The Component retrieval problem in printed circuit board assembly

The minimization of the makespan of a printed circuit board assembly process is a complex problem. Decisions involved in this problem concern the specification of the order in which components are to be placed on the board, and the assignment of component types to the feeder slots of the placement machine. If some component types are assigned to multiple feeder slots, then the additional problem emerges of selecting, for each placement on the board, the feeder slot from which the related component type is to be retrieved. In this paper, we consider this Component Retrieval Problem for placement machines that operate in a similar way as the Fuji CP II. We explain why a simple forward dynamic programming scheme cannot provide an efficient solution to this problem, thereby invalidating the correctness of an earlier published approach. We then present a polynomial algorithm that solves the problem to optimality. The analysis of the Component Retrieval Problem is greatly facilitated by its reformulation as a longest path problem in a PERT/CPM network with design aspects; Finding the minimal makespan of the assembly process thus amounts to identifying a design for which the longest path in the induced network is shortest. As an alternative interpretation, the Component Retrieval Problem can be viewed as a shortest path problem with side-constraints. The complexity of these network problems is analysed, and it is proven that the polynomial solvability of the Component Retrieval Problem is caused by the speci c structure it in icts on the arc lengths in the network. In the absence of this structure, the network problems are shown to be NP-hard in general.operations research and management science;

The assembly of printed circuit boards : a case with multiple machines and multiple board types

In this paper a typical situation arising in the assembly of printed circuit boards is investigated. The planning problem we face is how to assemble boards of different types using a single line of placement machines. From a practical viewpoint, the multiplicity of board types adds significantly to the complexity of the problem, which is already very hard to solve in the case of a single board type. In addition, relatively few studies deal with the multiple board type case. We propose a solution procedure based on a hierarchical decomposition of the planning problem. An important subproblem in this decomposition is the so-called feeder rack assignment problem. By taking into account as much as possible the individual board type characteristics (as well as the machine characteristics) we heuristically solve this problem. The remaining subproblems are solved using constructive heuristics and local search methods. The solution procedure is tested on real-life instances. It turns out that, in terms of the makespan, we can substantially improve the current solutions. Keywords: heuristics, PCB-assembly, feeder rack assignment problem.operations research and management science;

A dynamic programming algorithm for the local access network expansion problem

Technological innovations and growing consumer demand have led to a variety of design and expansion problems in telecommunication networks. In particular, local access net- works have received a lot of attention, since they account for approximately 60% of total investments in communication facilities. In this paper we consider the Local Access Network Expansion Problem, in which growing demand can be satisfied by expanding cable capacities and/or installing concentrators in the network. The problem is known to be NP-hard. We present a pseudo-polynomial dynamic programming algorithm, with time complexity O( nB²) and storage requirements O( nB ), where n refers to the size of the network, and B to an upper bound on concentrator capacity. The cost structure in the network is assumed to be decomposable, but may be non-convex, non-concave, and node and edge dependent otherwise. Computational results indicate that the algorithm is very efficient and can solve medium to large scale problems to optimality within (fractions of) seconds to minutes.mathematical economics and econometrics ;

A Dynamic Programming Algorithm for the ATM Network Installation Problem on a Tree

This paper considers the ATM Network Installation Problem on a tree. To install sucha communication network, decisions concerning the location of hardware devices, the capacity installation on links, and the routing of demands have to be made simultaneously. The problem is shown to be NP-hard. By exploiting the tree structure we show that the problem can be solved to optimality using a pseudo-polynomial time dynamic programming algorithm. Computational experiments on real-life problem instances indicate that the algorithm is highly e#cient. 1 Introduction Modern telecommunication networks are capable of processing multiple telecommunication services on a single physical network. These so-called broadband networks usually consist of several hierarchical network layers. At the top layer #often referred to as the Backbone#, large capacity nodes serve large geographical areas. These areas are decomposed into smaller regions, eachof which is served by nodes located in lower layers of the ne..

The Component Retrieval Problem in Printed Circuit Board Assembly

The minimization of the makespan of a printed circuit board assembly process is a complex problem. Decisions involved in this problem concern the specification of the order in which components are to be placed on the board, and the assignment of component types to the feeder slots of the placement machine. If some component types are assigned to multiple feeder slots, then the additional problem emerges of selecting, for each placement on the board, the feeder slot from which the related component type is to be retrieved. In this paper, we consider this Component Retrieval Problem for placement machines that operate in a similar way as the Fuji CP II. We explain why a simple forward dynamic programming scheme cannot provide an efficient solution to this problem, thereby invalidating the correctness of an earlier published approach. We then present a polynomial algorithm that solves the problem to optimality. The analysis of the Component Retrieval Problem is greatly facilitated by its ..

The Assembly of Printed Circuit Boards: A Case With Multiple Machines and Multiple Board Types

In this paper a typical situation arising in the assembly of printed circuit boards is investigated. The planning problem we face is how to assemble boards of different types using a single line of placement machines. From a practical viewpoint, the multiplicity of board types adds significantly to the complexity of the problem, which is already very hard to solve in the case of a single board type. In addition, relatively few studies deal with the multiple board type case. We propose a solution procedure based on a hierarchical decomposition of the planning problem. An important subproblem in this decomposition is the so-called feeder rack assignment problem. By taking into account as much as possible the individual board type characteristics (as well as the machine characteristics) we heuristically solve this problem. The remaining subproblems are solved using constructive heuristics and local search methods. The solution procedure is tested on real-life instances. It turns out that, in terms of the makespan, we can substantially improve the current solutions