A world-class designer for diversified manufacturer of precision metallic components and systems for the automotive industry, energy and mobile industrial markets. The company is a leading edge supplier of engine, transmission, driveline, modules & systems and mobile aerial work platforms. The company wants to determine the production order quantity for its engines. Annual demand for engine is 160,000 units. Setting up equipment costs $2.75. The holding cost is $1.50 per engine per year. The company operates its production facility 300 days per year. Their capability is producing 850 engines per day. The cost of each engine is $3000.
a. Determine the production order quantity (POQ) and the number of 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 minutes, based on a $25 per hour setup labour cost?
b. As part of its new JIT program, the company has signed a long-term contract with its customers and will take orders electronically for the engines. Setup cost will drop to $0.5, but the company also reassessed its holding costs and raised them to $2 per unit. Determine the new production order quantity 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 minutes, based on a $25 per hour setup labour cost with the new policy?
c. Suppose the company retains a service crew to repair machine breakdowns that occur on an average of four per hour, according to a Poisson distribution. The crew can service an average of five per hour, following approximately the exponential distribution in service times. The salary and benefits for a crew would be $25 per hour. The company operates 8 hours each day. It has been estimated that the waiting time cost is $25 per hour in the line, in terms lost productivity.
What is the utilization rate of this service system?
What is the average downtime for a machine that is broken?
How many machines are waiting to be serviced at any given time?
What is the probability that zero machine is in the system?
What is the average time a machine 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?