CH-12-14 Managing Waiting Lines – Service Management: Operations, Strategy, Information Technology : Book Guide

This Document Contains Chapters 12 to 14 Chapter 12 Managing Waiting Lines TEACHING NOTE Because customer waiting is inevitable, the challenge is to make this waiting experience less painful. The chapter explores the psychology of waiting to give the student an appreciation for the subtle effect that waiting has on people. The chapter is nonquantitative and can be used effectively to give the less mathematically-sophisticated students an appreciation of queuing systems and the terminology without any reference to formulas. This chapter has been well received by students because they can identify with the topic from experience. They also enjoy the opportunity to discuss imaginative ways of dealing with the queuing problem. SUPPLEMENTARY MATERIAL Case: FBO, Inc. (HBS 9-678-117) The fixed-based operator at a large metropolitan airport must decide if the current concept of pooling refuelers and trucks to service scheduled airlines should be continued. LECTURE OUTLINE 1. The Economics of Waiting 2. Queuing Systems 3. Strategies for Managing Customer Waiting The Psychology of Waiting That Old Empty Feeling A Foot in the Door The Light at the End of the Tunnel Excuse Me, But I Was Next 4. Essential Features of Queuing Systems (Figure 12.1) Calling population (Figure 12.2) Arrival process (Figures 12.3, 12.4, 12.5, 12.6, 12.7, 12.8) Queue configuration (Figures 12.9, 12.10) Queue discipline (Figure 12.11) Service process (Figures 12.12 and 12.13) TOPICS FOR DISCUSSION 1. Suggest some strategies for controlling the variability in service times. Answer: a) One approach to controlling service time variability is to limit the services provided or to standardize them. Fast food restaurants provide an excellent example of both approaches: they offer a limited menu and they standardize the ways in which the workers provide the service. b) Another approach is to partition demand into categories such as we see for commercial customers at banks or express lane customers at supermarkets. c) Pizza delivery services can "guarantee" delivery within a specified time by controlling variability through several measures. They standardize the preparation of the pizzas and they locate stores strategically throughout the town. They also organize the delivery people so each one can make several deliveries on each trip. d) [Student Coralie Cushny prepared this example of a particular restaurant in a major metropolitan city.] The student reports that this restaurant controls variability on Christmas day by using a "reservation-only" policy. Management schedules "seating" for two and one-half hours beginning at noon and accepts enough reservations to fill the restaurant at each seating. Diners are charged a fixed fee and they may choose a complete meal from an abbreviated menu offered especially for the holiday. Drinks are billed separately. The most obvious controls on the variability of service times are scheduled reservations and service times for each seating that are limited to a specified length of time. The abbreviated menu simplifies food preparation and allows more standardization. The fixed price for the meal facilitates the final billing to some extent, which is an important consideration in a situation where most customers will be leaving at approximately the same time. 2. Suggest diversions that could make waiting less painful. Answer: • Offer attention diversions such as television, video games, travel posters, music, and magazines. • Group waiting people in clusters to promote interaction. • Acknowledge the customer's presence; inform the customer about the waiting time, and advise the customer about any requirements or limitations of the service for which she/he is waiting. • Make the customer aware of any other services the organization might offer, promote community services, scenic sites, etc., and provide information about non-competing organizations. • Provide music. • Provide live entertainment (e.g., strolling musicians in a restaurant divert attention while customers wait for service). • Provide toys for young children. • Make periodic changes in waiting room decor in order to minimize monotony for repeat customers. • Make the customer's waiting time a part of the total service process by having him/her filling out information forms, or performing other preliminary tasks. • Offer educational materials such as videotapes relating to the customer's needs (e.g., a diabetic person can be shown a tape relating to the condition). • Offer refreshments. 3. Select a bad and good waiting experience, and contrast the situations with respect to the aesthetics of the surroundings, diversions, people waiting, and attitude of servers. [Student Bill Kilday contributed the following experiences.] Answer: a) Bad experience at a Southwest Conference football game in October 1992: The stadium had fallen a long way from its glory days in the 1950s and 1960s when it was the home of the national-contending team. But, now wooden bleachers wobble, splinter, and even disintegrate in some places. The facility is dirty and service is bad. The worst part of the service occurs at the refreshment stand. Only one drink stand serves one end of the stadium and it is severely understaffed by members of a Boy Scout troop who do their best to serve the hot, parched and, sometimes, surly college students. The host school officials, accustomed to home games that draw an average of 16,000, failed to appreciate the impact that 35,000 visiting University of Texas Longhorns would have on demand for refreshment services. The stand itself is located in direct sunlight and out-of-sight of the playing field so customers are unable to follow the game activities while waiting in the lines, sometimes for 45 minutes. There is little queue discipline. Customers are selected from the calling population according to who can make eye contact with a Scout. The shortest-process-time rule is not followed, i.e., drinks are not dispensed until an order is placed. Service might have been facilitated if one or two Scouts were dispensing drinks and placing them on a tray from which order-takers could pick them up and hand them to the customers as needed. Also, there is no division of queues, e.g., one line for "express" customers who are getting just one or two drinks and another line for those who are buying drinks for a "herd" ... the University of Texas Longhorns are the visitors! b) Good experience at Memorial Stadium, University of Texas at Austin, in September 1992: This school employs a system known as the Student Draw in which tickets are issued randomly for games. Typically, a crush of students appears at the stadium each Monday morning before home games. This could be a truly unpleasant experience but the Athletic Department staff manages the system very well. The queues are operated according to the shortest-process-time rule, i.e., different lines exist for the different services required. Four windows are allocated to serving the Student Draw, another window serves dated tickets for other games, and two more windows serve general public sales. These latter sales take the longest time per customer so, by designating special windows for them, the longer, but faster moving Student Draw lines are not delayed. Even with this effective management, the wait still is moderately long. But, the perceived wait seems short because of the surroundings and diversions. The ticket area is air conditioned (an important consideration in Austin!) and dividers enforce queue discipline. The best part of the wait is that highlights of previous Longhorn victories are played on television monitors, a device that might encourage ticket sales. The service is automated to a large extent and the service personnel are well trained, courteous, and professional. [Beginning with the 1997-98 term, the university offers the students an opportunity to purchase season tickets in advance instead of participating in the draw.] Bad Waiting Experience: Waiting at a crowded DMV with dull, uncomfortable seating, minimal entertainment options, impatient fellow customers, and indifferent staff. Good Waiting Experience: Waiting at a modern coffee shop with cozy seating, free Wi-Fi and magazines, friendly patrons, and attentive baristas who engage with customers positively. The good experience contrasts with the bad one by offering a pleasant environment, engaging diversions, a positive atmosphere among people, and proactive, friendly service. 