Game—Where Did the Demand Go? Teaching Demand Censoring with the Newsvendor Challenge

1. Introduction

The increasing availability of data and advancements in technology contributed to a growing trend in data-driven problem solving within organizations (Gallien et al. 2015, Mišić and Perakis 2019, Erkip 2023). As a result, educators are shifting toward teaching data-driven methods using data to construct decision models (Diamant 2024) as opposed to more traditional modeling approaches that rely on stronger assumptions without deriving them from data. One area of application is inventory control, in which organizations make ordering decisions before observing uncertain demand. The effective use of data is shown to improve demand forecast accuracy and resulting inventory order decisions given cost and revenue trade-offs (Levi et al. 2015, Lin et al. 2022, Van der Laan et al. 2022). Decisions may even be derived from data directly without explicitly forecasting the uncertainty (Mišić and Perakis 2019, Goltsos et al. 2022, Erkip 2023, Van der Haar et al. 2024).

A well-known example of an inventory decision-making problem under uncertainty is the newsvendor model. In the newsvendor model, a once-off order needs to be placed prior to observing uncertain demand. Real-world examples include stocking up before the holiday season, planning inventory of goods to sell at concerts, or replenishing perishable goods with very short lifespans.

The newsvendor problem is commonly taught using an analytical approach (Cachon and Terwiesch 2006, Chopra and Meindl 2016). In this approach, a demand distribution is assumed to be known to the newsvendor. The newsvendor is then tasked with determining the optimal order quantity that maximizes expected profit. This order quantity, therefore, balances the opportunity cost of missed profits resulting from underordering with the wasted cost resulting from overordering. Naturally, this approach is only effective when the distribution of demand uncertainty is known, which is not the case in practical settings (Qin et al. 2011).

If historical data are available, we can extend the model to a data-driven one in which demand has to be learned based on samples or available data features (Huber et al. 2019). The use of data features should make decisions more accurate, albeit at increased complexity. Historical sales data can be used by organizations as a proxy to estimate future demand, but data are often censored in that the true historical demand, including lost sales from underordering, is unknown. In situations in which demand is censored, organizations face the challenge of correctly accounting for lost sales occurrences. In online settings, for instance, organizations may derive true demand from the browsing behavior of consumers (Madeka et al. 2022). For physical retailers, this estimation is more challenging. Nevertheless, failing to consider demand censoring can have a detrimental effect on organizations’ profits.

We develop a data-driven newsvendor challenge to teach these concepts to students in a relatable, easy to understand manner. To enhance the practicality of the learning experience, we let students play as surfboard rental providers. Every day for a period of one year, they have to decide how many surfboards to take to the beach to rent out to potential surfers. Taking boards to the beach has a cost per board, whereas the demand for rentals is only observed during the course of the day. We provide students with a two-year historical data set of surfboard rentals. Data features include daily temperatures that are correlated with demand for rentals, historical rentals, and historical numbers of surfboards available for rent at the beach per day. The latter causes censoring of the true demand for rentals as past rentals on a given day cannot exceed the availability of boards on that day. By assuming the role of surfboard rental providers and using this data set, students are tasked with deciding how many boards to take to the beach given a specific forecasted temperature.

Through this practical and engaging approach, we aim to prepare students for real-world scenarios in which accurate forecasting and effective decision making are critical. In addition, the challenge allows for discussions on the importance of balancing time spent on prediction versus time spent on prescriptions and decision making. Inspired by Bloom’s taxonomy (Bloom et al. 1964), we propose three learning objectives:

1. Analyze and identify instances of data censoring in various real-world scenarios, understanding its impact on data analysis and decision-making processes.

2. Evaluate the implications of overage and underage costs in decision making under uncertainty, applying mathematical models to balance these costs effectively.

3. Synthesize knowledge of predictive and prescriptive analytics to assess how reliance on advanced prediction tools influences the efficacy of prescriptive strategies, proposing solutions to enhance overall decision-making performance.

