Introduction:
The routing function in a production system design is concerned with determining the most efficient path for material flow through the production plan. It involves making decisions regarding the sequence of operations, the allocation of resources, and the utilization of machines. The correct answer is option 'D', which states that the routing function is primarily concerned with machine utilization. In this response, we will explain why machine utilization is the main focus of the routing function in a production system design.

Machine Utilization:
Machine utilization refers to the degree to which machines are being used efficiently in the production process. It is a critical aspect of production system design as it directly affects the overall productivity and efficiency of the system. The routing function aims to optimize machine utilization by ensuring that machines are used to their full potential and are not idle or underutilized.

Factors Affecting Machine Utilization:
Several factors can influence machine utilization in a production system. These include:

1. Production Schedule: The routing function determines the sequence of operations and the allocation of machines for each operation. By carefully planning the production schedule, the routing function can minimize idle time and maximize machine utilization.

2. Machine Capacity: The routing function takes into account the capacity and capabilities of each machine in the production system. It ensures that machines are allocated tasks that they can handle efficiently, thus avoiding bottlenecks and maximizing utilization.

3. Maintenance and Downtime: Machines require regular maintenance and may experience downtime due to breakdowns or repairs. The routing function considers these factors and schedules maintenance activities and downtime in a way that minimizes the impact on machine utilization.

4. Material Flow: Efficient material flow through the production plan is crucial for optimizing machine utilization. The routing function determines the most efficient path for material flow, minimizing the distance traveled by materials and reducing idle time for machines.

Conclusion:
In conclusion, the routing function in a production system design is primarily concerned with machine utilization. It aims to optimize the use of machines by planning the production schedule, allocating tasks to machines, considering machine capacity and capabilities, managing maintenance and downtime, and ensuring efficient material flow. By focusing on machine utilization, the routing function contributes to the overall productivity and efficiency of the production system.