4. Suggest ways that service management can influence the arrival times of customers. Answer: • Use appointments or reservations. • Fill appointment times with walk-ins. • Advertise the times during the day or week when the facility seldom is busy. • Offer inducements such as double stamps on Wednesdays, gifts for the first specified number of customers to arrive, reduced or matinee rates for early theater performances or meals. • Offer reduced rates for the service on weekends (e.g., telephone rates). • Segment the market by time sensitivity (e.g., retired people with no schedules, business people at lunch time, and students after school). 5. When the line becomes long at some fast-food restaurants, an employee will walk along the line taking orders. What are the benefits of this policy? Answer: • The most immediate benefit is to discourage customers from reneging. Once an order is taken, the customer feels committed to follow through. • Taking orders from customers while they are in line saves time when the counter is reached. The only tasks remaining are taking money and filling the order, which reduces service time and increases the capacity to serve. • Such a strategy establishes customer contact early in the encounter and might avoid having to play "catch-up ball" later. • Personnel who are "on the floor" taking orders during busy times also can keep watch for tables that need to be cleaned and made ready to accommodate the new customers. INTERACTIVE CLASS EXERCISES The class breaks into small groups with at least one international student in each group, if possible. Based on overseas travel, each group reports on observations of waiting behavior from a cultural perspective. For example, banks operating internationally have found that queue procedures working well in a retail bank in England produce disastrous results in the Middle East, where there is no custom for joining and maintaining a queue. However, I have found from personal experience in Finland that they make a science of queue control using chimes and electronic arrows to direct customers to the next available server. EXERCISES 12.1 (a) The arrival rate per minute is 1/15 = 0.067 arrivals per minute. We use Equation (2) with λ = 0.067 and t = 5 = 0.28 not very good odds. (b) We use Equation (3) substituting for “n” as required Arrivals: n Probability: f(n) 0 0.72 1 0.24 2 0.04 12.2 We use Equation (3) with λ = 4 and t=1 substituting for “n” as required Arrivals: n Probability: f(n) 0 .018 1 .073 2 .147 3 .196 4 .196 5 .156 6 .104 7 .060 8 .030 9 .013 The distribution is not symmetrical about the mean of 4 because arrivals must be greater than zero and thus the distribution is truncated. 12.3 We use Equation (2) with λ = 0.4167 and substituting for “t” as required t F(t) 0 .000 1 .341 2 .565 3 .713 4 .811 5 .875 6 .918 7 .946 8 .964 9 .974 10 .984 After 10 minutes the distribution is approaching an upper limit of 1.0. CASE: THRIFTY CAR RENTAL On the basis of your experience and the description of Thrifty’s operations, describe the five essential features of the queuing systems at the customer counter, the garage, and the car wash. Customer Counter Calling population The calling source consists of a subpopulation (multiple). The arrivals at the customer counter can be divided into: a) clients who have made prior arrangement to pick up a vehicle for tourism or business purposes b) clients without prior arrangements c) clients who are returning vehicles (If the service for the clients who pick up the vehicle for tourism is not the same as for those who pick up for business, then we can distinguish between clients who utilize the vehicle for tourism and those who utilize the vehicle for business purposes). The population in our case consists of an infinite number of clients (the population is large enough to assume that an infinite population serves as an adequate approximation). Arrival process At the customer counter, clients might arrive singly or in bulk to pick up or return the vehicles (i.e., single or group or families). The arrivals of clients without prior arrangement are totally uncontrolled but a degree of control can be exercised by anticipating the time of delivery and the time of return for those clients who have made prior arrangements. Even though we cannot say with finality that the distribution of arrival rates is always described adequately by the Poisson, there is much evidence to indicate that this often is the case, because the arrival process of these clients is probabilistic. Therefore, the theoretical Poisson probability distribution is used widely to describe such type of an arrival process. The arrival process for those clients without prior arrangement is stationary in the sense that the parameters and form of the probability distribution that describe the arrival process does not change over time. The arrivals of clients without prior arrangement are completely independent of other arrivals as well as of any condition of the waiting line. The random arrival rate can vary with time so the demand for service is dynamic. The time between arrivals of those with prior arrangement or those who are returning vehicles is deterministic, because a degree of control can be exercised. Queue configuration The queue configuration is multiple because: a) the service capacity at the counter can be adjusted to match changes in demand by increasing the number of people behind the counter, and b) division of labor is possible by assigning one or more attendants to deal with those clients who have made prior arrangements or who are returning vehicles (the service can be differentiated). Queue discipline For clients without prior arrangement, the "first-come, first served" (FCFS) rule is applied. They are treated alike because no information other than position in line can be used to identify the next customer for service (i.e., the rule is static). Clients with prior arrangements or those who are returning vehicles are placed in separate, distinct queues, and the rule of FCFS is used within this class of clients. If the vehicle desired by a client is not available at a given location, then the arriving client is rejected. Service process The customer counter has multiple servers to process clients. The multiple servers can be described as parallel as illustrated in Figure 2. Parallel channels are variable, so when peak demand occurs, more attendants are added. Service times at the counter are probabilistic, and because the service is brief and simple to perform, the assumption of exponential density function is usually valid. Garage Calling population The calling source consists of a subpopulation. The arriving vehicles at the garage are composed of: a) vehicles that need periodic "normal maintenance" b) vehicles that need special maintenance action The source also can be divided in terms of the type of vehicle, i.e., compact automobiles and subcompact automobiles. The population is finite for each location because the number of vehicles is not very large. Arrival process The arrivals of vehicles at the garage are not controlled by the team of mechanics (even though the arrivals of these vehicles can be controlled partially when they are in the service area). The time between vehicles arriving at the garage is a random variable. The Poisson distribution can be used as a valid approximation to describe the rate of vehicles arriving at the garage, because the arrival process is probabilistic and independent. The time intervals between the arriving vehicles are completely random, and the exponential distribution can be used to describe the times between the arriving vehicles. Queue configuration The service is differentiated, i.e., some vehicles need normal and periodic maintenance, and others need special maintenance. Every garage is a standard side-by-side bay design, thus the queue configuration is multiple. Queue discipline Some priority rules are placed for those cars needed within the next six hours on the basis of the company's known demand and reserve policy. For the other vehicles that receive normal treatment, the first-come, first-served rule is applied. Service process At the garage, there are multiple servers who are stationed to serve vehicles in each outside bay and who also will alternate on vehicles placed in the middle bay. Two apprentices perform all normal maintenance and two journeymen mechanics do special maintenance. The servers are not variable, but the teams are fixed in terms of number of servers. Service time is probabilistic