A production process is used to produce 20 different items, under intermittent batch production. When inventory or projected inventory of an item drops to a certain level, a production order is released for Q units of that item. Because product demand is random, production orders create a random pattern of jobs released for production. Jobs in queue are processed by order of release date, i.e., first in/first out.
For simplicity, assume all 20 items have the same demand rate (about 20,000 units annually for each item), with demand for all items occurring at a uniform rate throughout the year. Moreover, all 20 items have the same production rate (the production line runs at 100 units per hour), and the same setup/changeover time (3 hours).
The plant runs 3 shifts in round-the-clock operations, on a 5-day work week (250 days per year). Of the 24 hours per day, about 16.33% are consumed by shift changes, breaks, maintenance, machine breakdown, etc. This leaves an effective capacity of approximately 20 hours per day, available for setups and running the line.
The items in question all sell for $50 per unit. Direct materials cost is about $20 per unit. One process operator (required for both setup and running the line) earns $15.00 per hour. Historically, the process has been changed over about 300 times per year, for a total of about 900 hours of lost production time. A total of about $1500 of setup-related scrap material is generated annually. The carrying cost rate is 20%.
You are going to conduct an EOQ analysis for the proper order quantity (lot size) for these items. Since we have 20 identical items (just to simplify the problem), they will all have the same optimal lot size. Your assignment is to review the simple EOQ model, and compute what the EOQ formula would suggest as the optimal lot size.
What is annual demand for a single item (D)?
What is the annual carrying cost per unit (H) ?
What is the cost per order (per setup) (S)?
What would the EOQ formula, Q =uggest as the optimal lot size?