Because good solutions can be obtained without mathematical analysis, the challenge can readily be applied to both technical and nontechnical courses. We successfully played the challenge with such diverse cohorts. First, our challenge was introduced as part of the elective course “operations analytics” in the Master in Business Analytics, which attracts students with prior knowledge of predictive methods seeking more hands-on experience in data-driven decision making. Second, we played the challenge in the Master in Sustainability, which is less focused on methodologies. We emphasize how to share the key insights to different audiences in the debrief section (Section 3.3). The small competition between students was perceived to spur motivation and sparked a lively class discussion after playing the challenge.

In conclusion, the data-driven newsvendor challenge offers an engaging and practical way to teach students decision making under uncertainty based on censored data. With this paper, we aim to share our experience and the open-source challenge with the academic community.

2. Literature

The newsvendor problem has a long history, dating back to the introduction of a mathematical model for banks to trade off having too much versus too little cash deposits (Edgeworth 1888). In inventory management, the problem was first introduced by Arrow et al. (1951), referring to it as the “newsboy problem.” More recently, literature adopted the neutral nomenclature newsvendor problem. This problem requires a newsvendor to order newspapers at the beginning of the day before facing uncertain demand during the day. Having too little inventory results in lost sales, whereas having too much results in excess stock that needs to be discarded. This overage versus underage trade-off is a common challenge in many decision-making problems with uncertainty.

Numerous studies investigate the newsvendor model in various contexts. Overviews are provided by Khouja (1999) and Qin et al. (2011), whereas Porteus (2008) offers an excellent tutorial. Traditionally, papers assume that decision makers know the exact distribution of the observed random demand. This assumption is relaxed in the data-driven newsvendor model; see, for example, Thiele (2004), Levi et al. (2015), Van der Laan et al. (2022), and Lin et al. (2022). The data-driven newsvendor can be further generalized to include observations of relevant features, such as weather or location (Ban and Rudin 2019).

Demand censoring is particularly relevant to data-driven decision making, which occurs when key aspects are missing from the available data. For instance, sales data may be included in data sets as a proxy for demand. However, actual demand may exceed available inventory such that the true demand remains unobserved. The impact of demand censoring on the newsvendor problem is discussed, for instance, in Godfrey and Powell (2001), Besbes and Muharremoglu (2013), Huber et al. (2019), and Besbes et al. (2022). Censoring generally makes problems more complex to solve (Lugosi et al. 2023). If the newsvendor decision is made repeatedly over multiple periods, a decision maker can learn from the past order decisions and, hence, potential demand censoring (Besbes et al. 2022, Lugosi et al. 2023).

The body of literature on data-driven inventory control decision making and appropriate solution approaches has grown significantly in recent years (Erkip 2023). Solution approaches can generally be divided into two main categories—sequential predict then optimize or simultaneous smart predict and optimize—which utilizes the problem structure to prescribe actions (Huber et al. 2019, Mišić and Perakis 2019, Elmachtoub and Grigas 2021, Goltsos et al. 2022, Van der Haar et al. 2024). Each approach has merit, depending on the setting at hand. We highlight that a risk of sequential predict then optimize is that decisions are often made using predictions based on a sample mean, which can lead to suboptimal results and a waste of data. Furthermore, when demand censoring occurs, resulting prediction models may be misspecified if demand censoring is not accounted for.

For our challenge, different solution approaches can be applied depending on the technical skills and prior knowledge of the students. We provide a debrief for both technical and nontechnical audiences in Section 3. We refer the interested reader and instructor to Bertsimas and Kallus (2019) for example applications of regression (k-nearest neighbor, local linear, classification and regression trees) and random forests or Bottou (2012) for neural networks. Censoring can also directly be accounted for by using, for instance, Tobit regression. The foundational idea originated from Tobin (1958) and was later coined Tobit regression by Goldberger (1964), playfully referring to the model’s creator as well as its structural similarities to probit models. For an excellent review of Tobit models, see Amemiya (1984). For a comprehensive discussion, the following textbooks are recommended: Goldberger (1964), Maddaia (1977), and Judge et al. (1991).