for both types of maintenance and using the assumption of exponential density function usually is valid. Here we can observe the concept of pooling. The two apprentices form a single service facility and the two journeymen also form a pool. Car Wash Calling population The population is divided into compact and subcompact automobiles. The population can be described as homogeneous if the service of washing is identical in terms of time required for both types of cars. In this case all of the cars coming to the wash constitute a homogeneous population. The population consists of a finite number of cars at each location. Arrival process The arrivals of cars at the car wash are random; therefore the time between arriving cars is a random variable. Because the arrival of cars at the wash is completely independent, the Poisson distribution can be used to describe the rate of arrivals, and the exponential distribution describes the time between arrivals. Queue configuration Because two people wash, rinse, and buff, the queue configuration is single queue with single service facility. Queue discipline All of the cars coming to the wash are treated alike, i.e., the first-come, first-served rule is applied. (Some priority rules can be applied for those vehicles that are requested within the next six hours.) Service process At the car wash a team of two people do the service jointly. Even though the team consists of two, it can be considered as a single server, because the servers are not parallel. The number of the people in teams is fixed. The service is brief and simple to perform and the service time is deterministic for the rinse and wash if the system is automatic. If the wash is not automatic, the service time is probabilistic. The two people are forming a pool. They gather together at the car wash to form a single service facility. CASE: EYE'LL BE SEEING YOU 1. In this chapter, we referred to Maister's First and Second Laws of Service. How do they relate to this case? Answer: Maister's first law deals with expectations versus perceptions. Mrs. F. brought a book with her because she anticipated the possibility of a modest wait. But when she arrived and discovered that she was the only one there and that all previous names on the sign-in sheet were crossed off, she reasonably expected to be seen relatively soon. The fact that she had not been seen almost three hours later obviously was counter to her expectations. This "insult" was exacerbated when two later arrivals were seen ahead of her, creating what appeared to her to be unfair treatment. The encounter with the first staff person resulted in another divergence from her expectations. She was a long-time patient who was familiar with the customary routine of the initial screening so, once again, she knew what to expect, but when the staff person declined to "read" the prescription from her glasses, those expectations were not met. In fact, the only expectations that were met related to the previously experienced callousness of the staff, but this could hardly be seen as a positive factor. Unfortunately, the favorable effect of the pleasant waiting room was not enough to offset the negative impact created by the failure to meet her expectations. If Dr. X had seen her before she departed, he would certainly have discovered first-hand Maister's second law that says, "it's hard to play catch-up ball." He would have had to deal with a patient who was upset by the preceding treatment at the hands of his staff. 2. What features of a good waiting process are evident in Dr. X's practice? List the shortcomings that you see. Answer: The positive features of a good waiting process in this case all involve the process and facility. The waiting room is pleasant and comfortable and magazines are available so patients can occupy their time. Part of the actual waiting "line" is concealed because more than one patient can be accommodated out of sight in the various "back" areas, i.e., in the screening room, examination rooms, and dilating area. The screening activities are part of the waiting process, but they alleviate a little of the patient's anxiety or impatience by creating the impression that he or she is finally in the service loop. The negative features of the process in this case involve the personnel. They always appeared either curt or unresponsive because they failed to explain to Mrs. F. why the late comers were taken ahead of her, they gave her no reason for the delay or any indication of how much longer she would have to wait, and they left her sitting for long periods without seeing if she needed anything or offering reassurance that she hadn't been forgotten. 3. Do you think Mrs. F. is typical of most people waiting for a service? How so? How not? Answer: Most people expect to be kept waiting to see a physician and in this respect Mrs. F. was very typical. She modified her expectations when she arrived because of the empty waiting room and the waiting list with all previous names crossed off. Students discussing this case have felt these revised expectations were reasonable. The students also have agreed that Mrs. F. finally did what most people would do when they are kept waiting an unreasonable length of time, i.e., depart without seeing the physician. Mrs. F. was atypical in two ways: first, it is generally felt that she was more "patient" than most people would be in similar circumstances and that she should have walked out sooner; second, the students felt that most people would not have let their physicians know how they felt about their experiences. 4. If Dr. X were concerned with keeping the F family as patients, how could he have responded to Mrs. F.'s letter? Write a letter on Dr. X's behalf to Mrs. F. Answer: If it were important to Dr. X to keep Mrs. F. and her family as patients (or any other persons), there are many things he could and should do. He might phone Mrs. F. and apologize for the length of time she was kept waiting and the rudeness of his staff. He might also tell her that he values her and her family as patients and he is instituting measures to be sure no patient is subjected to such treatment again. He might thank her for letting him know what happened and giving him an opportunity to correct the situation. Many students have even suggested that he offer Mrs. F. and her family some financial consideration such as "the next visit free!" [Students Ron Chovanec and Lisa Wildes submitted this sample letter.] Dear Mrs. F.: I offer my deepest apologies for your recent bad experience on January 5, 1989. The treatment you were shown and the length of time you had to wait is completely inexcusable. You and the rest of your family are valued patients of mine and I hope this most unfortunate experience does not cause me to lose your patronage. I personally guarantee that this will not happen again. I hope you will make another appointment with us to have your problem taken care of. This service, of course, will be provided free of charge. Thank you for expressing your concerns. Please let me know immediately if you have any other problems. Sincerely yours, Dr. X, M.D. Dear Mrs. F, Thank you for your feedback. I sincerely apologize for the inconvenience you experienced and assure you that we are addressing your concerns to improve our service. We value your trust and hope to continue providing the high-quality care you deserve. Best regards, Dr. X 5. How could Dr. X prevent such incidents in the future? Answer: Dr. X can take several steps to prevent such incidents in the future. First, he must communicate to his staff that they are to treat patients with consideration and with respect. To this end he might provide them with opportunities such as formal sensitivity training and role-playing. He should realize that the way his staff treats a patient is a reflection on him as well. Explanations and apologies for a delay should always be extended. Patients should also be kept informed of how much longer they might have to wait and be given an opportunity to reschedule their appointment if it is not convenient for them to wait for a long time. In general, the staff members (and Dr. X) should realize that they are there to serve the patients' needs. Dr. X also can institute various measures to avoid unnecessary and unpleasant waiting by patients: a) Avoid over-booking appointments. b) Schedule a few minutes periodically throughout the day solely as "catch-up" time. c) Institute formal or graphic ways of keeping track of how long each patient is waiting. d) Give his staff responsibility for notifying him "that patient Z is waiting in room 3," if he has finished with treatment of the current patient and is just socializing. e) Supply his patients with survey cards asking for their evaluation of the service he is providing and for their suggestions ... this simple device would allow him to see if unfortunate occurrences are rare or if they happen frequently enough to require action on his part. Students have also been dismayed that conversations between Dr. X and a patient could be overheard in adjoining examination rooms. In general they seem to feel that Dr. X either did not recognize or did not care that the service he provides includes more than just the few minutes that he actually spends with the patient. It also includes the complete package from the time the patient schedules an appointment until the patient's treatment is completed. Dr. X could implement regular staff training to improve customer service and establish a feedback system to promptly address patient concerns. Additionally, ensuring thorough and empathetic communication with patients can help prevent misunderstandings and dissatisfaction. 