In this book quantitative approaches are proposed for production planning problems in automated manufacturing. In particular, techniques from operations research provide ways to tackle these problems. Special attention is given to the efficient use of tools in automated manufacturing systems. The book presents models and tests solution strategies for different kinds of production decision problems. A case study in the manufacturing of printed circuit boards highlights the methodology. The book will help to understand the nature of production planning problems in automated manufacturing and show how techniques from operations research may contribute to their solution.

Assembling printed circuit boards effciently using automated placement machines is a challenging task. Here, we focus on a motion control problem for a specific type of placement machines. More specifically,the problem is to establish movement patterns for the robot arm, the feeder rack,and -when appropriate- the work table, of a sequential, pick-and-place machine. In this note we show that a (popular) greedy strategy may not always yield an optimum solution. However, under the Tchebychev metric, as well as under the Manhattan metric, we can model the problem as a linear program, thereby establishing the existence of a polynomial time algorithm for this motion control problem. Finally, we give experimental evidence that computing optimal solutions to this motion control problem can yield significantly better solutions than those found by a greedy method.

In this note we study the complexity of the tool switching problem with non-uniform tool sizes. More speci cally, we consider the problem where the job sequence is given as part of the input. We show that the resulting tooling problem is strongly NP-complete, even in case of unit loading and unloading costs. However, we show that if the capacity of the tool magazine is also given as part of the input, the problem is solvable in polynomial time.

We present statistical evidence that in professional tennis the probability of winning a point may depend on whether the serving player serves from the deuce court or from the ad court. Moreover, in this case of distinct win-probabilities, we show how to calculate the probability of winning a game, as well as winning a tiebreak.