Operations Management in the Service Industry

1. Rossini’s is a high-scale Italian restaurant which has 24 tables that can seat about 100 customers. On average, the restaurant has about 3 tables available. When customers arrive and find no table available, they wait in the waiting area inside the restaurant. The waiting area can accommodate 20 customers. The restaurant has found that when their waiting area is full, arriving customers do not enter and go to other restaurants in the area. Rossini’s is considering expanding its waiting area to accommodate 25 customers. Explain (intuitively) how does expanding the waiting area affect the following measures (i.e., whether the following measures increase, decrease, or stay the same).

(a) Restaurant’s daily sales. (b) Customers’ average waiting time to get a table. (c) Average number of available tables in the restaurant. (d) Average number of customers in the restaurant.

2. Each year, an average of 400 people pass the New York State’s bar exam and enter the legal profession. On average, a lawyer practices law in New York State for 35 years. Thirty years from now, how many lawyers would you expect to be in New York State?

3. Ships arrive at a port facility at an average rate of two ships every 3 days. On average, it takes a single crew 1 day to unload and load a ship. Assume that interarrival and service times are exponential. The shipping company owns the port facility as well as the ships using that facility. It is estimated to cost the company $1000 per day that each ship spends in port. The crew servicing the ships consists of 100 workers, who are each paid an average of $35 per day. A consultant has recommended that the shipping company hires an additional 40 workers and split the employees into two equal-sized crews of 70 each. This would give each crew the unloading and loading time of 1.5 days on average. Which crew arrangement would you recommend to the company? (Consider each crew as one server.)

4. The ticketing counter of a major airline has four agents who serve its passengers. Passengers arrive at the rate of 110 per hour according to a Poisson process. They wait in the line to check in with the agents and get their boarding pass. The time it takes an agent to serve a passenger is about 2 minutes with standard deviation 3 minutes. The waiting line for ticketing has been long, resulting in some customers missing their flights. Thus, the airline is considering increasing capacity of the ticketing by adding one more agent. If the airline adds the fifth agent,

(a) How much, on average, would this reduce the passengers’ waiting time to get their boarding pass? (b) How much, on average, would this shorten the line for ticketing? (c) What fraction of time would the agents be idle?

5. Solid Construction has just made the winning bid of $5.4 million to construct a new plant for a major manufacturer. The manufacturer needs the plant to go into operation within a year. Therefore, the contract includes the following provisions:

• A penalty of $300,000, if Solid has not completed construction by the deadline of 47 weeks from now.

• To provide additional incentive for speedy construction, a bonus of $150,000 to be paid to Solid, if the plant is complete within 40 weeks.

Solid is assigning its best construction manager, David Perty, to this project to help ensure that it stays on schedule. Mr. Perty has earned the confidence of management through many years of exemplary performance with the company. He began as a carpenter fresh out of community college and soon became the youngest foreman in the company, so he knows the construction business from the ground up. While a foreman, he went back to college part time at night to earn his business degree. Immediately after earning his business degree with honors, Mr. Perty was promoted to construction manager. He has been serving the company in this capacity now for 14 years, and rumors have it that he may be next in line to move into top management in a year when the retirement of the company president will cause some shuffling of the top positions. Although Mr. Perty would welcome this opportunity, he does not feel any hurry to move up. Despite its many stresses, he thoroughly enjoys the challenges of being a construction manager, including the opportunities to apply the latest project management techniques. Mr. Perty is very pleased to receive this latest assignment as the project manager for such an important project. He looks forward to the challenge of bringing the project in on schedule, and perhaps earning more respect form top management. However, since he is doubtful that it will be feasible to finish within 40 weeks without incurring excessive costs, he has decided to focus his initial planning on meeting the deadline of 47 weeks. He will need to arrange for a number of crews to perform the various construction activities at different times. Table 1 shows his list of various activities. The third column provides important additional information for coordinating the scheduling of the crews. For any given activity, its immediate predecessors (as given in the third column of Table 1) are those activities that must be completed by no later than the start time of the given activity. Similarly, the given activity is called an immediate successor of each of its immediate predecessors. For example, the top entries in this column indicate that

1. Excavation does not need to wait for any other activities.

2. Excavation must be completed before starting to lay the foundation.

3. The foundation must be completely laid before starting to put up the rough wall, and so on. When a given activity has more than one immediate predecessor, all must be finished before the activity can begin.

In order to schedule the activities, Mr. Perty consults with each of the crew foremen to develop an estimate of how long each activity should take when it is done in the normal way. These estimates are given in the rightmost column of Table 1. Adding up these times gives a grand total of 80 weeks, which is far beyond the deadline for the project. Fortunately, some of the activities can be done in parallel, which substantially reduces the project completion time.

6. A studio is planning to release two digitally enhanced classical movies of 1950s. Marketing Department has identified three customer segments, namely, A, B, and C, and their corresponding population and reservation prices as follows:

Find the studio’s optimal pricing strategy. Specifically,

(a) Should the studio offer the movies individually or in bundles or both, and how much it should price them?

(b) What is the total consumer surplus and untapped market under the optimal pricing strategy?