Operations Management Assignment

1) Arabica, located in Toronto, is Canada's largest online retailer of coffee and coffee equipment, and imports coffee beans from several countries. Arabica operates 250 days a year and sells an average of 100 pounds of Sidamo (Ethiopia) Fair Trade Organic beans a day. After ordering, beans are always shipped from Ethiopia within exactly 9 days. Annual holding costs per pound is estimated to be 40% of the per pound cost of beans. The ordering cost is $20 per order. The cost of a pound of coffee beans is $5. 

a. What is the economic order quantity (EOQ) for Sidamo Fair Trade Organic coffee beans? What is the average inventory? What is the expected total number of orders per year?

b. What are the total annual holding costs of the stock for Sidamo Fair Trade Organic coffee beans? What are the total annual ordering costs for Sidamo Fair Trade Organic coffee beans? Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost, and show the optimal economic order quantity (EOQ) and the minimum total inventory cost.

c. If Arabica orders in quantities of 1200 pound or more, it can get a 1% discount on the (entire) cost of beans. Should Arabica take the quantity discount?  Would your answer change if the deal is for 1500 pounds or more?

d. The demand for the Sidamo Fair Trade Organic beans is assumed to be normally distributed with a variance of 400 pound per day. Assume that management has specified that no more than a 2% risk of stockout is acceptable. What is the standard deviation of demand during lead time? What is the safety stock needed to attain a 2% risk of stockout during lead time? What is the demand during lead time? What should be the reorder point? What is the number of kanbans? What is the annual holding cost of maintain the level of safety stock needed to support a 2% risk of stockout?

2) Organic milk is stocked at a grocery store each week.  At the end of the week unsold milk is reduced in price by 60% and always sells for this lower price instantly. The demand for organic milk is normal with a mean of 250 gallons and variance of 36 gallons.  Assume a service level of 91% and that the store purchases milk for $5 per gallon.

a. Find the price a fresh gallon of milk sells for.

b. Calculate the per gallon cost of underestimating demand. Calculate the overage cost per gallon. 

c. Determine the optimal stocking level.

d. Calculate the stockout risk and the safety stock for the order level in 2(c).

3) Green Corporation, located in Guelph, is a world-class designer and 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.  Green wants to determine the production order quantity for its engines. Annual demand for engine is 160,000 units. Setting up equipment costs $2.50. The holding cost is $1.25 per engine per year.  The company operates its production facility 320 days per year. Green has a capability of producing 800 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? Determine the number of orders (setups). 

b. As part of its new JIT program, the company has signed a long-term contract with its customers and Green 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. How do your answers to 3(a) and 3(b) provide insight into a JIT purchasing strategy?

d. 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?

Q4) An international business operation manager is considering buying a smartphone and phone service plan. There are three service plans to choose from, all of which involve a weekly charge of $25. Plan A has a cost of $0.35 a minute for daytime calls and $0.10 a minute for evening/night/weekend calls. Plan B has a charge of $0.45 a minute for day time calls and a charge of $0.05 a minute for evening/night/weekend calls. Plan C has a flat rate of $75 with 200 minutes of calls allowed per week and a cost of $0.30 per minutes beyond that, day or evening/night/weekend.

a. Determine the total fee under each plan for this case: 150 minutes of daytime calls and 50 minutes of evening/night/weekend calls in a week. 

b. Prepare a graph that shows total weekly daytime cost for each plan against daytime call minutes.

c. If the manager plans to use the service for only daytime calls, over what range of call minutes will each plan be optimal.

d. Suppose that the manager expects both daytime and evening/night/weekend calls. At what percentage of calls minutes for daytime calls would she be indifferent between plans A and B?