6. List constructive ways in which customers can respond when services fall seriously short of their requirements or expectations. Answer: a) Customers of any service (and physicians' patients are customers) must first be certain their expectations are realistic. [Medical patients, in particular, also must realize that they are responsible for their own health, i.e., they must practice good health habits, avoid poor health habits, choose their physicians wisely, ask questions of their physicians, inform themselves as fully as possible about pertinent conditions and treatments, discuss costs openly with physicians, and above all, they must insist that their physicians deliver the care for which the physician is charging.] b) When service falls short of requirements or realistic expectations, the customer should bring the problem to the attention of the provider, preferably in a pleasant, non-confrontational manner. This mightbe in a face-to-face discussion, over the telephone, in a letter, or, perhaps, through an intermediary. Some services facilitate such feedback by providing suggestion boxes or customer survey forms. c) Customers might resort to more formal procedures if initial attempts to correct problems fail. For example, they can appeal to organizations such as the Better Business Bureau and professional licensing and review groups. Particularly serious or illegal problems should be brought to the attention of the courts, either through private action or such public agencies as the state and federal judicial systems. d) Customers can "vote" with their dollars and use other providers. They also can let others know about inadequate service providers, which extends the effect of one's vote. e) Customers also should vote at the ballot box for legislators who will be most likely to protect consumers' interests and they can let their legislators know about serious problems. Case Follow-up: Mrs. F. waited six weeks for a response from Dr. X. She then sent a copy of the letter to the County Medical Society, not to file a complaint, but to request assistance in relaying the letter to Dr. X. His only response to Mrs. F. was to send her a copy of her past eyeglass prescriptions. He did, however, send a letter to the Medical Society person who had relayed Mrs. F.'s letter claiming his office had been so busy that particular day that they had allowed morning patients to reschedule their appointments for that afternoon [recall the empty waiting room and the receptionist's reaction to the distressed patient who had missed her morning appointment]. He also said that he would take issue with anyone who suggested that his staff was rude. His letter indicated no concern at all that a patient was kept waiting, was kept waiting without explanation while others who arrived later were treated ahead of her, and that she was ignored the entire time. The clear implication of his response was to suggest that the only problem that existed was Mrs. F.'s for being unhappy about the treatment she received. Most students are not at all surprised that Dr. X failed to respond to Mrs. F.'s letter until she went through the Medical Society. Moreover, one student said that she has worked in a physician's office and such letters were routinely "screened out" by the staff and not passed along to the physician. Mrs. F. posted her first letter to him by certified mail with restricted delivery that required his signature. Either his staff did not inform him that the postal service was attempting to deliver a letter that required his signature or, if informed, he chose to ignore it. CASE: FIELD STUDY Data collection would be facilitated by assigning teams of two or three students to conduct the field study. The time of day should be noted when collecting time between arrivals because, as noted in Figure 12.5, the mean arrival rate usually varies throughout the day. Thus, if data on arrivals is collected over several days, the same hour should be selected each time. Students with a statistical background should be able to use a program such as MiniTab to perform the necessary curve fitting to establish if the theoretical distributions (Poisson and/or Exponential) have be realized. Chapter 13 Capacity Planning and Queuing Models TEACHING NOTE In this chapter we address the challenges of capacity planning for services and the strategic role of capacity planning. An early example of "naïve" capacity planning is shown later in the chapter to be inadequate for services because the queuing aspect of service systems is ignored. The most useful of the analytical queuing models are developed next with examples. These models are used to gain insights and better understanding of the queuing phenomenon. For example, the M/G/l model is used to demonstrate that variation in arrivals and service times both contribute equally to congestion. The managerial implications of these insights are stressed. No attempt to derive the queuing models is made because the intent is to use the models to understand service operations and to make projections of waiting times for capacity decisions using a variety of planning criteria. Calculations using queuing models can be quite tedious. For this reason, in the exercises students are encouraged to use Appendix C "Values of Lq for the M/M/c Queuing Models" instead of the M/M/c formulas. A Computer Simulation Supplement to the chapter includes a demonstration and workshop in the use of ServiceModel, commercial simulation software found on the textbook website: http://www.mhhe.com/support/. SUPPLEMENTARY MATERIAL Case: Manzana Insurance - Fruitvale Branch (HBS 9-692-915) Manzana Insurance must reengineer its operations to match the competition that has begun to issue policies with a one-day turnaround. Queuing models are used to evaluate the performance of alternative process redesigns and capacity additions at the bottleneck. LECTURE OUTLINE 1. Capacity Planning (Figure 13.1) Strategic Role of Capacity Decisions 2. Analytical Queuing Models (Figure 13.2) Relationships Between System Characteristics Standard M/M/l model (Figure 13.3 and Table 13.1) Standard M/M/c model (Figures 13.4, 13.5, and Table 13.2) M/G/l model General self-service M/G/* model Finite queue M/M/l model Finite queue M/M/c model 3. Capacity Planning Criteria Average Customer Waiting Time (Tables 13.3 and 13.4) Probability of Excessive Waiting (Table 13.5) Minimize the Sum of Customer Waiting Costs and Service Costs (Table 13.6) Probability of Sales Lost Because of Inadequate Waiting Area TOPICS FOR DISCUSSION 1. Discuss how one could determine the economic cost of keeping customers waiting. Answer: Internal customers (i.e., those who are employed by the organization) have an economic cost of waiting equal at least to their hourly wages. However, customers who are external to the organization will evaluate the cost of waiting based on the opportunity they are forgoing. A story has been told about a prominent executive who billed his physician for keeping him waiting. When customers balk, renege, or never return because of excessive waiting, the cost is equivalent to the sum of all their future business. 