Challenges and games are shown to increase students’ engagement and learning (Hamari et al. 2016, Kong 2019, Boutilier and Chang 2023). Perhaps the most well-known game widely taught in operations and supply chain management is the “beer game” of Sterman (1992), explaining the well-known bullwhip effect. Examples of data-driven, game-based teaching include applications in transportation and distribution (Dalal 2022), portfolio selection in stock markets (Villalobos 2007), and blockchain technology (Wendt et al. 2024). The newsvendor problem has also been gamified, such as that of Surti and Celani (2019). Yet we are not aware of games incorporating the data-driven version with demand censoring as in our case.

3. Using the Challenge in the Classroom

The challenge is designed to suit students with different levels of technical expertise. This includes (executive) students with little to no knowledge about operations and statistics and technical audiences, such as students pursuing a Master in Business Analytics. Accordingly, we provide different debriefs in this section. With a specific debrief, especially relying on Ban and Rudin (2019), one could also use the game in a PhD course.

3.1. Context

Students are assigned the task of managing surfboard rentals on a tropical island, engaging in an exercise that mimics a real-world newsvendor scenario. The task involves making a single order of surfboards from a central shop each day, which is then taken to the beach and rented out during the course of the day. No subsequent orders are allowed on the same day. The students are provided with information on the cost of ordering surfboards, the rental fees chargeable to customers, and the salvage value for any surfboards not rented out during any given day. A unique aspect of this exercise is the consideration of daily temperature variations, which affect surfboard demand. An extensive description of the task is provided in the student handout in Appendix A.

The challenge unfolds in one round, in which students spend approximately 50 minutes analyzing data to forecast demand and finalize their order quantities. Following this, results are collected, and a 30-minute debrief session is conducted, including explaining the optimal solution approach and commonly observed strategies. If time allows, students can play an additional round on new data to distill the learnings. Figure 1 outlines our suggested classroom timeline.

We recommend presenting the challenge directly (as described in the student handout in Appendix A) without any prior explanation of the trade-offs inherent to the game. Doing so encourages students to discover and understand the concepts as they tackle the challenge.

3.2. Solution and Playing the Challenge

The solution and detailed instructions for facilitating and playing the challenge are available in a separate Teaching Note. Additionally, we include a refresher on the feature-based newsvendor model for instructors, which may be useful to guide the challenge.

3.3. Debrief

3.3.1. General Nontechnical Audiences.

Once all submissions are in, we collect the results and combine them in the instructor’s spreadsheet, which accompanies the Teaching Note. Immediately sharing the results with the students typically leads to excitement and discussions among the students. For this reason, we delay sharing the results and first invite students to share their impressions from playing the challenge. Typical questions that we ask include the following:

1. What did you find difficult?

2. Did you create a forecast, and if so, which model did you use?

3. How much time did you spend on the prediction model versus the ordering decisions?

4. Did your order quantity differ from your forecast, and if so, why?

Typical answers and discussions include that the time pressure makes it challenging. It is indeed noticeable that different students progress at different speeds. Note that we played the game before the era of generative AI; hence, students code their solutions from scratch or do the full analysis in Excel. We suggest monitoring class performance and provide sufficient time until the majority of the class has reasonable solutions. We felt that a little time pressure helps to keep students engaged. Most students answered that they developed a forecast and spent the majority of the allotted time on the forecast. They occasionally increased the order above the forecast, but these decisions were largely made based on intuition. The overage–underage trade-off is typically not prioritized by students. We conjecture that this result may be the case in many firms. From our executive teaching experience, we noticed that firms typically invest in data analytics tools for forecasting, but little effort is dedicated toward the optimization of the actual decision making. We feel this is a valuable debrief discussion point.

