**Behavioural Inventory Decisions**

Operations management is a discipline focused on efficiency in business operations and the production of goods and services. It uses models that simplify reality by assuming people are rational versus irrational, enabling us to make inventory planning or operations decisions relatively easily. In reality, it is much harder to predict how people act and therefore how much inventory should be stocked. These types of questions are now answered in the developing field of behavioural operations research, which combines operations research with behavioural economics.

Behavioral operations research combines existing rudimentary models with factors such as irrational human behavior. This can play a pivotal role in helping firms maximize their efficiency and increase profits through improved inventory planning. Notably, stock-outs have serious ramifications; Harvard Business Review found that depending on the product category, a stock-out causes 21% to 43% of consumers to buy a product from competitors instead.

With my keen interest in the psychology behind decision-making and appetite for challenge, UBC Sauder Professor and Canada Research Chair in Operations Excellence Tim Huh encouraged me to explore the field of behavioral operations research. Our research focuses on understanding how inventory decisions are made and why inventory managers fail to make the right operations decisions, such as understocking when they could have maximized profits by overstocking above the typical demand level. ****

**Our Idea**

Our research question started out quite broad with simply trying to understand how people make decisions under uncertainty. Since this was our first empirical study in behavioural operations research, we began by exploring the literature, where we identified that much of the research in the area uses the newsvendor model. Further, it led us to become more interested in how people react to unknown distributions or changes in distribution. In real life, this is similar to an inventory manager not having enough data to forecast demand or needing to make decisions about multiple, heterogeneous products. We were also curious as to whether people would be able to learn or adapt their knowledge as they received more feedback. Thus, our research questions became: how do people respond to changes in distribution, and how close are people in finding the optimal quantity with limited demand information? ****

**Newsvendor Model**

The newsvendor model explores how perishable goods, like newspapers, should be ordered to optimize inventory when demand is uncertain (Arrow, Harrish, & Marschak, 1951). Its application is far reaching; it can be used to calculate how many airline tickets to overbook to minimize losses from last-minute cancellations, or evaluate retail inventory levels to balance variety and price for budget-sensitive shoppers.

The model shows that when demand is uncertain and the selling price is constant, if the cost of the good is low, then the optimal inventory level is to overstock above average demand. This is because the revenue that you would get from selling each unit of the good can offset the additional cost of overstocking a few more even if they do not sell. Conversely, if the cost of the good is high, then you should understock below average demand for the optimal inventory level. This is a simplification of the model. It normally includes additional factors that affect the true price of the good like disposal costs for overstocking. ****

**Behavioural Newsvendor Models**

Procurement managers and other decision-making executives working in operations often have limited information about the true distribution of their products to which they may apply the newsvendor model to (Bolton et al., 2012).** **They generally only have historical demand information which can resemble either a uniform or normal distribution. The newsvendor model has been adapted to work with different distributions including the normal distribution and the uniform distribution. We used the uniform distribution which is a limitation in our study as we would have liked to be able to test the normal distribution if we had more participants. The normal distribution can be used in a future follow-up study depending on the results of this one.

Reducing the amount of information that people can use will result in them falling back on certain biases or trying to learn and find patterns in the demand for them to use. These biases and the patterns that people learn will not necessarily be the correct ones that help them find the optimal ordering quantity. Hence, in many different versions of behavioural newsvendor studies (Schweitzer and Cachon, 2000; Bolton and Katok, 2008; Bolton et al., 2012), the conclusion is that people deviate from the optimal inventory ordering quantity.****

**Pull-to-Centre Bias**

Cited as the reason why people do not choose the optimal quantity, the pull-to-centre bias is one of the most common biases in behavioural newsvendor models (Schweitzer and Cachon, 2000; Ren and Croson, 2013; Ovchinnikov et al., 2015; Bolton et al., 2012; Lee and Siemsen, 2016; Bolton and Katok, 2008; Moritz et al., 2013; Bostian et al. 2008). The bias describes how people tend to settle on order quantities between those of the average demand and the actual optimal inventory amount (Zhang and Siemsen, 2018). People are inherently attracted to choosing the average demand as they tend to conclude that it is the quantity that is ordered the most often. However, the newsvendor model statistically proves that the average demand is rarely the optimal ordering quantity.****

**Study Methodology**

The design of our experiment is a survey-style simulation performed using the PythonAnywhere platform. Our participants will be first or second year undergraduate students who are taking a course on decision-making. These students are unlikely to have encountered the newsvendor model in their studies thus far, but Bolton, Ockenfels, and Thonemann (2012) concluded that undergraduate students make similar decisions to operations managers when faced with the same newsvendor ordering problem.