2. Example 13.1 presents a naïve capacity planning exercise and was criticized for using averages. Recall the concept of a "bottleneck" from Chapter 5, "Supporting Facility and Process Flows," and suggest other reservations about this planning exercise. Answer: As we learned in the Supporting Facility chapter, the bottleneck operation in a service product flow process determines the system’s capacity. The naïve analysis assumes each server performs all of the activities including mixing and baking cookies for each customer to order. Realistically such an operation could afford only one oven shared among all the servers. To avoid making the oven a bottleneck, the process most likely would be a product layout. Depending upon the task times and line balancing, the employees would perform specialized jobs such as order taker/drink dispenser, sundae maker, cookie mixer, and baker (to allow consolidation of orders per batch). 3. For a queuing system with a finite queue, the arrival rate can exceed the capacity to serve. Use an example to explain how this is feasible. Answer: With a finite queue, arrivals who find the queue full have no choice but to balk. Thus, the rate of arrivals might exceed the service rate and the system will reach steady state, because the finite queue effectively turns away excess arrivals, thereby diminishing the realized demand. A parking lot is an ideal example of a queuing system with a finite queue of zero. When the lot is full, subsequent arrivals cannot be served and must look elsewhere. 4. What are some disadvantages associated with the concept of pooling service resources? Answer: Service resources can be either human or machine in nature, although one could argue that public parks (i.e., trees, open space, and creeks) represent a shared recreational resource that is neither human nor machine. Pooling of service resources can occur between subparts of a single organization or between separate organizations entirely. In many respects, it is more difficult to pool human resources than machine resources, simply because people interact with one another and their jobs in a highly variable (some would allege irrational) manner – machines do not, and so the objections that can be raised when people are formed into a service pool might originate either with the workers ("poolees") or the decision makers ("poolers") within an organization. It would also appear that pooling between organizational subparts is normally less difficult than between separate organizations, because there is a presumed hierarchy of authority in the former case that can foster or impose a unifying perspective of the pooling concept. In other words, there is more of a closed environment within which the pooling occurs. In all of these various circumstances, the potential organizational objections to the concept of pooling service resources are too numerous to describe exhaustively here. Some of what we feel are the more "important" objections revolve around the following: • Definition of "equitable" economic responsibility for the shared resources such as wages, equipment depreciation, and insurance coverage. • Definition of managerial responsibility for the shared resources such as who decides what work (and in what order) these resources will perform and who evaluates (and by what methods) the need for changes in work priority. • Sensitivity of information that actually or potentially would become shared as a direct or indirect unintended result of the resource sharing. • Perceived value to one of the participating organizations associated with "ownership" of the resources to be shared. • Lack of congruence between the overall goals related to pooling the resources and the operative sub-goals of the pooling participants. While it would not appear on any formal list of objections, mistrust (in all of its general ramifications) among participants might be the most important reason that pooling of resources is not accomplished more often than it is at present. Our experience suggests, however, that technical feasibility points to pooling as an excellent cost-saving and capacity-improving measure, but the mistrust which tends to exist between separate organizations creates an excessively large barrier to the actual implementation of a pooling concept and continues to be a hindrance to its "success" even after implementation. 5. Discuss how the M/G/* model could be used to determine the number of emergency medical vehicles that are required to serve a community. Answer: For the M/G/* model, the probability of n customers in the system is given by the Poisson distribution with * = */* as the mean and critical parameter. Thus, using this distribution, the number of customers or busy ambulances can be determined to ensure that a certain service level is obtained. Service level is defined as the probability that a call will receive immediate service from an idle ambulance. For example, if a 95 percent service level is desired, one need only determine the average arrival rate * and service rate * per ambulance and use the Pn formula to determine the necessary size of n. INTERACTIVE CLASS EXERCISE Go to SerivceModel on the textbook Web site (http://mhhe.com/support ) and select the Customer Service Call Center demo model. Using a computer projector run the animated simulation and display the result. Have the class explain in terms of queuing theory why the revised layout has achieved remarkable reductions in average and maximum hold times. The reduction in holding times for the future Customer Service Call Center is explained by two significant changes from the current system. First, the pooling of all of the CSR's to handle any incoming call (bill payment, account inquiry, and sales) effectively achieves a single queue. Second, the use of Voice Response Unit to handle approximately 30 percent of the routine customer calls without the assistance of a CSR contributes to reducing times significantly. After the simulation is completed, go to the bar chart menu and display the location utilization bar graph. Note that under the future system, the entire staff of CSRs is used approximately 50 percent of the time. However, under the current system the CSRs assigned to sales (numbers16-20) are used 95 percent of the time! The CSRs assigned to account inquiry (numbers 8-15) are used only 25 percent of the time. EXERCISE SOLUTIONS 13.1 (a) (b) 13.2 13.3 (a) (b) When there are three or more in the system, an arrival will find insufficient parking space. 13.4 (a) The arrival rate must increase by 0.5 customers per hour to justify a second telephone. (b) 13.5 (a) (b) (c) n Pn Cumulative Pn 13.6 (a) When there are three or fewer ships in the system, an arrival will find mooring available, assuming the docked ship is unloading. Note: 19/20 = 0.95. Does not meet U.S. Coast Guard regulations. (b) Yes, consider expansion because you save $1000 – $480 = $520/day 13.7 (a) (b) (c) Traffic will block the street when there are four or more cars in the system. n Pn Cumulative Probability 0 1/3 = .333 .333 1 2/9 = .222 .555 2 4/27 = .148 .703 3 8/81 = .099 .802 The probability of traffic being blocked is equal to 1 - .802 = 0.198. (d) This is a single queue, multiple server arrangement or M/M/c system. Thus, can be found using Appendix C. #Tellers c $10c $5cLs Total 1 -unfeasible- — — — — 2 .333 1.333 $20.00 $6.67 $26.67 3 .045 1.045 $30.00 $5.23 $35.23 Recommend two tellers. 13.8 (a) (b) (c) Waiting cost savings $70 (3.2 - 1.6) = $112 Less the radar cost of – 100 yields Savings of $ 12/hour Recommend adopting radar 13.9 (a) Assume we have two independent M/M/1 systems with for each system. (b) Use M/M/2 Model with * = 10/12 = 5/6 = 0.833 and c = 2. From Appendix C, we find the value for . (c) Savings from pooling: $5(1.42 - 1.02) = $2 per hour. 13.10 Determine arrival rate * for parts (b), (c), and (d). For example, in question (b), set * = 6 arrivals/hour and assume that changes in 1/* (time between arrivals) are proportional to changes in the amounts of gasoline that is to be added: Original fill-up criterion: when tank is 1/8 full Amount of gasoline added: (7/8) tank New fill-up criterion: when tank is 1/4 full New gasoline amount added: (3/4) tank Thus: Calculation of Waiting Times and Cars in Line Question * (cars/hour) * (cars/min) * (cars/min) * (a) 6 0.10 0.250 0.40 0.267 6.67 (b) 7 0.1167 0.250 0.467 0.41 7.5 (c) 10.5 0.175 0.250 0.7 1.6 13.3 (db) 7 0.1167 0.269* 0.434 0.33 6.6 (dc) 10.5 0.175 0.318** 0.55 0.67 7.0 *Revised Mean Service Time: **Revised Mean Service Time: CASE: HOUSTON PORT AUTHORITY The Houston Port Authority (HPA) is faced with three alternatives in handling wheat exports. It can: (l) continue operating with one crew; (2) add an additional work crew; or (3) purchase a pneumatic handling system. Alternative 1: In the present situation, we have an example of an M/M/l queuing model because it meets the following criteria: 1. Infinite population of callers arriving independently; Poisson distribution of arrival rate. 2. Single waiting line with no length restrictions and no balking or reneging. 