An operation manager of a chemical manufacturing plant must determine the lot size for a chemical that has a steady demand of 1,260 gallons per day. The production rate is 7,980 gallons per day, annual demand is 441,000 gallons, setup cost is $200, annual holding cost is $0.21 per gallon, and the plant operates 350 days per year.
a. Determine the production order quantity (POQ), the number of orders and the time between orders. What is the total annual setup cost? What is the total holding cost per year? Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost, and show the optimal production order quantity and the minimum total inventory cost. What is the setup time in hours, based on a $25 per hour setup labour cost?
b. Determine the duration of the active production interval, t. Determine the maximum inventory. Determine demand during the production interval. Using a second appropriately labelled diagram, graph active production interval (t), POQ, and the maximum inventory level.
c. As part of its new JIT program, the company has signed a long-term contract with its customers and the company will take orders electronically for the engines. The lot size (production order quantity) will drop to 20,000 gallons. Determine the new setup cost per order and the number of orders (setups). What is the total annual cost of managing the inventory with the new policy? What is the setup time in hours, based on a $25 per hour setup labour cost with the new policy?
d. Suppose the plant's operation manager is considering setting up a customer service station manned by one employee. The operation manager believes that an average of 24 customers per hour arrive, according to a Poisson distribution. It takes an average of 2 minutes to serve a customer. The salary and benefits for an employee would be $25 per hour. The plant operates 8 hours each day. It has been estimated that the waiting time cost (i.e., opportunity cost) is $50 per hour in the line, in terms of lost productivity. What is the utilization rate of this service system? What is the average time a customer spends in the system? How many customers are waiting to be served at any given time? What is the probability that zero customer is in the system? What is the average time a customer spends in the queue? What is the total daily waiting cost based on time in the queue? What is the total daily service cost? What is the total daily cost of the queuing system?