After the discussion, we show the results and ask feedback from the top and bottom performers in a constructive manner. We then continue to show the optimal strategy (as discussed in Section 2.3 of the Teaching Note) and commonly observed student strategies. For less technical students, the key steps and concepts can be highlighted more conceptually. The instructor can steer the discussion toward real examples in which data censoring occurs and how to cope with this rather than discussing methodological concepts. For all students, we encourage the use of Figures 2 and 3 in the Teaching Note during the debrief.

3.3.2. More Technical Audiences.

The instructor may perform a more technical debrief discussion for technical audiences. Interested students may consult Ban and Rudin (2019) for various (often very tractable) solution approaches to the newsvendor problem using data. These approaches include sample average approximation, empirical risk minimization, and kernel optimization methods. Notably, we encourage the discussion to explore the impact of employing more complex prediction models on the prescriptive solution. It is often found that simpler prediction models, such as (piecewise) linear models, can be more tractable and efficient for solving large-scale problems. As a result, simpler models can be a practical choice despite the potential benefits of more sophisticated models. Ban and Rudin (2019) also include regularization approaches to prevent overfitting.

Students interested in advanced regression models may explore those specifically designed to address censoring or truncation. The core concept involves truncating the dependent variable at a specified lower or upper bound. For instance, whereas household expenditures might exhibit a linear relationship, they can be truncated at zero, disrupting this linearity. Rather than resorting to nonlinear estimators, one can apply sophisticated models that specifically handle censored observations, such as Tobit regression (Goldberger 1964). We refer interested students and instructors to the excellent review of Amemiya (1984) and references therein.

A vast number of realistic extensions exist to better reflect reality. Technical students who wish to better understand how the model could be adjusted to include correlated demand may be referred to section 3.2 of Ban and Rudin (2019). Furthermore, the impact of adding fixed order costs could be used to connect the challenge’s learnings to other sessions in operations management, such as the economic order quantity model. Inventory carryover between periods could also be highlighted and connected to sessions on safety stocks or a vast literature on dynamic, sequential decision problems.

It is worth noting that some students may choose to skip the prediction stage altogether and focus solely on the decision-making aspect of the challenge. For instance, we observed some students utilizing methods such as clustering temperatures into ranges and then determining the best orders for each cluster. This approach can be effective and is consistent with advanced prescriptive methods that do not rely on an explicit forecast (Mišić and Perakis 2019). An example of such an approach is that of Bertsimas et al. (2019), in which the authors develop decision trees for personalized medicine without explicitly forecasting the demand thereof, or Van der Haar et al. (2024), in which the authors adjust the loss function of supervised learning algorithms to include overage and underage (as opposed to typical forecast errors). We recommend discussing these approaches in class following the challenge.

4. Feedback and Experience

We played the challenge as part of the elective course “operations analytics” in the Master in Business Analytics program for two consecutive years. We also played it in the Master of Sustainability program but discuss the feedback from the business analytics program. These students possess knowledge on predictive methods and use the elective to gain more hands-on experience on data-driven decision making. The class size was relatively small with 20 students working in groups of two to three students. Typically, less than 20% of the students achieve excellent performance close (within 5%) to the optimal strategy, whereas the remainder fail to realize that demand is censored or to adapt the order quantity to account for the overage–underage trade-off. The small competition between students is perceived to spur motivation and develop better solutions. Learnings from our initial trial runs include that students reacted positively to the challenge. Their general comments were all positive with some requesting more time. Overall, we received a score of 5.7/7 on understanding the importance of demand censoring and 5.05/7 on understanding the importance of overage versus underage. Of the total students, 65% indicated the challenge to be their preferred teaching method, 15% prefer a case study, 10% prefer a conventional theoretical class, and the remaining 10% prefer a mix. The detailed responses are provided in Appendix B.