3. A first-come, first-served queue discipline. 4. One server with a negative exponential distribution of service times. Facts: 1. Cars are unloaded by a crew that is paid a combined hourly rate of $50. 2. A demurrage charge of $20/hr. exists for each car, from time of arrival to time of release. 3. Partially unloaded cars from one 8-hour shift are first in line for the next shift. 4. The HPA operates 24 hours per day, 250 days per year. Cost determination: 1. To determine the cost of service, we must break total cost down into personnel costs and demurrage cost. Assigning a cost of $50/hr. for personnel, the total cost of personnel for one day would be: $50 x 24 = $1200/day. 2. The calculation of the demurrage charge requires us to calculate the average waiting time in the system for a car, or Ws. In this example: * = 1.5 cars/hour (arrival rate) * = 2 cars/hour (service rate) which means the loaders are busy, on the average, 75 percent of the time. 3. Service time: 4. At a cost of $20/hour, a two hour time in system means a $40 demurrage charge per car. Because 36 cars arrive per 24 hour shift, this amounts to: 36 cars x $40/car = $1440 5. Combined with the personnel cost, total cost per day of operation is: $1440 + $1200 = $2640/day Alternative 2: Alternative 2 recommends the addition of a second work crew. This is an example of an M/M/C queuing model, where all of the previously mentioned criteria are met. In addition, the service rates across channels are independent and equal. Consult Appendix C with  = .75 and c = 2 and find Lq = 0.123. But Ls = Lq +  = 0.873. Therefore, at a cost of $20 per hour, a 0.58 hour time in system means an $11.60 demurrage charge per car. Because 36 cars arrive per day, this amounts to: 36 cars/day x $11.60/car = $417.60/day But, because we have doubled our personnel, total personnel costs would be: $1200 x 2 = $2400/day Combined with demurrage costs, the cost per day is: $2400 + $417.60 = $2817.60 The total cost above is $177.60 more per day than with a single crew, so Alternative 2 should be eliminated. Alternative 3: The third alternative is an M/G/1 Model with V(t) = 0, using a single, skilled operator who is paid $15 per hour to operate a pneumatic loading device which has a constant service rate of 3 cars per hour. Therefore: * = 1.5 cars/hour, * = 3 cars/hour, , and V(t) = 0 Therefore, at a demurrage cost of $20/hour, a .50 hour time in system means a $10.00 demurrage charge per car, and because 36 cars arrive per day, total demurrage costs would be: In addition, personnel costs will be: $15 x 24 = $360 Combined with demurrage the total service cost is: $360 + $360 = $720/day Analysis of the three alternatives: Alternative 2 is excluded because its cost is more than Alternative 1. Comparing Alternatives 1 and 3, we see that 3 is better as far as cost is concerned, because it saves HPA: $2640 - $720 = $1920/day The cost of the pneumatic handling machine is $500,000 installed, but HPA requires a 5-year payback period on any capital investment. Therefore, projecting the savings over five years results in: $1920/day × 250 days/year × 5 years = $2,400,000 Given the 5-year payback period requirement, HPA should adopt Alternative 3. Comments: The only problem with this analysis is the use of the payback period. This is a poor method of accepting and rejecting projects because, in times of inflation, the savings that might be realized in five years should be discounted back to the present. A net present value method of analysis would make the pneumatic alternative even less appealing. Another factor to consider is if you want to automate the loading facility completely. If the loading device fails, or goes down at times for routine maintenance, no loading could take place whereas an absent employee could be replaced by another employee. CASE: FREEDOM EXPRESS 1. During periods of bad weather, as compared with periods of clear weather, how many additional gallons of fuel, on the average, should FreeEx expect its planes to consume owing to airport congestion? Answer: Planes arrive at DCA with a rate * = 20 per hour and with landing rates of *c = 60 per hour during clear weather and = 30 per hour when the weather is bad. Assume the single runway acts as a server and use the M/M/1 queuing formulas to answer the questions. 2. Given FreeEx's policy of ensuring that its planes do not run out of fuel more than 1 in 20 times while waiting to land, how many reserve gallons (i.e., gallons over and above expected usage) should be provided for clear-weather flights? For bad-weather flights? Answer: To determine the length of queue upon arrival and, thus, the expected wait, we use the distribution of customers in service. Repeated use of the formula yields the number in system when the cumulative probability exceeds 95 percent (and, thus, FreeEx would need to invoke its request to land out of order 1 out of every 20 arrivals). (a) Clear weather: Reserve Fuel Over Expected = 60 - 30 = 30 gallons (b) Bad weather: Reserve Fuel Over Expected = 320 - 120 = 200 gallons 3. If FreeEx must pay $200 to charter a bus to transport its passengers from Dulles to Washington National, should it exercise the option of permitting its aircraft to land at Dulles during bad weather? Answer: Note that the option of landing at Dulles or National creates a two server system. (a) Use National only Expected fuel use while waiting and landing: (6 min.)(20 gal./min.)($2.80/gal.) = $336 (b) Dulles/National option ( * = 40, * = 30,  = 1.33, servers = 2) Using Appendix C by interpolation Lq = 0.951 + (1.345-0.951)/3 = 1.08 But Ls = Lq +  = 2.41 and Ws = Ls/* = 0.06 hours or 3.6 minutes Conclusion: Take the option! CASE: RENAISSANCE CLINIC (A) 1. Assume the waiting lines at the receptionist, the nurse clinician, and the doctor are managed independently with a FCFS priority. Using queuing formulas and the assumption that patients exiting from an activity follow a Poisson distribution, estimate the following statistics: a. Average waiting time in each of the queues: b. Average time in the entire system for each of the three patient paths: c. Overall average time in the system (i.e., expected time for an arriving patient): d. Average idle time in minutes per hour of work: Answer: Receptionist Queue: Nurse Clinician Queue: Physician Queue: b. Path Receptionist (R) Nurse (NC) Physician (MD) Total Time (min.) RNC 4.5+1.5 4.0+2.0 12 RNCMD 4.5+1.5 4.0+2.0 26+4.0 42 RMD 4.5+1.5 26+4.0 36 c. Average Time =  (path time)(path probability) = 12(17/30) + 42(3/30) + 36(10/30) = 23 d. 2. What are the key assumptions involved in your analysis above? Discuss the appropriateness of each in this situation. Answer: • Poisson arrival rates (not very likely if appointments are used). • Exponential service times (very unlikely for the Physician because of consultation). • FIFO queue discipline (unlikely following Receptionist if appointments are used). • Independence among the servers (unlikely because nurse might consult with Physician). • Time independent demand (unlikely because demand will vary by time of day). 3. What would be the impact on the above calculations of adding a second doctor to the clinic and sharing the doctor queue between them on a "first MD available" basis? Answer: We now have an M/M/2 system with  = 13/15 = .867. From Appendix C, we find Lq  0.2. Wq = Lq(1/) = (0.2)(1/13) = 0.0154 hours or 0.92 minutes. Physician idle time assuming each serves half the patients: [1– (6.5/15)]60 = 34 minutes The result is a dramatic reduction in patient waiting time (26 min. to about 1 min.), but it is obtained at the unacceptable cost of increased idle time per hour (8 min. to 34 min.) for the physicians. 