Company AutoTimeStamp is one of several businesses in the field of software for automatic scheduling, used by large corporations and institutions to optimize workers shifts, classroom distributions, and to solve several types of large allocation problems.

The market has been growing at an average of 40% per year for the last five years. At the moment, there are no major players in the market - specialized companies and products, adapted to specific markets (airlines, education, factories, hospitals, etc.) have, at best, single digit market shares.

Recent advancements in research, including the successful inclusion of Machine Learning technology, suggest that it is possible to create high quality multi-purpose software, able to adapt to different contexts and markets with minimal human intervention (current scheduling software usually requires an extensive configuration process for each client). For that reason, analysts forecast a major change in the market profile, with no more than a handful of significant players providing solutions for virtually the entire market. However, not everyone agrees with this view - some experts and analysts believe that, although promising, these early versions of multi-purpose scheduling software are flawed and not ready for commercialization and production.

AutoTimeStamp has, for the last few years, specialized in scheduling solutions for airlines, optimizing the allocation of crew and planes. The company, like most of its competition, understands that there may be an urgent need to redefine its business plan and product development policy. For that reason, management has called an important meeting to kickstart this decision process. All the staff playing some type of management role, as well as some people working on key technical and scientific roles, were invited by the CEO via email, which stated:

All of us at AutoTimeStamp are aware of the buzz around all-round scheduling software, which some say is arriving to change the market. In the last few years, we have seen a few failed attempts to produce nonspecialized scheduling software, but recent technological advances suggest that this time things may be different.

I believe it is also time for AutoTimeStamp to make a decision concerning its future, and I would like your help and contribution to run a thorough decision process. In this meeting, we shall combine ideas, knowledge, information, and points of view to establish some kind of workable framework. Please take some time to think about this problem before the meeting, and gather some numbers and facts that you think may be relevant to the discussion. Although we shall discuss several possible paths for the future of our business, we can definitely say that we will end up doing one of two things: either we keep on improving the solutions we offer to airlines, based on our main product AirStamp, or we consider focusing on developing a new multi- purpose scheduling product. Some of you may argue we can try both, but youll have to convince the rest of us that we have the resources to do so.

During the decision process, and especially once we agree on a decision, the board will be involved. Although they have the final say, it is my conviction that our expert opinion will be very influential, probably decisive.

When the meeting takes place, the CEO starts by listing the advantages and disadvantages of what he perceives as the three main alternatives:

1. Business as usual: keep on improving AirStamp and attempt to profit from the expansion of the market.

   Advantages: no need for significant investment and/or hiring, no risk of designing bad product, since a solid basis exists and is working. In case the new type of flexible software products end up not succeeding, the current market share of 20% of the worlds airlines is enough to keep the company profitable and perhaps even growing.

   Disadvantages: if the new multi-purpose scheduling software end up working as well as some predict, then both market share and profitability of AutoTimeStamp will decrease significantly, perhaps leading to the end of the company or its absorption by a bigger player, at a low price.

2. Slowly abandon AirStamp and make a strong investment to attempt to develop a multi-purpose scheduling software. This would require hiring new staff, spending a large amount of money, and risking the future of the company in case the new software is not successful.

   Advantages: should the market move towards this new type of software, AutoTimeStamp could play an important role and secure a large share of a much bigger cake, in case it manages to develop a good product. In addition, profitability is likely to increase significantly if a single multi-purpose solution can be implemented for many different clients. AutoTimeStamp products, namely AirStamp, already provide one of the most automated user experiences of current scheduling software, and the company is well ahead of most competition in terms of technological capabilities.

Disadvantages: a significant investment is required, a large chunk of it on new hires. Machine Learning Engineers and other highly qualified people are not easy to find. Finally, if the development of this new type of software does not produce a viable alternative to current solutions, AutoTimeStamp would have lost a lot of time and money, and very likely a large part of the current airline clients. Even if this type of software is indeed the future of the business, that does not mean that AutoTimeStamp is among the major players in this new market: no one knows who is going to be able to produce the best products of this type.

3. Do not abandon AirStamp and its development, while still investing in a multi-purpose product. This alternative is similar to the previous one, but a larger investment is required so that AirStamp is not abandoned. On the other hand, in case the new type of product fails to deliver, the future of AutoTimeStamp as a major player in the airline market is viable. The CEO believes the board may very well not provide the resources required to play on both tables.

At this point, the marketing director reminds the participants of the Scheduling Solutions Conference that will take place in about sixteen months. The main attraction of this conference is the presentation of the new products, and a competition will award prizes for the best test or beta versions of new multi-purpose scheduling software. Every business in the field, as well as many clients and major tech companies, want to participate, meaning that only invited companies may participate in the conference and in the competition (about 100 invitations will be sent).