We also identified some points for improvement during our initial runs. Students vary in terms of technical implementation skills. Hence, some students spent too much time on trying to implement (complex) predictive models. They typically miss both demand censoring and the newsvendor trade-off as they run out of time to implement the prediction models. To ensure that these students do not fall behind, we, therefore, provided a chance to finalize the strategy at home at students’ own pace before providing a debrief.

In case time is limited, we can set overage equal to underage such that only demand censoring plays a critical role. In trial runs, having only demand censoring still created a significant challenge for the students. Yet this may reduce the learnings on understanding the importance of overage versus underage. The lower feedback rating of the students on this component stems from our experiments in which we set underage equal to overage. In general, we recommend playing the proposed numerical setting as outlined in this paper so as to maximize student learning.

5. Conclusion

In conclusion, the newsvendor challenge with data and demand censoring offers an engaging and practical way to teach students about decision making under uncertainty. The challenge’s focus on real-world data, demand censoring, balancing time between prediction and prescription, and trading off overage versus underage allows students to gain hands-on experience with decision-making techniques. Students also gain a deeper understanding of how data can inform business decisions. Furthermore, the challenge’s flexibility allows it to be used in a wide range of courses from technical courses focused on operations analytics to more general courses. Overall, the challenge has served as a valuable tool to prepare students for the challenges of data-driven decision making in today’s business world. It also stimulates fun, in-class competitions among students. Alternatively, it can easily be used as an at-home assignment. The code needed to generate the data along with all plots are made available as open source.

Appendix A. Student Handout

You are an entrepreneur living on a picturesque, tropical island. Your local beach offers ideal surfing conditions throughout most of the year. There used to be a surfboard rental provider here, but they unfortunately left the island some years ago. The only surf shop on the island is now located several kilometers inland in another village, limiting access to surfing for both locals and tourists alike. Being an avid surfer yourself, you capitalized on this gap in the market and have recently started your own surfboard rental business.

You have a limited budget and cannot afford to buy your own surfboards. You have therefore set up an agreement with your contacts at the surf shop to rent surfboards from them on a daily basis. You transport these surfboards to the beach and, in turn, rent them out to the surfers there. You do not have to rent a fixed number of surfboards from the surf shop every day and can assume an uncapacitated availability of surfboards. However, since you transport these to the beach, you only have one opportunity at the beginning of each day to decide how many surfboards to take to the beach for rental. You have to return the surfboards for cleaning and quality control at the end of each day.

Each surfboard that you take to the beach has an initial cost of 10 euros, which you have to pay to the surf shop. However, you can rent out each surfboard for 20 euros. At the end of the day, you return all the surfboards to the rental shop. Any surfboard not used by customers does not require cleaning, and you receive a salvage price of 5 euro for each unused surfboard from the rental shop.

The shop manager is meticulous in her accounting. She has provided you with a comprehensive data set containing the historical orders and rentals of the previous surfboard rental provider who worked on the island from 2022 until the end of 2023. In addition, the manager recorded the temperature daily, as there appears to be a positive correlation between temperature and rentals. This complete data set is provided in the accompanying excel sheet. For illustrative purposes, Table A.1 provides a sample of the training data that you can use to decide on the optimal number of surfboards to take to the beach at the start of each day in 2024. Note, it turns out that, due to the tropical nature of the island, the weather conditions can change rapidly from one day to the other. There seems to be little to no correlation between days.

Table A.1. Training Data Set

Table A.1. Training Data Set

Date	Temperature	Order	Sales
01/01/2022	27	66	66
02/01/2022	28	57	57
03/01/2022	14	57	42
04/01/2022	27	61	61
05/01/2022	20	61	57
06/01/2022	17	60	53
07/01/2022	27	59	59
08/01/2022	16	62	56
09/01/2022	15	64	46
10/01/2022	28	60	60
$⋮$	$⋮$	$⋮$	$⋮$
31/12/2023	10	66	30

Your task is to determine the optimal number of surfboards to take to the beach at the start of each day in 2024, with the goal of maximizing your profits. You have access to the temperature forecast at the start of each day (see the accompanying excel sheet). Table A.2 provides a sample of the temperature data. Given your task of maximizing profits, determine the number of surfboards you should rent for each day of 2024 and use these values to complete the “Order” column of Table A.2.