4. The clinic is considering adopting a queue priority system that is determined by the time of entry into the system at the receptionist. How might patients waiting for the doctor react to this policy? Answer: The physician queue is affected because, when patients are diverted to the physician by the nurse, they often would join an existing queue, but would be taken before others waiting in line based on their arrival at the receptionist. Patients in the physician queue, not knowing this, would think the FCFS rule was being violated and feel an injustice had been done. Chapter 14 Forecasting Demand for Services TEACHING NOTE Forecasting is a process of making future projections using a variety of techniques that range from expert judgment to sophisticated statistical models. The introductory material on subjective forecasting models is particularly appealing to students. The Delphi technique is best demonstrated by the interactive exercise where students are asked to speculate on a future development such as: "In what year will the U.S. have a woman for president?" The popular technique of exponential smoothing is treated in depth and includes adjustments for trend and seasonality. The concept of feeding back an error component to revise the forecast is an important insight for students to appreciate. SUPPLEMENTARY MATERIAL Case: Perrin Freres (HBS 9-175-087) In order to prepare monthly pro-forma statements for a French bank, the sales of champagne must be forecast. The time series data includes both trend and seasonal components. LECTURE OUTLINE 1. The Choice of Forecasting Method (Table 14.1) 2. Subjective Methods Delphi technique Cross-impact analysis Historical analogy 3. Causal Models Regression models Econometric models 4. Time Series Models N-period moving average (Table 14.2) Simple exponential smoothing (Table 14.3 and Figures 14.1, 14.2) Forecast error Relationship between * and N Exponential smoothing with trend adjustment (Table 14.4 and Figure 14.3) Exponential smoothing with seasonal adjustment (Table 14.5) Exponential smoothing with trend and seasonal adjustments (Table 14.6, 14.7, and Figure 14.4) Summary of exponential smoothing TOPICS FOR DISCUSSION 1. What characteristics of service organizations make forecast accuracy important? Answer: Demand for services can vary by the season of the year, the month, day of the week, and hour of the day. Planning for staff levels that can meet the expected demand must be done in advance in order to make full use of perishable service capacity. Accurate forecasts of customer demand allow effective management of service capacity that will avoid creating idle resources and excessive customer waiting. 2. For each of the three forecasting methods (i.e., time series, causal, and subjective), what costs are associated with the development and use of the forecast model? What costs are associated with forecast error? Answer: Developmental costs include data collection, model structuring, computer programming, and model validation. Time series modeling is the least costly to develop and use because it tracks only one variable and uses a simple computer model. Causal models such as multiple regression analysis are more costly because considerable data-collection time and analysis is needed to identify the appropriate dependent variables and to validate the model. Subjective models are labor intensive by nature. After the models are developed and implemented, forecasting costs include collecting revised data on the dependent variables which, in the case of time series models, can be done automatically and in real time using point-of-sale computer terminals. Subjective forecasting models are the most expensive, because experts must be reconvened each time a new forecast is required. The costs associated with forecasting vary with the forecasting applications. For example, time series models often are used to forecast demand over the short term (e.g., hourly demand at a fast food restaurant) and the costs of error are measured in idle resources or waiting customers. Causal models often are used for long-range planning decisions such as site selections for motels. Errors can result in poor investment decisions or an inadequate estimate of capacity needs. Subjective models are used for "crystal ball" projections of the future for which very long-range planning is based. An error in this case can result in making business decisions based on anticipated trends that never materialize. 3. The number of customers at a bank likely will vary by the hour of the day and by the day of the month. What are the implications of this for choosing a forecasting model? Answer: A forecasting model such as exponential smoothing should be selected, because it is appropriate for a short-term planning horizon. The exponential smoothing model with seasonal adjustment could be developed to account for the hourly and daily variations. However, the forecast probably would be disaggregated by hour of the day and day of the month (e.g., Fridays between 2 and 3 p.m.) and then each period would be subjected to simple exponential smoothing. 4. Suggest a number of independent variables for a regression model to predict the potential sales volume of a given location for a retail store (e.g., a video rental store). Answer: • Number of VCR's per household • Level of education • Number of children per household • Age of head of household • Residential population density 5. Why is the N-period moving-average model still in common use if the simple exponential smoothing model has superior qualities? Answer: Although exponential smoothing has the properties of (1) old data are never discarded, (2) older data are given progressively less weight, and (3) the calculation requires only the most recent data and a smoothing constant, we still find the N-period moving-average in use, in particular, in investment and economic analysis. The calculation of the N-period moving-average is easily understood by the general public and has been used for decades. Control theory, which uses a feedback mechanism, is the foundation of exponential smoothing and involves a level of sophistication that is not obvious in the simple calculation of the exponential forecast. 6. What changes in α, β, and γ would you recommend to improve the performance of the trendline seasonal adjustment forecast shown in Figure 11.4? Answer: The trendline seasonal adjustment forecast illustrated in Figure 14.4 seems to overshoot the actual data, particularly for the summer months (i.e., 7 and 8). This might be owing to the increasing values for the winter months that are misinterpreted as a trend as seen in the trend column in Table 14.7 for the months beginning with February. To moderate the influence of the trend component in the forecast, we can reduce the value of (e.g., 0.05). A recalculation of the Excel spreadsheet with ( =0.2, =0.05, and =0.3) yields a MAD of 123. INTERACTIVE CLASS EXERCISE Conduct a Delphi forecast exercise to obtain a consensus on the year when a woman will be elected President of the United States. List on the blackboard the dates of future U.S. presidential elections (e.g., 2012 through 2048) and a final entry of "never." In the first round record the number of student votes for each year and for the "never" entry. Divide into quartiles (see shaded cells in example below). In the second round, request students in the 1st and 4th quartiles to defend their positions. Take another vote and divide into new quartiles. Ask students in the 1st and 4th quartiles to give reasons why the opposite quartile is incorrect (i.e., ask the 1st quartile students why the 4th quartile students are incorrect and ask the 4th quartile students why the 1st quartile students are incorrect). Take a final vote and divide into new quartiles. The sample board display show below for a class of 24 students (6 to a quartile) illustrates how the mid-quartile range is reduced progressively demonstrating that consensus is being achieved. Year 1st Round 2nd Round Final Round 2016 2020 2 2024 4 2 2028 2 2 2 2032 3 2 2 2036 3 4 2 2040 2 3 4 2044 2 3 4 2048 2 2 4 2052 3 4 3 Never 1 2 3 EXERCISE SOLUTIONS 14.1 The smoothed value for September (t = 9): Forecast for October customers 14.2 14.3 14.4 14.5 Month Jan. 15 15 – – Feb. 18 15.3 15 3 Mar. 22 15.97 15.3 6.7 Apr. 23 16.673 15.97 7.03 May 27 17.7 16.67 10.33 Jun. 26 18.53 17.7 8.3 Jul. 18.53 Aug. 18.53 14.6 Month Jan. 15 15 0 – – Feb. 18 15.3 .06 15 3 Mar. 22 16.02 .19 15.36 6.64 Apr. 23 16.90 .33 16.22 6.78 May 27 18.20 .52 17.22 9.78 Jun. 26 19.45 .67 18.73 7.27 Jul. 20.12 Aug. 20.79 14.7 14.8 14.9 14.10 CASE: OAK HOLLOW MEDICAL EVALUATION CENTER Assignments: 1. Given the information available and your knowledge of different forecasting techniques, recommend a specific forecasting technique for the study. Consider the advantages and disadvantages of your preferred technique, and identify what additional information, if any, that Mr. Abel would need. Answer: A plot of the data given in Tables 14.8 through 14.10 indicates a generally upward trend in patient demand and expenses. A plot of Table 14.10 points out the seasonality of demand for the Evaluation Center services. This variation in demand during the year corresponds to primary and secondary school schedules and points out the dependency of the Center on referrals from the school system. The best technique to apply to this problem appears to be exponential smoothing with adjustment for trends. The obvious disadvantage is the lag in response between the forecast demand and actual demand. Additional information that might be helpful includes: (l) the reason for the dip in demand in 2007 and (2) the experiences of "competitive" services in terms of demand and expense trends. 