulated as a quadratic assignment problem. The overall problem is solved heuristically and this approach brings suboptimal, but in practice good enough component insertion sequences and feeder permutations.

On the solutions of stochastic traveling salesman problems

Abstract We consider the n-city traveling salesman problem where the distances between the cities are nondeterministic. Our purpose is to estimate the expectation of the length of the optimal tour. This is done by calculating the expectations of a lower bound and an upper bound for the length of the optimal tour. Because the upper bound is formed by the well-known nearest neighbour rule, we can simultaneously find the cases where this rule is effective in the mean. If we let the number of cities grow, we obtain symptotic results that are totally determined by the behaviour of the distribution of the distance between any two points in the neighbourhood of the distance zero.

Job grouping in surface mounted component printing

Abstract The arrangement of operations in a production line for mounting the surface components on a printed circuit board is discussed. The production program includes a wide range of different products, which causes frequent set-up operations. The overall efficiency of the production line depends heavily on how the printing operations are organized. Set-ups cause delays which can be cut down by selecting carefully the feeders for the components and by solving a suitable sequence for the products. We describe an integrated production management system for job grouping. The system utilizes approximate algorithms for minimizing the number of component switching instants. A discussion of the exact minimization by using mathematical 0/1 integer programming approach is also given. The revision of the production management system has had a major impact on the productivity, and an increase of ca. 58% in the number of component insertions per hour is observed.

Determining the Proper Number and Price of Software Licenses

Software houses sell their products by transferring usage licenses of various software components to the customers. Depending on the kind of software, there are several different license types that allow controlled access of services. The two most popular types are the fixed license, which gives access rights for an identified workstation, and the floating license, which restricts the number of simultaneous users to a certain bound. The latter of these types is advantageous when the users do not demand full-time services and occasional lack of access is bearable. The problem of deciding the number of floating licenses is studied in the present paper. Based on the expected usage profile of the software, we calculate the minimal number of licenses that guarantees that the customers get service better than a given lower bound. The problem is studied by using certain queuing models, known as the Erlang toss system, the Erlang delay system, and the Engset model. None of these analytic models consider, however, the transient period that we analyze by means of simulation and by the so-called modified offered load approximation. We also give simple formulas presenting how the number of software licenses needed to keep the probability of nonaccess below a given blocking level grows as a function of the offered load, which is the proportion of the time used in the case that all requests were successful. Results of the study may be used for setting license prices and for determining the proper number of licenses.

ON-LINE PACKING WITH BOXES OF DIFFERENT SIZES

The packing of boxes distributed to different customers from a central depot is under consideration in this study. The boxes are of various sizes and they arrive on a conveyor belt one at a time. The on-line situation is assumed, which means that at each stage we only know the layout of the previous boxes on the partially filled pallet and the size of the box to be placed next but we have no information about the forthcoming ones. Further it is not allowed to move boxes already placed. The objective is to produce efficient and stable loads by an on-line packing algorithm, which can be implemented in automated systems. The algorithms we develop are based on the well-known first-fit and best-fit principles and their efficiency has been tested empirically.

Determining the manual setting order of components on PC boards

Abstract The task of designing efficient and easy-to-learn sequencing for manual installation of electrical components on a printed circuit board is studied at a computer monitor manufacturer. Advantageous sequences can be characterized by several nonstrict rules: use both hands equally in the insertion, proceed from top to bottom and from the edges to the center, take the closest next part, and so on. Three different ordering methods are discussed: line sweeping, traveling salesman clustering, and weighted 3-matching. Line sweeping gives a very different layout from those of traveling salesman clustering and weighted 3-matching.

On optimal multilevel indexed sequential files

We study here the optimal design of static multilevel indexed sequential files and analyse the expected comparison costs. There are one or more indices, at one or more levels, containing a variable number of fields each consisting of the address of a lower-level index or of a record. The records are arranged in ascending order by key value. The highest-level index is a one-way list which is searched sequentially until the proper range of keys is found, then a search of that portion called block of the next level index is performed. Finally we o%ain a block of records containing the target key and this is searched sequentially until the target key is matched, see for example [ 1) or (51. We assume that the number of index levels is k and the cost of searching a single field of the index at level i is Ci, while the cost of searching a single record field is G. In the following the original file is thus consider-ed to be index level zero. We further assume that the probability of request for each record of the file is equrl and that the size of the file is n records. Table I The search cost i + 3j of the jth record of block i. Optimal fried length blocks in the case n = 12 are clenoted by ard optimal variable block lengths by -

Divide and conquer for the closest-pair problem revisited

In this paper the divide-and-conquer approach to the two-dimensional closest-pair problem is studied. A new algorithm is proposed by which a closest pair, i.e. a pair of points whose distance δ is smallest among a set of N points, is found in θ(N) expected time when the points are drawn independently from the uniform distribution in a unit square. The worst-case running time of the algorithm is θ(N log2 N). The method is to project the points onto one of the coordinate axes, and to compute an initial guess for the smallest distance δ by considering the [N/2] pairs of successive projected points. The shortest of these pairwise distances is a good approximation for the final δ. It is then used in the subsequent merge phases of the divide-and-conquer algorithm to keep the average work minimal. A modification of the basic algorithm guarantees θ(N) performance in the average case and θ(N log N) performance in the worst case.