The marketing director says that if the company decides to go with alternative 2 or 3, then he will work with management to try to get an invitation, but there is no guarantee of success. If the company does not show an investment in a new type of product, it wont get an invitation. If the company does invest and still does not get an invitation and the possibility to present its product, then the new product is unlikely to take off, no matter how good it is. Finally, winning one of the three competition prizes would surely attract the attention of many new clients, and a lot of publicity as well.

Before the meeting is over, the CEO asks the participants to enumerate some of the main factors that may influence the outcome of this process, in addition to all the events and uncertainties described before. The participants mention:

• The competition behaviour - how many companies currently operating in this market will try to develop this type of new product, and how many succeed.

• Will major tech companies try to profit from their virtually unlimited resources and access to qualified and experienced staff to enter the market, now that it promises profitable opportunities?

• It is a well-established fact that the scheduling software sector has been growing at about 40% per year, but the airline scheduling sector growth has been much lower (10%). What will the general demand be? Many predict that new multi-purpose products, if successful, will attract many new clients from different sectors (theyll be cheaper and easier to use and implement), but how many?

• Should AutoTimeStamp proceed with alternative 2 or alternative 3, it may be useful to consider the possibility to abandon the investment in a new type of product. Participants agree that, in case AutoTimeStamp is not invited to the conference, it will not be too late to abandon the design of the new product, and this could indeed be the right choice, regardless of the investment made up to that point.

The board and management have agreed that, for simplicity's sake, the objective of the analysis should be the number of clients willing to pay an annual fee for AutoTimeStamp products (demand measured in number of clients within 3 years). This objective depends on the market share, but also on the total size of the sector. Investment costs need not be considered - a ceiling of 10M for investment, in addition to the current operation costs of the company, is available for the next few years, mostly for

0. The CEO ends the meeting. He asks everyone to gather some numbers and as much information as possible, so that a quantitative approach to the decision process may be attempted. The goal is that every probability is quantified (for example, how likely is an invitation to the conference?), as well as investment costs, future profitability, and market share. A new meeting is scheduled for two weeks later. When it takes place, there is a lot of new information, and some preliminary decisions, regarding the way the decision problem is framed:

staff (new hires and overtime). This ceiling means that alternative 3 (as defined by the CEO in the

previous meeting) is viable, but with a smaller investment in the development of a new product.

• In addition, and also for simplicitys sake, the behaviour and success of competition should not be

  included as variables at this stage.

• It has become clear that, due to its reputation as a technologically advanced company, AutoTimeStamp

  will receive an invitation to the Scheduling Solutions Conference as long as it commits to presenting a

  new multi-purpose product.

• AutoTimeStamp has also determined that the growth of the market for scheduling software will depend

  mainly on the success of the new type of product and has therefore decided not to include this variable

  as an individual uncertainty in the analysis.

• The success of the new type of multi-purpose scheduling software is measured by a variable called

  market shift. This can be large, moderate, or low. Estimated probabilities, based on market analysis and technological surveys, are 60% for a large market shift, 15% for a moderate shift and 25% for a low shift.

• Based on the number of participants in the conference, as well as the profile of the companies that will likely be present, the best estimates for the probability of winning a prize are of about 35%, if a successful product is developed, and 0% if it isnt. It is too soon to know how likely it is that AutoTimeStamp develops a successful product, but the Technology Director believes a probability of 75% is reasonable, provided a strong investment is made, and 45%, if a smaller investment is made (alternative 3).

  A Decision Tree has been built to deal with this problem. Based on market analysis and forecasts, the demand for AutoTimeStamp products, depending on the outcome scenario, is included. Notice that the current number of clients paying an annual fee to AutoTimeStamp is about a thousand. The information contained in the decision tree is listed in the following Table:

• 

• The CEO has agreed on a risk averse utility function for the demand in number of clients, given by the following function (utility U as a function of demand d):

  () = ^0.3112/ 17

  Note that: U(d = 9000) = 1.00

  U(d = 0) = 0

Please Answer all these questions:

• Using this utility function and the information listed above, redraw the decision tree and include

• the necessary values, namely utilities and probabilities. If necessary, you can make assumptions, provided these are justified.

• Perform the rollback to obtain the optimal policy. Justify your answer.

• Would your answer be different if the expected demand was used as the decision criterion, rather than the utility function? Justify.

Alternative Market shift Success of new Auto Time Stamp product Competition prize Demand (n of clients) Large 200 1 Moderate 800 Low 1400 Yes 9000 Yes Large No 2600 No 100 2 Yes 1500 Yes Moderate No 900 No 50 Low No 50 Yes 9000 Yes Large No 2600 No 150 3 Yes 1500 Yes Moderate No 900 No 600 Low No 900