Deck 5: Managing Flow Variability: Safety Capacity

Question 1

A mail order firm has a total of 12 Watts lines coming into the customer service department (CSD), which has five customer service representatives. On average, two potential customers call CSD every minute. Each customer service representative requires on average 2 minutes to serve a customer. On one of the days two of the Watts lines happen to be down (as a result only 10 Watts lines are available that day). As a result, the mail order firm can expect that
(a) The proportion of potential customers getting a busy signal will
(i) Increase
(ii) Decrease
(iii) Remained unchanged
(b) The average waiting time that customers experience will
(i) Increase
(ii) Decrease
(iii) Remained unchanged
(c) The average utilization of customer service representatives will
(i) Increase
(ii) Decrease
(iii) Remained unchanged.

Answer 1

(a) The proportion of potential customers getting a busy signal will increase, since the queue capacity has decreased
(b) The average waiting time in queue will decrease since customers that are blocked from entering the process now are those that would have waited a long time when the lines were up.
(c) The average utilization of customers will decrease since more are blocked and thus fewer are served.

Question 2

A manufacturer of auto parts has just learnt about the Toyota production system and is trying to implement JIT. Traditionally there has been no control on the amount of work in process inventory between stages (it has been known to exceed 500 parts between some stages). As a first step the amount of work in process inventory between stages is limited to a maximum of 20 parts. What, if any, impact does this have on the output from the factory on the short term?

Answer 2

Limiting the maximum size of the buffer to 20 parts is equivalent to limiting the queue capacity. Reducing the queue capacity reduces the throughput. Thus, limiting the work in process inventory will lead to a reduction in the output from the factory.

Question 3

A mail order company has one department taking customer orders and the other handling customer complaints. Currently each department has a separate telephone number. Each department has 7 Watts lines served by two customer service representatives. Calls come into each department at the rate of 1 per minute. Each customer service representative takes on average 1.5 minutes to serve a customer. A proposal has been put forward to merge the to departments and cross train the workers. The new department would, as a result, have 14 watts lines served by four customer service representatives. As the operations manager, you know that
(a) The proportion of callers getting a busy signal will
(i) Increase
(ii) Decrease
(iii) Remained unchanged.
(b) The average utilization of customer service representatives will
(i) Increase
(ii) Decrease
(iii) Remained unchanged

Answer 3

(a) The proportion of callers getting a busy signal will decrease. Callers will now get a busy signal only if there are 14 people in the process. This is equivalent to having 7 people in each of the two previous processes. In the previous setup, some callers would get a busy signal if either of the two processes had 7 people.
(b) The average utilization of customer service representatives will increase since more customers now enter the process and are served.

Question 4

Star Brite Media (SBM), an independent video rental store, carries digital projection systems that customers can rent out together with new, high-definition DVDs. The store manager is forecasting that, in an average week, about 21 customers would ask to rent a projection system, the exact number of requests per week being random and may be assumed to be Poisson distributed. Their projection rental time is estimated to follow exponential distribution with a mean of about 3 days. (SBM is open 7 days per week.)
a. What is the minimum number of projection systems Sandra should buy to ensure a service level of 90%, i.e., that the probability that a projection system is available when a customer requests to rent one is about 90%? (Assume that customers who are interested in renting a projection system but do not find one available do not wait, but go to find one at another store.)
b. Instead of buying outright, SBM has the option of leasing the projection systems at a special rate of $199 per month per projection system. (This includes insurance on the systems.) What is the break-even price that SBM should charge per day for renting out a projection system? (Assume 30 days per month, an average rental length of 3 days, and a service level of 90%.)

Question 5

Jasper Valley Motors (JVM) is a mid-sized, family-run auto repair shop. To assure customer satisfaction, JVM has kept a fleet of four "loaner" cars that customers may drive while their vehicles are being serviced. In an average week, 15.5 major repairs are scheduled for which owners request a loaner car (the service department is open five days per week). Of course, the exact number of loaner requests is random, and the time between requests may be assumed to be exponentially distributed. If a loaner car is not available when a customer needs one, JVM's policy is to take $50 off the cost of the service as compensation for the customer inconvenience, as they must find alternate transportation to and from the shop. Most repairs are done within a day but some take longer, requiring the customer to keep the loaner car for several days. It has been observed that on average, a customer keeps a loaner car for 1.2 days, and the actual time may be assumed to be exponentially distributed.
a.What is the probability that a customer who requests a loaner car from JVM will actually get one?
b. What is the percentage utilization of JVM's fleet of loaner cars? On an average day, how many loaner cars are on JVM's lot (i.e., not loaned out to customers)?
c. Suppose JVM leases the loaner cars from an automaker at a rate of $350 per month per car, which includes insurance. Max estimates that it costs $12 per "loaner", which covers the cost of the necessary paperwork when the car goes out as well as cleaning the car when it is returned. What are JVM's monthly costs of running the loaner car program (including discounts to those who do not receive loaners)? Assume 20 days in a month.

Question 6

According to the Wall St Journal, research has shown that women take about twice as long in public restrooms as men (roughly, 3 minutes to 1.4 minutes). It is therefore not surprising that waits at the women's restrooms are generally longer than at the mens'. As a consequence, many states have passed so-called Potty Parity Laws. (A Google search on "potty parity" yields over 300 results.) These laws aim to equalize waiting line lengths for restrooms at public facilities such as theaters and convention halls. Laws in Maryland and New York mandate an equal number of toilets for men and women (older facilities generally had more men's rooms). Other states mandate more toilets for women. For example, California requires a 4 to 1 ratio.
a. Assuming that a typical facility serves an equal number of men and women, would you expect the Maryland and New York legislation to be adequate in delivering equal waiting lines? Why?
b. The Colorado Convention Center in Denver has dealt with potty parity by installing movable walls between the men's and women's rooms. Capacity is allocated based on the make up of the group using the facility. Thus when a largely female group is in town, the women's room is allocated up to 75% of capacity. When a largely male group is having a meeting, the men's room gets up to 75% of capacity. What are the benefits of this approach? How does it compare to supply chain management techniques we discussed in class

Question 7

Mateo is COO of the company We-Do-Your-Taxes (WDYT). WDYT typically prepares taxes for physicians in three steps: step 1 involves a customer service representative (CSR) talking with a customer physician and receiving all relevant financial information (pay stubs, expenses, etc.); in step 2 another employee takes all the data from the CSR and fills out all relevant tax statements. Finally, in step 3, a third employee compiles all tax statements, and does a final quality check for completeness and mails out the tax statements to the governmental agency (the IRS) and a copy to the customer.Mateo is considering restructuring the WDYT business process around a "single-point-of-contact" in which a single employee would perform all three tasks of a customers tax preparation and filing.
a. What are the benefit(s) and disadvantage(s) of the single-point-of-contact process and why?
b. Mateo is also considering "Plan G" (G for growth) to expand the business by going after a more diversified clientele. Under Plan G, WDYT would also serve other professionals, including small business owners, in addition to the current customer base of physicians. Under Plan G, Mateo would authorize more hiring and expand capacity proportional to the increase in business (in terms of number of taxes prepared per month). How would Plan G impact the quality of service in terms of responsiveness ?