2. Develop forecasts for patient, staffing, and budget levels for next year. Answer: Table 4 gives the data for developing a patient-load forecast using exponential smoothing with trend . Shown below is a summary of the patient load forecast for 2013 using exponential smoothing with trend adjustment : Assuming there are no changes in the level of efficiency and given the 2013 forecast for patient loads, the following calculations of proportions are performed to determine the hours by specialty that are required to meet the demand: Staff hrs./wk. For 2013 are calculated based on exponential smoothing with trend adjustment : Table 5 shows the forecast for expenses for 2013 using exponential smoothing with trend . CASE: GNOMIAL FUNCTIONS, INC. Assignments 1. Given the information available and your knowledge of different forecasting techniques, develop a recommendation for utilizing a specific forecasting technique in the subsequent study. The final contract negotiations are pending, and so it is essential that you account for the advantages and disadvantages of your preferred technique as they would apply to the problem at hand and point out any additional information you would like to have. Answer: Two forecasting techniques were selected to forecast the future sales for Dynasol. A scattergram plot of Dynasol's sales, both in units and in dollar sales, reveals a linear relationship from September 2012 to February 2014. The graph shown below immediately suggests the use of simple linear regression to predict the sales for the next twelve months. However, as we shall see, simple linear regression has limitations. A more popular forecasting technique, exponential forecasting, also is used to develop a forecast for the next twelve months. The methods are described very briefly below. A regression model requires that we use historical data as a base to forecast the values of the dependent variables in future periods. A simple linear regression weighs equally all of the past data in determining the coefficients in the equation that are the predictors of the dependent variable. And, of course, the regression line minimizes the distances from the actual data points to the line. The major drawback with regression models lies in the dangers of extrapolation, which will be discussed later. The other technique used in the analysis, exponential smoothing, has a set of properties that make it a good technique to use. Exponential smoothing is used most widely when the data represent a relatively constant pattern. The technique smoothes out the randomness or blips in the data. There are several reasons why exponential smoothing is used: all past data are considered in the smoothing process, more recent data are given more weight, very few data are required to update the forecast, it is relatively inexpensive to use, and the rate at which the model responds to changes in the underlying pattern of data can be altered by adjusting the smoothing constants in the equations. When a trend, which is the average rate at which the data change from one period to another, is spotted in the data pattern, it can be taken into account in the smoothing process. The changes in the trend also can be smoothed in a manner similar to smoothing actual observations. The data that are provided in the case can be described as "limited" at best. Although the market appears to be growing at a phenomenal rate, there seems to be no hint as to when the market for this product might actually slow down in its life cycle. There are dangers in extrapolating the data out twelve months into the future without any other information. On the other hand, the demand for the product could continue for a long time. The problem facing the analyst lies in trying to predict the market in the face of little knowledge and much uncertainty. Extending the simple linear regression line into the future would be naive. 2. Assume that you are a member of DynaSol's small marketing department and that the contract negotiations with GFI have fallen through irrevocably. The company's top management has decided to use your expertise to develop a forecast for the next 6 months (and, perhaps for the 6-month period following that one as well), because it must have some information on which to base a decision about expanding its operations. Develop such a forecast, and for the benefit of top management, note any reservations or qualifications you feel are vital to its understanding and use of the information. Answer: Analysis using regression: The scattergram plots of sales in terms of units and dollars for both Dynasol and the total market are linear. Dynasol unit sales have an of nearly .98 and the dollar sales have an of .97. The total market sales in both units and dollars seem to be related less linearly, but their s are both in the .90 range. Overall, there seems to be a very strong relationship between sales of this product and time, as the high s would seem to indicate that time can predict more than 90 percent of the variation in sales. Twelve-month forecasts can be constructed using the simple linear equations from Table 6 derived from the data in the case. The forecasts are shown in Table 7 where Month 19 (x in equation) is March 2014. Analysis using exponential smoothing: Exponential smoothing with a trend factor is selected to forecast sales during the next 12 months. Beginning with Month 1, September 2012, a rolling exponential smoothing forecast with trend is made for the next month using the actual data from Table 14.12 in the textbook. Month 19 forecast is the final exponentially-smoothed forecast. Months 20 to 30 are determined by adding in the appropriate constant trend adjustment: 4.42 for Dynasol units, 10.33 for Dynasol $, 40.81 for Market units, and 79.83 for Market $. The results of the forecasts for future sales and future market share are shown in Table 8. Conclusions: The simple linear regression technique weighs all of the past data equally to derive the coefficient (slope) that is used to determine the forecast values. Exponential smoothing, on the other hand, puts more weight on the most recent data values, which might lead to a higher estimate of future sales. In reviewing the forecasts, this is precisely what we see has occurred. The exponential smoothing technique gives us consistently higher estimates of future sales, both in unit and dollar terms. However, surprisingly, the discrepancies are not large. Although market share fluctuated back and forth over the last 18 months, both models predict a steadily increasing market share in the future simply because the average trend in the market share was upward during that period. What do we conclude at this point? If management were to accept an interval estimate, then we can use the sales that are predicted by regression as a lower bound and the sales that are predicted by exponential smoothing as an upper bound. No one knows when the market will slow or turn down or when something exogenous to the system will happen that will alter drastically the present rate of sales. If managers are generally optimistic about future sales and if they think the product is still in the growth cycle of its life, then they accept with confidence the estimates given and expand the business. However, if they feel that the market for this product might decline, or that the competition will increase, or if they have other information about the economic climate that is not available to the analyst, then they should regard the forecasts as high and expect the sales to be lower. By using the old data as a test data set, we see that the models are highly reliable as long as everything remains constant. It is up to the managers to decide if they believe things will remain constant. Solution Manual for Service Management: Operations, Strategy, Information Technology James A. Fitzsimmons, Mona J. Fitzsimmons 9789339204471