Optimizing capacity assignment of multiple identical metrology tools

In modern semiconductor manufacturing facilities, metrology capacity is becoming limited because of the high equipment cost. This paper studies the problem of optimally assigning the capacity of multiple identical metrology tools in order to minimize the risk of defective wafers on heterogeneous production machines. We assume that the output of each production machine is assigned to only one metrology tool. The resulting problem is formulated as a Multiple Choice Multiple Knapsack Problem (MCMKP), which combines the Multiple Choice Knapsack Problem and the Multiple Knapsack Problem and does not appear to have been studied in the literature. A greedy heuristic and an improving heuristic are also proposed. Numerical experiments are performed on randomly generated instances to analyze and compare the solutions of the heuristics with solutions obtained with a standard solver.