Table A.2. Test Data Set

Table A.2. Test Data Set

Date	Temperature	Order
01/01/2024	16	$\dots$
02/01/2024	21	$\dots$
03/01/2024	24	$\dots$
04/01/2024	18	$\dots$
05/01/2024	17	$\dots$
06/01/2024	21	$\dots$
07/01/2024	23	$\dots$
08/01/2024	19	$\dots$
09/01/2024	23	$\dots$
10/01/2024	20	$\dots$
$⋮$	$⋮$	$⋮$
31/12/2024	24	$\dots$

Let’s see how you fare against your peers in this challenge.

Appendix B. Feedback from Students on the Newsvendor Game

We asked the following questions:

• Q1. What is your general feedback on the game?

• Q2. The game helped me to understand the importance of predictive and prescriptive analytics (1–7).

• Q3. The game helped me to understand the importance of trading of overage versus underage (1–7).

• Q4. Which method do you usually prefer?

• Q5. Do you have any remaining comments?

Table B.1. Overview of Student Feedback

Table B.1. Overview of Student Feedback

Q1	Q2	Q3	Q4	Q5
I liked it a lot. I would have liked to have more time to think about the solution at home, but I understand that the time pressure is part of the challenge.	7	7	Game
Fun	7	7	Game
	6	5	Case study
	5	5	Game
It would be better to have it as take-home exercise; otherwise, we don’t have much time to think and compute the code.	3	4	Case study
Nice game to get familiar with problem. Time constraint really good for interview practice.	6	6	Game
It’s helpful in the sense that you can apply theoretical concepts under time pressure that force you to take the right decisions quickly and recognize crucial underlying characteristics.	6	5	Game
Although my group struggled a bit with time, I really liked the game!	5	5	Game
It was very interesting (especially the follow-up session was useful), but to be honest, time was too little for me. Probably doing it as a short-term homework (one or two days) would have been easier for me.	6	4	Theoretical class	As stated above, a longer time frame would have been nice (and would leave the chance to, e.g., include different overage/underage cost).
It’s good; it challenges us to step up although it creates a huge competition in the class, and no one is willing to help each other because everyone wants to be on top. But it is a good method to ensure everyone is participating in the classes.	5	6	Game	We should have more code along sessions.
I liked it. The time pressure made it hard to implement all thoughts. Maybe something similar is also good as an individual homework where everyone competes.	6	5	Game
I really liked the game to have a playful way of learning these things. I think it’s really useful and more alternate to classic teaching of just reading the slides.	7	6	Mix of all together
The game was fun and straight to the point, helps understand the basics of operations in a real-life situation.	6	6	Game
It was fun! It was especially interesting to find important patterns by yourself. It is good to discuss afterward where the problems were and what to avoid next time.	6	5	Game
I liked it as, in my opinion, hands-on exercises help to understand certain topics like this one.	5	4	Combination out of all three
I think it could be a good strategy, but I needed more follow-up, more step by step what we would have to do, because I lost a lot of time before I really understood the problem.	3	3		The best choice for me will be play a game but having more theoretical support first.
It’s an engaging way to learn and apply knowledge on a more practical exercise.	5	5	Game
It would have been better to suggest different models that should/could be used.	6	3	Theoretical class
There could have been more information on how to start solving it before (but, also, I don’t have enough Python knowledge, so that could just be me).	7	6	Case study
I liked the game a lot! I think that it was nice to have a hands-on exercise with time pressure, which pushed us to think quickly.	7	4	Game	According to me, it wasn’t really related to the newsvendor problem that we saw earlier (with underage and overage) since you made it easier. So it could be nice to also include to really link it with the previous chapter.