Students will play four models, where they are told that they are operations managers needing to make orders for some of their perishable goods. Each model is broken into two treatments corresponding to whether the cost of the good to the operations manager is high or low, hence resulting in different optimal order quantities according to the newsvendor model. Each game has 50 rounds, allowing us to test if they learn by comparing their initial choices with their choices nearer to the end of the game.

*Model with Constant Demand Distributions and Ten Demand Points*

The first model is a baseline to compare against the newsvendor model to see if people deviate from the optimal order and by how much. Participants have enough information to calculate the optimal newsvendor quantity if they manage to deduce that this is the model that underpins the game because they are given two pieces of information. First, they are told the distribution, which stays constant throughout the game. They are also given ten demand data points which they are told are predictions from a market survey by experts about what demand can be. However, these ten demand points should only be used as guidelines as the real demand can be and often is a different number.

We will also use this model to see if people are subject to the pull-to-centre bias by comparing their orders against the average. If the pull-to-centre bias is true, then our expectation is that people will order quantities below the optimal and close to the mean when the product has a low cost. In contrast, people will order quantities above the optimal and close to the mean when the product has a high cost.**

*Model with Unknown but Constant Demand Distribution and Ten Demand Points*

For the second treatment, participants are not told the distribution of the product they are ordering in the 50 rounds of the game. The only demand information they can use is the ten data points that we provide for them each round. These ten data points change for each round, hence participants who wrote down all the data points as they went through the experiment should be able to deduce more information about the distribution. Our main expectation is that participants will choose to order closer to the average than to the optimal order quantity which follows the pull-to-centre bias. We also expect that they may order the average amount more often than with participants that are told the distribution like in the first model.**

*Model with Changing Demand Distributions and Ten Demand Points*

In the third treatment, participants are still told the distribution, but this distribution changes each round. For instance, the distribution for the first round could be numbers between 50 and 150 distributed evenly, and then 30 to 130 distributed evenly in the second round. They are still given ten demand points to help them as guidelines. We would take this model and compare each round against the newsvendor optimum. Similar to the first model, we expect the pull-to-centre bias to lead people to order quantities below the optimal and close to the mean when the product’s cost is low, and that they will order quantities above the optimal and close to the mean when the product’s cost is high. By using changing distributions, we aim for participants to have a fresh start to each round which may help reduce other biases that come from playing a continuous game like chasing the actual demand from the previous order.**

*Model with Unknown but Constant Demand Distribution and Feedback*

The most unique from the previous models, the last model enables us to see if a continuous game will help a person learn to make the optimal decision. Participants will start with ten demand points like all the previous models, but they will not be told the distribution that underlies the demand points. Each round, they will be told the actual demand for the round and then this amount is added to the historical demand data that they are given such that in the 50th round, they should have 59 data points to assist them in making their decision. Similar to the first model, we will mainly be testing the results from this model against the optimal newsvendor quantity. Our expectation for this model is that there will also likely be some pull-to-centre bias, but we are curious to the extent of this bias. Perhaps the lack of having a defined mean by providing the distribution will mean that there is less of a pull towards the centre.

**Limitations**

The most prominent limitation in our experiment is that COVID-19 has moved school online which makes conducting laboratory tests much more difficult. We have had to pivot to conducting the study online which means that there are aspects to the environment that we cannot control for our participants. Another limitation is that our game is only 50 rounds, which was set primarily to fit in with the undergraduate classes where we would be drawing our sample from. In Bolton and Katok (2008), they demonstrated that learning does continue beyond 50 rounds in their 100-round study, hence a longer study may allow us to see that participants learn more later on.****

**Implications**

Within most studies using the behavioural newsvendor model, there are no well-known papers that have utilized changing distributions. By doing so, we will be examining how people make decisions under significant demand uncertainty in a way that has extensive real world implications. This is because operations managers rarely make decisions for just one product, and smaller companies may not have the data to do complete analyses to figure out that there is one underlying demand distribution.

Hence, it is useful to see how people react and perhaps even learn to make better decisions as they become more familiar with the product. Furthermore, smaller businesses that lack the capital to invest in advanced inventory management and forecasting systems may be able to use the newsvendor model with some limitations to strengthen their predictions. Additionally, this study is proof that even as a business student, it is possible to innovatively combine your passions, such as mine in the psychology of decision making, with emerging business topics to develop interesting research questions that have real world impact. I hope you can leverage your passion in a way that solves problems or simplifies the increasing complexity of today’s market landscape.