Reference no: EM132986709

Operations Management

1. ABC Manufacturing has a small plant where they make three different products. All products use welding, paint and final assembly. Product A requires 15 minutes on welding, 8 minutes on paint and 12 minutes on assembly. Product B requires 12 minutes on welding, 15 minutes on paint and 9 minutes on assembly. Product C is not painted and requires 20 minutes on welding and 10 minutes on assembly. Assume that the firm runs two shifts and has 920 minutes available per day on each resource. The firm estimates maximum daily demand to be 50 for A, 60 for B and 50 for C. Assume the firm can sell each A for $1000, each B for $1200 and each C for $800. Assume that resource costs and labor in the plant are fixed costs and that the firm would like to maximize the profits it makes by manufacturing the three products in the plant.

a) Formulate the problem of maximizing the daily profits as a linear program. Let A, B and C denote the number of each type of product the firm will make.

b) The firm is considering paying either the welding, paint or assembly operators extra money to schedule overtime. Each hour of overtime costs $50 fully loaded. Conceptually describe how you would decide whether overtime should be scheduled on any of the three processes (welding, paint or assembly) by evaluating the linear programming output.

2. Krunchy Kreme, in making its famous doughnuts, begins with the three-step process shown below. There are three dedicated workers, each assigned to one step. Mixing the dough is performed by one worker. Creating the doughnut shape from the dough is performed by the second worker. Batches of doughnuts from Shaping are processed in a flavoring machine in the third step, staffed by the third worker. We shall ignore the remaining tasks required to make doughnuts, such as frying and packing, for simplicity because they have ample capacity and require negligible labor time.

All setups are done by the workers. A setup must be performed in each step of the process for each batch after the batch reaches the worker. Suppose that the batch size is 100 doughnuts.

a) What is the capacity of the above process in doughnuts per hour?

b) Suppose demand is sufficient. What is the (actual) utilization of the three workers staffing the operation?

c) For what range of batch sizes is Mixing the bottleneck?

3. The CQ EMBA Bagel and Coffee Shop is a small coffee shop with branches only in Ithaca and Kingston. They serve hungry CQ EMBA students as well as other townspeople who happen to drop in their stores. They have found the number of fresh raisin bagels demanded by their customers per day is uniform between 1 and 50 per day (i.e., they are equally likely to sell any number of bagels between 1 and 50). It costs Crazy, the owner of the coffee shop, 35 cents to make a raisin bagel and Crazy sells one for $1.00. Any bagels not sold the day they are made are discounted to 20 cents, and sold as "day old" bagels. (Assume the demand for day old bagels is separate from the demand for fresh bagels and that all day old bagels are always sold).

a) How many raisin bagels should Crazy make each morning?

b) What is the probability that Crazy will have 2 or more unsold bagels left over at the end of any given day if Crazy uses the optimal policy in Part a)?

4. The CQ EMBA Bagel and Coffee Shop carries Gimme!'s freshly roasted coffee. The Kingston branch has the coffee shipped over from Ithaca. There is a fixed fee of $30 for each shipment of coffee. Gimme! charges the Bagel and Coffee Shop $12/pound for the coffee and the Bagel and Coffee Shop uses a 20% interest rate for holding cost. The Kingston branch uses 20 pounds of coffee per day with a standard deviation of 4 pounds per day. The lead time for new coffee to arrive to the Kingston branch once it is ordered is 4 days. Since the CQ EMBA students cannot live without coffee, the coffee shop would like to maintain a service level of 99.9%.

a) Currently, the coffee shop orders 200 pounds of coffee when the amount of coffee in inventory goes down to 100 pounds. What is the annual fixed ordering cost and holding cost if they continue to use this policy?

b) One of the EMBA students suggested that the coffee shop can improve its inventory policy by using an optimal reorder point and order quantity. Compute the optimal order quantity and reorder point the coffee shop should use.

5. My-law.com is a recent start-up trying to cater to customers in search of legal services who are intimidated by the idea of talking to a lawyer or simply too lazy to enter a law office. Unlike traditional law firms, My-law.com allows for extensive interaction between lawyers and their customers via telephone and the Internet. This process is used in the upfront part of the customer interaction, largely consisting of answering some basic customer questions prior to entering a formal relationship.

In order to allow customers to interact with the firm's lawyers, customers are encouraged to send e-mails to [email protected]. From there, the incoming e-mails are distributed to one of the three lawyers who are currently "on call". Given the broad skills of the lawyers, each lawyer can respond to each incoming request.

E-mails arrive from 8 a.m. to 6 p.m. at a rate of 10 e-mails per hour. Interarrival times are exponentially distributed. It takes the lawyer, on average, 15 minutes to write the response e-mail. The standard deviation of this is 20 minutes.

What is the average time a customer has to wait for the response to his/her e-mail?

a (avg. inter- arrival time) p (avg. service time) m (number of servers) u (avg. utilization) CVa (coef. of var.- arrival) CVp (coef. of var.- service)

6. The Centurion apartment building in downtown Chicago has a total of 240 rental units. It offers its new tenants an 18-month lease, which is renewed on a month-to-month basis if the tenant chooses to stay longer than 18 months. The leasing office reports that The Centurion signs about 80 leases with new tenants in an average year, and that 60% of tenants who move in end up staying in the building longer than 18 months. On average, the building is 90% occupied. You may assume that a negligible number of tenants break their lease in the first 18 months.

a) What is the average number of tenants who are in their first 18 months at The Centurion?

b) What is the average length of stay for those tenants who stay longer than 18 months (counted from when they first sign their original lease)?

7. All patients who arrive to the Emergency Department (ED) of Cleanland Clinic first go to Registration and then to Triage. Triage is staffed by two nurses. Triage is considering creating two separate lines, the first for patients with surnames starting with a letter in the range A-M, the second for N-Z. Each line would have a Triage nurse dedicated to serve only that line of patients. Assume that the average patient arrival rates to each line would be roughly the same. What effect do you think creating these dedicated lines will have on the average waiting time experienced by patients at Triage? Will the waiting time increase, decrease, or remain the same? Justify your answer.

8. What is the bullwhip effect? How can Vendor Managed Inventory help mitigate the bullwhip effect?

9.
a) Toyota uses the Andon system to (circle one):
(1) level or balance the production
(2) make mistakes known
(3) reduce setup times
(4) achieve just-in-time production
(5) manage relationships with suppliers

b) Provide a real-life, or everyday, example of poka-yoke.