6. Work-in-process (WIP) inventory

One item produced by a work-center has a setup cost $250 and annual demand of 20,000. Demand is deterministic and occurs at a constant rate. Raw material costs $1.50, the completed item valued at $2.25. The holding cost rate is 0.5 per year. The work-center could process 100,000 of these items per year if it did not make anything else. Historically, batches at the work-center spend approximately 80% of the time waiting and 20% of the throughput time in process.

1. Find the batch size that minimizes cost
2. Compute the inventory cost per year